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pa60Tbl. 113.10)KeHa 3JIeMeHTapHaH TeOpHH TenJIOBOii
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pa3JIHlJHblMH TepMOnpHeMHHKaMH.
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.n.eHTOB JIeHHHrpa.n.CKOrO HHCTHTYTa TOlJHOii MeXaHHKH
H OTITHKH H B KalJeCTBe YlJe6HOrO nOC0611H ,ll,JlH cTy.neH-
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Pe.n.al<TOp KaH.n. qJH3.-MaT. HaYK r. H. Il.Y/lbHC8


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M. M. DonoBa: «TepMoMeTpH51 H KaJlOpHMeTpHH» (113.lL. MfY, 1954),
H 6blJIO 6bI H3J1HllIHe HX 3.lLeCb nOBTOp51Tb.
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YCTaHoBHBwHM nOHHTHe 06 Y,QeJlbHOH TenJlOeMKOCTH KaK CBOHCTB

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npOBO.lLHocm. B 1791 r. rpa<p PYMq;Op.lL (EeH)KaMeH TOMCOH) PYKO-
BO.lLHCb ,QOBOJlbHO CMYTHblM npe.lLCTaBJleHHeM 06 3TOH BeJlHqHHe ' CTpOHT
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nJloxo npOBO.lLHliLHX TenJlO MaTepHaJlOB (MaJlOH nJlOTHocTH) - «TepMo-

eTp Ten
onpOXOLK.lLeHHH» (Passage-Thermometer) H BbIIIOJlHHeT pH,Q
1i3MepeHHH, CCblJlKH Ha KOTopbIe HMelOTCH BO MHorHX TpY,Qax H KOTopble
U.HTHPYIOTCH BnJlOTb .lL0 1927 r. AHaJlH3 pa60TbI PYMq;op.lLa nOKa3bIBaeT
'ITO f'rn MeT0'{ R cvn
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MeHH (1789 r.) OTHOCHTCH cpaBHHTeJlbHblH MeTO,Q HHreHrY3a (Ingenhouss),
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npoBO.lLHOCTH ). l' ). 2 . . . MeTaJlJlOB.
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Ii MaTeMamKOM <f>ypbe (1816 Ii 1822 rr.), KOTOpbIH C03.lLaJi CTPOHHYIO
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qeCKOrO xapaKTepa. 3TO .lLaJIO B03MOLKHOCTb 06'be.lLHHHTb O.lLHHM 06liLIiM
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CBoIJCTBa MaTepIiaJlOB - K03<p<pHu.IieHTa TenJIOnpOBO.lLHOCTIi.
TeopHH <f>ypbe n06Y,QIiJIa K C03.lLaHHIO pH.lLa HOBbIX MeTO.lLOB Ii3Me-
peHHH TenJIOnpoBo)J,HOCTH H TeMnepaTyponpoBo,QHOCTH; nOCJle.lLHS!H BeJlIi-
qIiHa 6bIJIa BBe.lLeHa MaKCBeJIJIOM H JIOP.lLOM KeJlbBIiHOM (B. TOMCOHOM),
KOTOpbIH ynoTpe6J1HJI TepMIiH Temperature-diffusivity - «Ko3C1J<pIiu.HeHT
pacceHHHH TenJIa», B TO BpeMS! KaK MaKCBeJlJI nOJlb30BaJICH TepMIiHoM
Temperature Conductivity. 3THM 3aHHMaJlIiCb, BnJIOTb,QO KOHu.a XIX CTO-
JIeTHH, <pIi3HKH, HMeBWHe B BH,QY npeHMYliLecTBeHHo .lL0CTaTOqHO onpe-
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TaJlJlbI, CnJlaBbl, .lLIi3J1eKTpIiKH; lllHpoKaH 06J1aCTb TeXHHqeCKIiX MaTe-
pIiaJlOB OCTaJIaCb nOqTH He3aTpoHYTOH. BbI.lLalOliLHMIicH HCCJle.lLOBaTe-
J1HMH (Ha30BeM OHrCTpeMa, Eep)Ke, KOJlbpaYllla, J1eHrMlOpa, XPH-
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I1HTeHcHBHoe pa3BIiTHe TeXHIiKIi B XX CTOJIeTHH, B KOTOpOM BH,QHoe
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TOqHO BcnOMHHTb XOTH 6bI aTOMHble KOTJlbI, HrpalOliLHe TY )Ke pOJIb, qTO
H 06blqHbie napoBbIe KOTJlH), .lL0JI)KHO 6blJlO oTpa3HTbcH H Ha TeXHIiKe
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oc060e BHHMaHHe TenJlOTeXHH'KH H TenJlo<pIi3HKH KOHu.a X I X Ii HallaJIa
XX CTOJIeTHH, npHqeM HX rJlaBHOe BHIiMaHHe YCTpeMJIeHO Ha C03.lL aHHe
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CBOIICTB TeXHIiqeCKHX MaTepIiaJlOB, B nepBYIO oqepe.lLb TenJlOH30JlHTO-
pOB, a 3aTeM H MeTaJlJlOB, TaK KaK TeXHHi<a H cTpOHTeJIbCTBO HHTepe-
CYIOTCH HMeHHO 3THMH MaTepIiaJIaMH. OTHocHliLIiecH CIO.lLa IiCCJle.lLOBaHHH
npoBo
HTCH Y)Ke B ropa3.lL0 MeHbllleH CTeneHH <pH3HKaMH, qeM TenJlO-
TeXHIiI{aMH; .lLOCTaTOqHO ynoMHHYTb HMeHa fpe6epa, HycCeJlbTa, 51K06a,
3. fpHqJ<pIiTca, BepHoTTa H ,Qp.
YKa3aHHbIH nepHO.lL pa3BHTIiH HaYKH H.lLeT napaJIJIeJIbHO C HaqaJlOM
pa3BIiTHH yqeHHH 0 nO,TJ:06HI1 H C yrJIy6J1eHHbIM KpHTHqeCKHM anaJIH30M
<pH3HqeCKoti CTOpOHbI TenJlOBbIX npou.eccoB. nonYTHo BbIHCHHETCH, qTO,
BonpeKH MHeHHHM HeKoTopbIX npe.lLlllecTBYlOliLHX HCCJle.lLOBaTeJIei'l, H3Me-
pf'HJH> Ten.TJORHX rROI''wTR Rf'TTTf'C'TR npHX011,T-ITCH npH3HaTb 0}1HOi'J H3 .
TpY.lLHeHWHX 3a.lLaq TeXHHqeCKOH <pH3HKH.




8


BBeoeHue


COlllJleMCH XOTH 6hI Ha TOT cpaKT, qTO Ha,QemHhIe ,QaHHhIe 0 TenJIOnpO-
BO,QHOCTH ,Qa)Ke TaKOrO IlIHpOKO paCnpOCTpaHeHHoro BemeCTBa, KaK
H 2 0, OTCYTCTBOBaJIH, BnJIOTh ,QO ony6JIHKOBaHHH M. 51K060M 13 1920 I'.
CBoero £pYH,QaMeHTaJIhHOrO HCCJIe,QOBaHHH IIO 3TOMY Bonpocy. .QPyroll
£p aKT - OIlll16KH 13 H3MepeHHH K03£prpHUHe
ITa TenJIOnpOBO,QHOCTH orHe-
ynopHhIX MaTepHa.IJOB IIPH BhICOI<HX TeMnepaTypax, npHBe,QIlIHe K HeBep-
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ycnexH 6JIarO,QapH MHOrOJIeTHell pa60Te He TOJIhKO OT,QeJIhHhIX yqeHhIX,
HO H UeJIhIX KOJIJIeKTHI30B. B pe3YJIhTaTe 3Toro npHMepHO 13 1920 I'.
HCnhITaHHH TeXHHqeCKHX MaTepHaJIOB Ha TenJIOnpOBO,QHOCTh BOIllJIH
13 npaKTHKY rOCY,QapCTBeHHhIX MeTpOJIOrHqeCKHX HHCTHTYTOB HaH60JIee
nporpeCCHBHhIX 13 TeXHHqeCKOM OTHOIlleHHH CTpaH: HapH,Qy C TeKymHMH
nOBepKaMH TepMOMeTpOI3 H nHpOMeTpOB TenJIOBh1e H3MepeHHH COCTaB-
JIHlGT 3a,Qaqy HaUHoHaJIhHOll £pH3ll'IeCKOll JIa60paTopHH (N. P. L)
BeJIHK06pHTaHHH, HaUHoHaJIhHoro 6IOpO CTaH,QapTOB (N. B. S) CIIlA,
HaUHoHaJILHoro HHCTHTYTa HCKYCCTB H peMeCeJI (Conservatoire Natio-
nal des Arts et Metiers) <1>paHUHH.
PyccKHe <tm3HKH H XHMHKH XIX H HaqaJIa XX CTOJIeTHH rJIaBHOe
CBoe BHHMaHHe YCTpeMHJIH Ha pa3pa60TKY MeTO,QOB KaJIOpHMeTpHH, HMeH
13 BH,QY HHTepechI £PH3HKH H XHMHH; MeTO,QHKa TenJIOBhIX H3MepeHHll
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ThlBaJIaCh. B KaJIOpHMeTpHH OTeqeCTBeHHhIe yqeHhIe ,QOCTHrJIH 3HaqH-
TeJIhHhIX ycnexoB; YKameM B. <1>. J1YrHHHHa Hero IlIKOJIY, M. M. no-
nOBa H ,Qp. -
B IlIHpOKOM MaCIlITa6e H C yqeTOM, 13 nepBYlO Oqepe,Qh, nOTpe6HOCTell
npOMhIIlIJIeHHOCTH MeTO,QHKa TexHHqeCKHX TenJIOBhIX H3MepeHHll CTaJIa
pa3pa6aThn
3TbCH 13 CCCP TOJIbKO nOCJIe OKTH6pbCKOll COUHaJIHCTHqe-
CKoii peBOJIlOUHH 13 nepHO,Q BOCCTaHOBJIeHHH HapO,QHoro X03HllCTBa Haillell
CTpaHhI, HaqHHaH C 1926 1'., Kor,Qa M. n. CTaueHKo B <1>H3HKo-TexHH-
qeCKOH JIa60paTopHH, PYKOBO,QHMOll A. <1>. Ho£P£Pe H M. B. KHpnHqe-
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pemHMa TeJI H CHCTeM. TaKHe npH60phI 13 TO :me BpeMH HJIH HeCKOJIhKO
paHee pa3pa6aThIBaJIHCh, KaK ynoMHHaJIOCb BbIIlIe, H 3a rpaHHuell.
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CTaJIH Tenepb Ha3hIBaTb).
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BBeoeHue


9


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MeTO,QHKH H3MepeHHH 3aKOHOMepHOCTH HeCTaUHOHapHoro TenJIOBOrO
pemHMa, pa3pa60TaTh MeTO,QhI CKO
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Ha,Qe)I{HbIX pe3YJIbTaTOB.
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HOBbIX CKOpOCTHhIX MeTO,QOB H C03,QaHa HOBaH TeXHHKa TenJIOBhIX H3Me-
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npHHHThIMH, HOBbIe MeTO,QbI n03BOJIHIOT BceCTopOHHe HCCJIe,QOBaTb TenJIO-
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OCHOBHblE 0603HAIJEHHSt


4ACTb OEPBA51

M3MKO-MATEMATH4ECKME OCHOBbI M3MEPEHMM
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12


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KaM. 3a nOJIO>KHTeJIbHOe HanpaBJICHHe rpa.lLHeHTa TeMnepaTypbl npH-
HHMaIOT HanpaBJIeHHe, B KOTOpOM TeMnepaTypa B03pacTaeT. l-130Tep'
MHqeCKOll nOBepxHocTbIO I1a3bIBaIOT reOMeTpHqeCKOe MeCTO TOqeK, HMeIO-
W.HX O.lLHHaKOBYIO TeMnepaTYPY.
4epe3 Ka>K.lLYIO TOqKY M BHYTPH Te.r.a MO>KHO npoBecTH, B .lLaHHbIH
MOMeHT, TOJIbKO O.lLHY H30TepMHqecKYIo nOBepxHocTb, TaK KaK B O.lLHOll
H TOll >Ke TOqI<e npOCTpaHCTBa O.lLHOBpeMeHHO He MOLKeT 6bITb .lLBYX
pa3JIHqHbIX TeMnepaTYp. HOpMaJIb K H30TepMHqeCKOii nOBepXHOCTH
COBna.lLaeT C rpa.lLHeHTOM TeMnepaTYp. 3a nOJIO>KHTeJIbHOe HanpaBJIeHHe
HOpMaJIH npHHHMaeTCH HanpaBJIeHHe OT nOBepXHOCTH C 60JIee BbICOKOll
TeMnepaTYPOll K nOBepXHOCTH C 60JIee HH3KOii TeMnepaTYPOH, T. e. npHMO
npOTH BOnOJIO>KHOe rpa.lLHeHTY.
Ha cpHr. 3 JIHHHHMH F l' F 2 . . . H306pa>KeHbI CJle.lLbI Ha nJIOCKOCTH
4epIC)hd pa3JI1I'I1ILIX lIJUlqJI\I1I'ICl:lUIX lIuuepxuuLlcii, l:UUlUelcmYIuw.lIX
pa3JIHqHbIM TeMnepaTypaM TeJIa .lLJIH .lLaHHorO MOMeHTa BpeMeHH. ECJIH


) __ KOJllilJeCTBO TenJla
l.] -- J1J1HHa.BpeMH.rp a llYC



 1. TenJIonepe.lLa4a KOH.lLYK
He" (TenJIOnpOBO.lLHOCTbW)
PacCMoTpHM OCHOBHbIe 3aKOHbI, noCpe.lLCTBOM KOTOpbIX MaTeMaTH-
qeCKH onHCblBaIOTCH pa3JIHqHbIe BH.lLbI TenJIoo6MeHa.
TenJIoo6MeH TenJIOnpOBO.lLHOCTbIO (KOH.lLYKIl.HeH) BHYTPH TBep.lLblX
TeJI, a TaK>Ke B >KH.lLKOCTHX H ra3ax, eCJIH B HHX OTCYTcTByeT nepeHoc
TenJIa KOHBeKIl.HeH, npOHCXO.lLHT COrJIaCHO TaK Ha3bIBaeMoMy «3aKoHY
<l>ypbe», KOTOpbIfI HBJIHeTCH o606w.eHHeM npocTeiiIlIero CJlyqaH npoxo-
>K.lLeHHH TenJIa qepe3 nJIOCKO-napaJIJIeJIbHYIO CTeHKY (cpHr. 2). B :=ITOM
cJIyqae KOJIHqeCTBO TenJIa Q, npOIlIe.lLillee .B TeqeHHe BpeMeHH 'L 4epe3
nJIow.a.lLb S OT rOpHqeH CTOpOHbI CTeHKH, HMeIOw.eH TeMnepaTYPY ii'
K XOJI0.lLH9ll ee CTOpoHe, HMeIOw.eH TeMnepaTYPY i 2 , BbIpa>KaeTCH paBeH-
CTJ30M;


COBoKynHocTb qHCJIeHHbIX 3HaqeHHH TeMnepaTypbI B .lLaHHbIii MOMeHT
BpeMeHH B pa3JIHqHbIX TOqKaX .lLaHHoro TeJIa HJIH CHCTeMbl, COCTOHw.ell
H3 HeCKOJI bKHX TeJI (cpHr. 1), Ha3bIBaIOT TeMnepaTypHbIM nOJIeM TeJIa
HJIH CHCTeMbI. TeMnepaTypa, Boo6w.e rOBopH, 6Y.lLeT CPYHKIl.HeH KOOp-
.lLHHaT TOqeK CHCTeMbI x, y, Z H BpeMeHH, KOTopoe 0603HaqHM 'L. B TOM
CJlyqae, KOr.lLa TeMnepaTypa BO Bcex TOqKaX CHCTeMbl He H3MeHHeTCH
C TeqeHHeM BpeMeHH, 6Y.lLeM rOBopHTb, qTO nOJIe TeMnepaTyp CTaUHOHap-
Hoe; eCJIH :>Ke TeMnepaTypa Bcex TOqeK C TeqeHHeM BpeMeHH H3MeHHeTCH,
Ha30BeM nOJIe TeMnepaTYP He-
CTaIl.HOHapH
M. B nOCJI, e.lLHeM
caMOM 06w.eM CJlyqae TeMnepa-
TYPY B .lLaHHoll' TOqKe M (x,
y, z) qaw.e Bcero 6Y.lLeM 060-
3HaqaTb 6YKBOH ll: II = II (x,
y, Z, 'L); eCJIH >Ke Te
nepaTypa
He H3MeHHeTCH CO BpeMeHeM,
6Y.lLeM .lLJIH ee 0603HaqeHHH
ynoTpe6JIHTb 6YKBY t: t =
= t(x, y, z).
B npaKTHKe, oc06eHHO B
JIa60paTOpHOH, Hepe.lLKH CJIY-
qaH, KOr.lLa TeMnepaTypbI Bcex
TOqeK HeKOTOporo 06DeMa
Me>K.lLY C060H paBHbI H 3TO
paBeHCTBO C06JIIO.lLaeTCH B JIIO-
60H MOMeHT BpeMeHH, TaK 'ITO II HJIH t He 3aBHCHT OT KOOP.lLHHaT x,
y, z; TaKoe nOJIe TeMnepaTYP 6Y.lLeM Ha3bIBaTb paBHOMepHbIM.
TeMnepaTypHoe nOJIe MO>KeT 3aBHceTb B qaCTHOM CJIyqae TOJIbKO
OT O.lLHOH KOOp.lLHHaTbI; TOr.lLa TeMnepaTypHoe nOJIe Ha3bIBaIOT O.lLHOMep-
HbIM; aHaJIOmqHbIH CMbICJI HMeIOT TepMHHbl .lLBYXMepHoe, TpeXMepHoe
nOJIe TeMnepaTYp.


Q __ J". t 1- t l. S ....
- X .,


p. 1)


A


:t


t,


t 2


ct:>HL 2. npOXO}KJ1eHHe TenJIa 4epe3 nJlOCKYIO
OJJ.HOpO.nHYIO cTellKY (A = const); AB - TeMne-
paTypHaH KpHBaH.




KpGTKOe U3.10:HCeHUe OCHOBHbtX nOHflTut'l U 3GKOHOB 0 Ten/loo6MeHe


15


14


ctJU3UKO-MGTeMaTU'lecKue OCHOBbt U3MepeHut'l Ten/lOBbtx Be/lU'tUH


nOJIe TeMnepaTYP CTaUl:IOUapHOe, 3TH nOBepXHOCTH coxpamllOT CBOH nOJIO-
)!{eHHSI HeH3MeHHblMH OTHOCHTeJIbHO TeJIa; OHH CMemalOTCSI, eCJIH nOJIe
TeMnepaTYP HeCTaUHOHapHoe. B TOM 'IaCTHOM CJIY'Iae, KOTOpblH npeJ{-
CTaBJleH Ha cplir. 2, H30Tep-
MH'IeCKHe nOBepxHocTH
npe)J.CTaBJISllOT C060M nJIO-
CKOCTH, napaJlJIeJlbHHe no-
BepxHocTHM, OrpaHH'IHBalO-
I.lI.HM cTeHKY.
J1l:1Hl:IH, nepneH)J.HKYJIHp-
Hble K H30TepMH'IeCKHM
nOBepxHocTHM Fl' F 2 . . .,
Ha3bIBalOT JlHHHHMM TenJlO-
Bora TOKa HJIH, KOpOLJe,
JlHHHHMH TOKa. YnO)J.c6J1HH
)J.JlH HarJlH)J.HOCTIf nepe)J.a'IY
TenJIa B TBep,TJ:OM TeJle TeLJe-
HHlO H)J.eaJlbHOU )KH)J.KOCTH,
MO)KHO CKa3aTb, 'ITO TenJlOTa
TeLJeT OT O)J.HHX H30TepMH-
LJeCKHX nOBepXH'OCTeH K
)J.Pyn:lM no JIHHI:ISlM TOKa
B HanpaBJIeHHHX, YKa3aH-
B LJaCTHblX CJIY'IaHX MorYT
B CJIYLJae, npe)J.CTaBJleHHOM


F1


ct:>Hr. 3. 1130TepMHlJecKHe nOBepXHOCTH F h F 2, . '.
F n-l> F n H JlHUHH TeOJIOBOrO TOKa B HepaBHOMep-
HO HarpeTOM TBep.nOM TeJle; S - uapY}KHaH no-
BepXHOCTb TeJla.


HHX Ha £PHr. .3 CTpeJIKaMH. J1I:1HHH TOKa
6bITb H npHMblMH JlHHHHMH, HanpHMep
Ha cpHr. 2.


B ro'IKe M He 3aBHCHT OT ee Koop)J.HHaT. Dpe)J.bl)J.ymee paBeHCTBO, BBe,TJ:H
B Hero q, MmKHO HanHcaTb B CJIe)J.YlOmeM npOCTOM cpopMe:
q = -),.grad t.


DOHHTHe TenJlOBOrO nOTOI<3, nO,TJ:06HO nOHHTHlO TeMnepaTypHoro rpa-
]l.HeHTa, MO)KHO pacnpOCTpaHHTb Ha JIIo60e TeMnepaTypHoe nOJIe. 3TO
KOJIH'IeCTBO TenJIa, npoxo)J.Slmee B e)J.HHHlI,Y BpeMeHH LJepe3 e)J.HHHUY
H30TepMH'IeCKOM nOBepXHOCTH B )J.aHHOM TO'IKe. TenJlOBOM nOTOK HBJIHeTCH
BeKTopOM, HanpaBJIemfe KOToporo COBna,TJ:aeT C HanpaBJIeHHeM nepe)J.aLJI:I
TenJIa B )J.aHHbIM MOMeHT H KOTOpHM 1:13MepHeT HHTeHCHBHOCTb 3TOM TenJIO-
nepe)J.a'IH.
<PYPbe npe)J.nOJImKHJI, 'ITO nponopUHOlJaJlbHOCTb Me)K)J.Y q H rpa-
)J.HeHTOM TeMnepaTypbl coxpaHHeTCH BO Bcex CJIYLJaHX.TenJlo06MeHa TenJlO-
npOBO)J.HOCTblO KaK )J.JlH CTaUHOHapHbIX, TaK H ]l.JIH HeCTaQ.HOHapHbIX
nOJleH, T. e. 'ITO Bcer)J.a 6Y)J.YT CYl.lleCTBOBaTb paBeHCTBa
q=-A.gradU" } (1.3)
q = -A. grad t


(1. 2)


Ehy fl:lnOTe3Y, SlBJlHlOmYlOCH 06061.lleHl1eM 3KcnepHMeHTaJIbHbiX )J.aHHbIX,
npHHHTO Ha3bIBaTb 3aKOHOM <Pypbe [21 . OHa JIe)Kl:IT B OCHOBe Bceii cOBpe-
MeHHoM TeopHH TenJIOnpoBo)J.HOCTH, Ha HeM OCHOBaHbl TenJIOBbie paCLJeTbl
H YCTpoikTBO BceB03MO)KHbiX npH6opOB. .
Depe)J.aLJa TenJla KOH)J.YKUHeM B )KH)J.KOCTHX H ra3ax ocyll(ecTBJlHeTCSI,
B 60JIbllIHHCTBe CJIY'IaeB, TOJIbKO HCKyccTBeHHblM nYTeM, TaK KaK npH
HeH30TepMH'IHOCTH CTeHOK cocY)J.a. B KOTOpOM HaxO,TJ:HTCH Macca )KH)J.KOCTH
l:IJlH ra3a. B HeM B03HHKalOT nOToKH, Bbl3BaHHbie HeO)J.HHaKoBoH nJlOT-
HOCTblO pa3J1WlHO HarpeTblx 'IaCTeH MaCCbl. .LLBI:I)KeHHe 3THX nOTOKOB
6Y)J.eT npeHe6pe)KHMO MaJIbIM, eCJIH rpa)J.l:leHTbl TeMnepaTYP MaJlbl H_BH3-
KOCTb )J.ocTaTOLJHO BeJII:IKa. HCKYCCTB'eHHO MO)KHO ocymecTBHTb nepe)J.a'IY
TenJIa TOJIbKO KOH)J.YKUHei'i, eCJIH cocY)J. C MaccoH ra3a I:IJIH )KI:I)J.KOCTH
HarpeBaTb cBepxy; HarpeTble MeHee nJIOTHble 'IaCTH ee pacnOJlO)KaTCH
cBepxy, 60JIee XOJlo)J.HHe oCTaHYTcH BHH3Y, H nepe)J.aLJa TenJla 6Y)J.eT
CJIe)J.oBaTb 3aKoHY <Pypbe. B 06bl'IHbiX npHpo)J.HblX YCJIOBHHX nepe)J.aLJa
TenJIa KOH)J.YKUl:leM B )KH)J.KOCTHX H ra3ax, KOHeQHO, TaK)Ke Bcer)J.a HMeeT
MecTo, HO OHa COnpOBO)K)J.aeTCH eme H nepeHOCOM TenJIa 'IaCTI:IUaMH,
COBepllialOmHMH He TOJIbKO HeBH)J.HMoe TenJIOBOe )J.BI:I)KeHHe, HO eme
H BH)J.I:IMble, Ha6JIlO)J.aeMble BI:I3yaJIbHO, nepeMemeHI:IH.



 2. 3aKoH <J>YPbe
YpaBHeHHe (1. 1) OTHOCI:ITCH K cTauHoHapHoMY TeMnepaTypHoMY
nOJIlO;
TO nOJle, KpoMe Tora, O,TJ:HOMepHoe, TaK KaK TeMnepaTypa t
B JIlO601:1 TOLJKe M CTeHKH 3aBHCHT TOJIbKO OT O,TJ:HOH KOOp,TJ:HHaTbl x.
OnbIT nOKa3!,lBaeT, 'ITO eCJIH TeMnepaTypbl Ii H 1 2 He CJIHlliKOM CHJIbHO
Me)K)J.Y u c0601:1 pa3J1HLJalOTCH, TeMnepaTypHoe nOJle H306pa)KaeTCH npHMoi:i
JIHHHel:l (cpHr. 2). Crre)J.oBareJIbHO, rpa)J.HeHT TeMnepaTypbl B 3TOM CJIY-
'Iae 6Y)J.eT BeJIH'Il:lHOll, He 3aBHCSlmell OT Koop)J.HHaTbl x H B CHJlY (1.1)
grad I =_!!!.... = t 1 -t 2 =

dx X A.S.'!; .


3)J.eCb Mbl nl:lllIeM 3HaK MHHYC, nOToMY 'ITO Ha oTpe3Ke dx TeMnepaTypa
na)J.aeT C t )J.O t - dt, KaK nOKa3aHO Ha cpl:lr. 2, a CTOSll.llee B npaBoll
'IaCTH nOCJIe)J.Hero paBeHcTBa Bblpa)KeHHe - BeJIH'IHHa nOJlO)KHTeJIbHaSl.
.LLP06b Q/).,S T npe)J.cTaBJIHeT C060ll KOJlH'IeCTBO TenJIa, npoxO)J.Hm ee 3a
e)J.HHHuy BpeMeHH B HanpaBJIeHHH x 'Iepe3 e)J.HHHu y nOBe p xHocTH K HeM Y
ne p ne ' u '=' '
H'{IiK) 'HTpllOll. JTY BeJllI'lIIUY IIa3LIB alOT Y)J.eJILIiLIM TellJIUULIM
nO.TOKOM [I] H 0603Ha'IaJOT q; B )J.aHHOM 'IaCTHOM CJIY'Iae TenJIOBOH nOTOK



 3. TenJloo6MeH KOHBeKlI,HeH. KpHTepHH nO)J.o6HSI
3a)J.a'Ia 0 TenJIoo6MeHe KOHBeKUl:lell TeCHellllIl:IM 06pa30M CBH3aHa
co CJIO)KHbTMH npoueccaMH, npOI1CXO,TJ:HmHMH Ha rpaHHue Me)K)J.Y TBep,TJ:blM
TeJlOM 1:1 conpHKacalOmei'lcSI C HI:IM )K1:I)J.KoH I:IJIH ra3006pa3Holl Cpe,TJ:OM,
KOf)J.a I:IX TeMnepaTypbl Me)K)J.Y C060ll pa3JII:l'Ia1OTcH. <p1:I3I:1'IeCKaH
nopoHa Bonpoca nO,J,p06no" paccMuTpunacTcfl n cnenUaJIhllblX TPY-
)J.ax no TenJIo06MellY [2]. LLJIH npaKTH'IeCKI:IX paC'IeTOB nOJIb3YlOTCSI




16


cPU3UKO-MO.TeJ.IQTU'leCKUe OCHOBbl U3MepeHUU Ten/lOBblX 8eAU'lUH


KpaTKoe U3/10:JICeHUe OCHOBHblX nOHRTUu U 3aKOHOB 0 Ten/loo6MeHe


17


npocTellwei1 CPOpMOll MareMaTHqeCKOrO OnHCaHHSI renJl006MeHa KOHBeK-
LlHell; 3TOT 3aKOH TenJlOOT,lJ:aqH npe,IJ:nOJIaraeT, qTO KOJlHqeCTBO TenJia
q"OHB' TepSIeMOe KOHBeKLlHell 3a e,IJ:HHHLlY BpeMeHH C e,IJ:HHHllbl nOBepX-
HOCTH TeJla S, npOnOpLlHOHaJlbHO pa3HOCTH TeMnepaTYP paCCMaTpHBae-
Moii TOqKM M 1 nOBepXHOCTH TeJla Us H cpe,IJ:bI 8, T. e.
q"OHB= qs=a,,'(u s - 6). (1. 4)
K03cpcpHLlHeHT nponopLlHOHaJlbHOCTH a" Ha3bIBaIOT K03cpqmLlMeHToM
TenJlOOT,lJ:atm KOHBeKLll1ei1 (n03ToMY MbI eMY 11 npHnHcbIBaeM 3HaqOK Ii.
BHH3Y), a CPOPMYJlY (1.4) - cpOPMYJlOll HblOToHa
HJlI1 3aKOHOM HblOToHa. TenJlonoTepSI C 3J1e-
MeHTa nOBepXHOCTM dS 3a 3J1eMeHT BpeMeHH o't
6Y,lJ:eT ,lJ:aHa 3aBHCMMOCTblO 1
oQ"oHB=aius- 8)dS.o't. (1. 5)
113 CPOPMYJlbI (1. 4) SIceH cpH3MqeCKlIll CMbICJI
K03cpcpHLlHeHTa TenJlOOT,lJ:aqH: 3TO - KOJlMqeCTBO
TenJla, TepSIeMoe (HJlM BocnpHHHMaeMoe) B
e,IJ:HHHLlY BpeMeHH e,IJ:HHHLleiI nOBepXHOCTI1 TeJla,
KOr,IJ:a pa3HocTb TeMnepaTYP Me:>K,lJ:Y nOBepx-
HOCTblO reJIa H Cpe,IJ:OlO COCTaBJISIeT O,IJ:I1H rpa-
,lJ:Yc.
B reopHH TenJlOnpOBO,IJ:HOCTM Q6bIqHO npH-
HHMalOT a,,=const, Ha caMOM ,lJ:eJle BeJlHqHHa
a" 3aBHCHT, KaK 6y)!.eT nOKa3aHO HH:llie, OT
MHomx cpaKTopoB.
HCCJle)!.oBaHHSIMM YCTaHOBJleHO, qTO B6JIH3M
nOBepxHocTM CTeHKH HMeeTCSI BeCbMa TOHKHlt
CJlOH >KHlI.KOCTH, nJIOTHO I{ Hell npMJIeralOIl.lMll,
Tal{ Ha3bIBaeMbIll nOrpaHHqHbIH CJlOll, BHyTpH
KOTOporo TenJIOnepe)!.aqa npOMCXO)!.HT no 3aKOHY
TenJlOnpOBO)!.HOCTlf B TBep)!.OM TeJIe, qTO cxeMa-
THqeCKM H306pa:>KeHO Ha CPHr. 4: TeMnepaTypHaH KpHBaSI B >KM)!.KOCTM
MJIH ra3e B6J1H3lf nOBepxHocTH TBep)!.oro TeJla MMeeT CPOPMY KPYTO cna-
lI.aJOl.lLell npHMoH JIHHHH. TOJlI.lLHHa norpaHWlHoro CJlOSI HaCTOJIbKO MaJla,
qTO rpacpHqeCKH reMnepaTypHbIe nOJIH B6JIH3H rpaHHLlbI pa3)!.e.rra TBep-
)!.oro TeJIa H :>KH)!.KOCTH H306pa:>KalOT JIHHHeH, HMelOl.lLell TOqKY pa3pbIBa
Ha 3TOH rpaHHLle (CPMr. 5). He3HaHHe TOJII.lLHHbI L H CHJIbHbIe KOJIe6a-
HHH ee OT BHeUlHHX YCJIOBHll SIBHJIHCb npHqHHOH BBe)!.eIIJIH )!.JlH npaKTH-
qeCKOrO nOJlb30BaHHSI K03cpcpHLlHeHTa TenJlOOT)!.aqH a. B 3TOM cJlyqae
BCSI CJIO:>KHOCTb npoLlecca TenJIOOT,AaqH nepeHoCHTcH Ha O,AHY BeJlHqHHY -
K03cpcpHLlHeHT TenJlOOT,lJ:aqH. Pa3JIHqalOT ,ABe pa3Ho
)!.HOCTH KOHBeK-
THBHOll nepe)!.aqH TenJIa: eCTecTBeHHYlO (HJlH cBo60)!.HYlO} H BblHY:>K)!.eHHYlO
KOHBeKLlHlO. nepBaH Bb13BaHa pa3JIHqHbIMM nJlO
OCTHMM HarpeTbIx


Us


<1JHr. 4. nOJle TeMnepaTYP
B nOrpaHHlJHOM CJIoe }KHJj-
KOCTH HJIH ra3a 2, OMblBalO-
Il.lero TBep}.lYIO cTeHKY S
TeJIa 1; L-TOJIIl.lHHa CJIOH.
MacllITa6 paccToHHHii-
CHJIbHO YKpynHeHHbIM;
ABCD - TeMnepaTypHaH
KpHBaH; M1N - HOpMaJlb
K nOBepxHocTH S.


n OXJIa:>KlI.eHHbIX qaCTeH )KM,AKOCTH HJIM ra3a, npwIeM HarpeTbIe, MeHee
nJIOTHbIe qaCTM ,ABHLI<YTCH BBej)X H npH 3TOM ,ABM:>KeHHH oT)!.alOT CBoe
TenJlO ,APymM qaCTHM; O)!.HOBpeMeHHO npOMCXO)!.HT )!.BHLKeHHe BHM3
XOJlO,rJ:HbIX qaCTell. <PHr. 6 H 7 HJlJllOCTpnpYlOT pa3J1HqHbIe cJlyqaM eCTe-
cTBeHHoH KOHBeKLlHH.


f -


Us


<I>Hr. 5. 06bllJHOe H306pa}KeHHe
TeMnepaTy-pHoH KpHBOH ABCD Ha
rpaHHLle pa3}.leJla TBepJ10rO TeJla 1
H }KHJ1KOCTH HJIH ra3a 2; BC-
«TeMnepaTypHblii CKalJOK»= us-B.


2
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MeIll,eHHH C HCT04UIIKOM TenJIa 1 H XOJlO}.l-
HOH cTeuKoM 3 C OKHOM 4; 5 - nOJl,
2 - nOTOJlOK. CTpeJlKaMH nOKa3aHbl
TOKII ecreCTI'£HHOH KOHBeKIJ,HH.


no)!. BbIHY:>K,AeHHOll KOI-lBeKLlnell TenJIa nOHHMalOT TOT BH)!. nepeHoca
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BJlHSIHHeM BneWHell npHqHHbI rI3 O)!.HHX MeCT npOCTpaHCTBa B ,Apyme.
npHMepOM MO:>KeT CJlYLl<HTb lI.ellCTBHe BeHTHJIHLlHOHHOll YCTaHOB







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lJ.>Hr. 7. TOKH ecTecTBeHHOM KOHBeK-
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weuHoM . B B03.nyxe B ropH30UTaJIb
110M nOJIO}KeHHH.
.

no)!.alOl.lLeH OXJIa t',AeHHbIll HJlM no)!.orpeTbIH B03,AYX B lI.aHHOe nOMel.lLe-
HHe. B03MO:>KeH H npOMe:>KYTOqHbIll CJIyqall, Kor)!.a TenJlo06MeH COBep-
waeTCH npH O)!.HOBpeMeHHOM ,AellCTBHH TOKOB CBo60,AHOll H BblHY:>K,AeH-
HOll KOHBeKLlHH
 TaKoiI cJlyqall BCTpeqaeTCSI B TenJIOBOll aHeMOMeTpHH,
Kor.n.a lIarpeTbIli npnCIlfIIIIK npll60pa nOMCIl.len D cJIa6L111 D03,AYWHblH
nOTOK (cpMr. 8).
2 KOHApubeB 2763


.
1 YCJIOBliMCH 0603HalJ3Tb CHMBOJlOM d 6eCKOHe1lHO MaJIOe H3MeHeHlie BeJlHlJHHbl,
3aBHCHIlI,cli TUJlblW UT KOupJJ.l1Hal; CHMHuJl
 6Y.At:1 O"HalJaTb 6
C"UH
lJHU MdJltJC UJMt:He-
HHe Be.
1I4HHbl, 3aBHCSlIl.leii OT BpeMeHH.


<1JHr. 8. OXJla}KJ1eHHe BepTHKaJlbHO pacnoJlo-
iKeHHoro LlHJlHHJ1pa B ropH30HTaJIbHO J1BH'
}KYll.leMCH C MaJlOH CKOpOCTblO W nOTOKe
B03J1yxa.




18


c1>U3uKo-MaTeMaTUIleC/we OCHOBbt U3MepeHuit TenAOBbtx BeJtUIlUH


KpaT/me U3JtO:1lCeHUe OCHOBHbtX nOHlITUil U 3aKOHOB 0 TeltAOo6MeHe


19


Ha O
HOM npMMepe 60
ee nO
p06HO paCCMOTpHM, KaK npOMCXO
HT
nepe
aqa Ten
a 01' HarpeTOrO TBep
OrO Te
a B ra3006pa3HYIO cpe
y
B YC
OBMHX eCTeCTBeHHOH KOHBeKUHH.
nYCTb TeMnepaTypa nOBepXHOCTH Te
a lis BbIllIe TeMnepaTypbI BHellI-
HeH cpe
bI 8; Tor
a Mo
eKY
bI ra3a, B3aMMo
eHcTBYIOw,He C nOBepx-
HOCTbIO TBep
oro Te
a, YBe
HqHBaIOT CEOIO KHHeTHqecKYIO 3HeprHI0
BH-
>KeHHH H,
a
ee,
BHraHeb XaOTMqecKH H coy
apHHcb C
PYrHMH Mo
e-
Ky
aMH, nepe
aIOT HM CBOIO 3HeprHIO. C YBe
HqeHMeM cpe
HeH KHlleTH-
qeCKOH 3HeprHH
BH>KeHHH Mo
eKY
 B03paCTaeT

HHa HX cB060
Horo
np06era M, c
e
OBaTe
bHO, YMeHblliaeTcH n
OTHOCTb ra3a, 6
H3KO pac-
nO
O>KeHHOrO K nOBepxHocTH. B CH
Y 3aKOHa ApxHMe
a, 061>eM MeHee
n
OTHoro ra3a BblTeCHHeTCH 60
ee n
OTHbIM XO
O
HbIM 061>eMOM r23a,
pacno
o>KemlOro Ha 60
bllIHX paccToHHHHX 01' nOBepxHocTM. .D.a
ee
npouecc nOBTopHeTcH. H TaKHM 06pa30M B03HHKaeT
BlDl{eHHe ra3a OKO
O
HarpeToH nOBepxHocTM TBep
oro Te
a. npM aHa
H3e onHC3HHoro 3
eCb
HE
eHHH YCTaHoB
eHo, qTO npouecc nepe
aqH Ten
oBoH 3HeprHH 01'
TBep
oro Te
a B cpe
y
O
>KeH 3aBHceTb 01' c
e
YIOliLHx £paKTopOB: TeM-
nepaTypbI nOBepxHocTH H cpe
bI lis H 8; 01' £pH3H'-leCKHX CBOHCTB ra3a,
KOTopbIe xapaKTepM3YIOTCH ero K03!jJcpHUHeHToM BH3KOCTH v" KO;:XPCPH-
uHeHTOM Ten
onpoBO
HOCTII A, H TeMnepaTyponpoBo
HOCTH a" OT
K03cpcpHuHeHTa 061>eMHOrO pacllIHpeHHH ra3a
 H 01' YCKopeHHH CH
bl
TH>KeCTH g. KpoMe Toro, xapaKTep
BH>KeHHH Ten
OBbIX nOTOKOB
O
>KeH
3aBMceTb 01' reOMeTlmqeCKHX oc06eHHOCTeM Te.JIa. HanpHMep, YCTaHoB-

ello, qTO

H TOHKHX npoBo
oK
BH>KeHHH nOTOKOB npoMcxo
HT 60
ee
HHTeHCHBHO, qeM

H TO
CTbIX npoBo
oK, TPy60K H UH
HH
pOB. feo-
MeTpHqeCKHe CBOHCTBa Te
a npHHHTO xapaKTepH30BaTb Onpe
e.JIHIOw,MM
pa3MepoM Te
a L [2J. KpaTKo MO>KHO HanHcaTb:
a. K = f (lis, 8, v z ' Az' a"
, g, L). (t.6)
TeOpeTH'IeCKH onpe
e
HTb 3aBHCHMOCTb Me>K
Y - BceMH 3THMH napa-
MeTpaMH y
aeTcH

H npoc
efIllIHx c
yqaeB,
a H TO npH
onyw,eHHHX,
H
ea
H3HpYlOliLMX pea
bHblH £pH3HqeCKHH npouecc Ten
006MeHa Me>K
Y
TBep
bIM Te
OM H cpe
OH. 3TO npHBO
HT K TOMY, qTO pe3Y
bTaTbI, pac-
CqHTaHHbIe no TaKHM cpopMy
aM, 3HaqHTe
bHO OT
HqaIOTCH 01'
aHHbIX
OnbITa, n03TOMY e
HHCTBeHHbIM Ha
e>KHbIM opY
MeM onpe
e
eHHH 3aBHCH-
MOCTH KO.3qxpMUHeHTa Ten
OOT
aqH 01' pa3
HqHbIX napaMeTpOB HB
HeTCH
on bIT.
Ho pa3bICKaHHe .3MnHpHqecKHX ct>OPMY
, CBH3blBaIOw,MX TaK MHoro
He3aBHCHMbIX napaMeTpOB, qpe3BbIqaHHO C
O>KHO H Tpy
oeMKO. 3TO
npHBe
o K He06xo
MMOCTH YMeHbllIHTb qHC
O napaMeTpOB c
e
YlOliLHM
06pa30M. 4aCTb napaMeTpOB 061>e
MHHeTCH B TaK Ha3bIBaeMbIe KpHTe-
pMH - BeJIHqHHbI Hy
eBoH pa3Mep, HOCTH COCTaB
eHHbIe H3 £pM3HqeCKHX
H reOMeTpnqeCKMX pa3MepHbIX Be
HqHH. HanpHMep,

H paCCMOTpeH-
Horo 3
eCb' c
yqa H eCTeCTBeHHOH KOHBeKUHH B03MO>KHO COCTaBHTb TP H
KpHTepHH:


KpHTepMH fpacrot}Ja


gL3
Gr =
'-Y- (U s - 0),
'Ie


KpHTepMH npaHJ1TJlH


Pr=
.
a"


OTBeT Ha Bonpoc, KaK Ha
O COCTaB
HTb T3KMe Kpl-iTepHH,
aeT TeOpHH
no
06HH, Ha KOTOpOH MbI 3
eCb OCTaHaB
MBaTbCH He 6y
eM [2J.
TeopHH nO
06I1H nOKa3bIBaeT, qTO 3aBHCMMOCTb (1. 6) Me>K
y MHO-
rnMI:l napaMeTpaMH MO:>KHO npe
cTaBHTb B c
e
YlOliLeM BH
e:
Nu = F (Gr, Pr), (1. 7)


KpHTepuil H}cceJlbTa. . . . . . . . . . . Nu =
.L
1-" '


CBH3bIBaIOw,eH TO
bKO TPH 6e3pa3MepHbIx napaMeTpa.
06pa60TaTb pe3Y
bTaTbI H3MepeHHH B BH
e 3aBHCHMOCTH (1. 7)
HaMHoro npome, qeM B BH
e (1. 6), TaK KaK qHC
O napaMeTpoB B ct>opMYJIe
CH
bHO YMeHbllIH
OCb. .
KpoMe TOro, 3anMCb B BH
e (I. 7) HMeeT H
Pyroe npeHMYliL eCTBo :
£pOPMY
bI THna (I. 7) 60Me 06w,He H rH6KHe, qeM £p O PMY1!bI THna (1. 6).
3TO MO>KHO npoH
moCTpHpoBaTb Ha c
e
YIOw,eM npHMepe. .D.onYCTHM,
qTO KpHTepHH Hycce
bTa B onbITax MeHH
CH B
Hana30He 01' 10
o
1000. 3TO H3MeHeHHe KpHTepHH Mor
o npoH30HTH no pa3HbIM npHqHHaM:
1) npH H3MeHeHHH B llIHpOKHX npe
e
ax KO.3ct>CPHQHeHTa Ten
OOT
aqH a K;
2) npH pa3HbIx no Ten
onpoBo
HOCTM BHellIHHX cpe
ax; 3) npH M3MeHe-
HHM reOMeTpHqecKHx pa3MepoB L. HaKoHeu, Mor
H 01' onbITa K OnbITY
M3MeHHTbCH
Be H3 .3THX Be
HqHH H
H Bce TpH. EC
H 6bI nOnblTaTbCH
CTpOHTb 3MnMpMqeCKHe 33BHCMMOCTH Ko;:xpcpHQMeHTa Ten
OOT
aqH npH
M3MeHeHHH O
Horo H3 napaMeTpoB H
H HeCKO
bKHX, TO no
yqH
OCb 6bI
60JIblliOe qHCJIO pa3
HqHbIX KOM6HHaQHH H CTO
bKO >Ke 3MnMpnqeCKMX
ct>OPMY
, KOTOpbIC HOClwn 6bI qaCTHbIH .xapaKTep: H3MeHHeTCH O
HH H3
napaMeTpOB, 01' KOTOpbIX 3aBMCMT a K , B TO BpeMH KaK OCTa
bHbIe
OCTaIOTCH HeH3MeHHbIMH. npH 3anHCH >Ke ypaBHeHHH

H Ten
OOT
aqH
B KpHTepHa
bHOM BH
e (1. 7) 31'01' He
OCTaTOK YCTpaHHeTCH, TaK KaK
6e3pa3
HqHO, KaKOH H3 napaMeTpOB MeHHeTCH npH H3MeHeHHH KpHTe-
PUH Nu 01' 10
o 1000.
C
e
cTBHeM 3TOro HB
HeTCH
Pyroii npaKTHqecKH Ba>KHbIH BbIBO
:
B03MO>KHO YCTaHoBHTb rpaHHubI npHMeHMMocTH 3MnHpHQecKoH £pOPMY
bI,
3anHcaHHoH B BH
e (t. 7). .D.
H paccMRTpMBaeMoro CJIYQaH MO>KHO YTBep-
:>K
aTb, qTO eC
M B OnblTaX KpHTepHH Hycce
bTa M3MeHH
CH 01' 10
o 1000,
TO B 3TMX npe
e
ax B03MO>KHO npHMeHHTb 3MnHpHqeCKYIO ct>OPMY
Y.
Bee 3TM HeCOtvlHeHHbIe npeMMyw,eCTBa 3anHCH 3aBHCHMOCTH KO.3ct>ct>H-
UMeHTa TenJIOOT
aqH 01' onpe
e
HIOliLHx ero napaMeTpoB B ct>opMe (1. 7)
npHBe
H K TOMY, qTO B HacToHw,ee BpeMH B Ten
OTeXHHqeCKHX H TenJIO-
£pM3HqeCKMX Hcc
e
OBaHHHX nO
b3YIOTCH 6e
pa3MepHbIMM KpHTepMaJIb-
HbIMH ypaBHetlHHMH.
I-1CCJle
OBaHHH nOKa3a
H, QTO ct>YHKuHoHa
bHYIO 3aBHCHMOCTb (1. 7)
B03MO>KHO npeAcTaBHTb B BHAe CTeneHHbIX ct>YHKUHH
Nu =C.(Gr)n.(Pr)m, (1. 8)


2*




20


tl>U3uKo-MaTeMaTu<teCfwe OCHOBbl U3MepeHui1 TenAOBbtX 8eAUrtUH.


KpaTfcoe U3AO:JfCeHUe OCH08HblX nOH!lTUi1 U 3aKOHOB 0 TenAOo6,'tIeHe
,


21


r
e C, n 1-1 m - nOCTOHHHbie OTBJleqeHHbie ql-lCJla, Onpe)1.eJlHeMbie Ii3
OnblTa.
Bbl60p CTeneHHOH CPYHKUI-II-I 06'bHCHHeTCH B OCHOBHOM
BYMH npl-l-
qI-lHaMIi: BO-nepBbIX, 3TO O
Ha Ii3 Hal-l60Jlee npOCTbiX 3aBI-ICI-lMOCTeH, 1-1,
BO-BTOPbIX, CTeneHHbie CPYHKUI-II-I - rl-l6Kl-le CPYHKUI-II-I, TaK KaK HMI-I
MO)!(HO OnHCaTb nOqTI-I JIl06ylO 3KCnepHMeHTaJlbHYlO KPHBYlO (B 06J1aCTH
I-ICCJIe
OBaHHH TenJlOOT
aqH) nYTeM COOTBeTCTBYlOlll.erO no
60pa qHCeJl
C, n, m.
flo nYTH YCTaHOBJleHHH, B BI-I
e KpHTepHaJIbHbiX ypaBHeHHH, 3MnH2
pHqeCKHX CPOPMYJI
JIH K03cpcpl-lUHeHTOB TenJlOOT
aqH HanpaBJleHbi HCCJle-

OBaHHH OTeqeCTBeHHbiX H HHOCTpaHHbiX TenJlocpH31-1KOB H TenJlOTeX-
HHKOB, H3yqalOlll.HX pa3J1HqHbie cJlyqaH TenJlo06MeHa Me)!(
y TBep
bIM
TeJlOM H cpe
OH. EOJlblllHe I-ICCJle
OBaHHH B 3TOM HanpaBJleHHH 6blJlI-I npo-
Be
eHbl H npOBO
HTCH B HaCTOHlll.ee BpeMH COBeTCKOH lllKOJIOH TenJlocpIi-
3HKOB, C03
aHHOH M. B. Kl-lpnHqeBbiM. ClO
a OTHOCHTCH pa60Tbi
M. A. MI-IXeeBa, A. A. rYXMaHa, B. K. flOMepaHueBa, n. c. 3HreHCOHa,
fl. K. KOHaKOBa, C. C. KYTaTeJla
3e H MHorHX
PYfHX, He roBOpH y)!(e
o pa60Tax caMoro M. B. KHpnl-lqeBa.
B KaqeCTBe KOHKpeTHoro npHMepa CPOPMYJIbl B KpHTepHaJlbHOM BH
e
npl-lBe
eM CPOPMYJlY
JlH onpe
eJIeHHH TenJlOOT
aql-l npH CB060
HOM
BH-
)!(eHHH )!(H
KOCTH HJlH ra3a. Pe3YJlbTaTbi onbiTOB no TenJlOOT
aqe, nOJlY-
qeHHble MHorHMH HCCJIe
OBaTeJlHMH H3 3KcnepIiMeHTOB C B03
YXOM,
BO
OpO
OM, yrJleKHCJIOTOH, BO
OH, rJlHuepHHOM H
PYfHMH cpeJ\aMH,
6bIJII-I 0606lll.eHbJ 1-1 npeJ\CTaBJleHbi B KpHTepHaJlbHOM BHJ\e M. A. .Ml-lxee-
BbiM. flpH 3TOM HCCJleJ\OBaJlHCb pa3Ho06pa3Hble 06'beKTbl - rOp1-l30H-
TaJlbHble H BepTI-IKaJlbHble npOBOJIOKH, TPy6bl, nJlHTbi H lllapbI. Pa3Mepb1
HX BapbHpOBaJlHCb B lllHpOKHX npeJ\eJlax, a I-IMeHHO: J\HaMeTpbI npOBOJlOK
H Tpy6 OT 0,015 J\O 245 MM; lllapoB - OT 30 MAt
o 16 M; BbiCOTa nJlI-IT
H TPy6 OT 0,25 J\O 6 M. C ra3aMH OnblTbI npOBOJ\HJIHCb B lllHpOKOM J\Hana-
30He J\aBJIeHHH OT 0,03 J\O 70 ama. Pe3YJlbTaTbl Bcex 3THX OnbITOB
o-
BOJlbHO XOpOIllO YKJlaJ\btEalOTCH B KpHTepHaJlbHYlO CPOPMYJlY BHJ\a
Nu cp '= C (Gr.Pr)
p,
cae nOCTOHHHbie C H n J\JlH OTJ\eJlbHbIX yqaCTKOB pa3J1l-1qHbi Ii HBJlHIOTCH
CPYHKUHeH aprYMeHTa Cr. Pr. I1x 3HaqeHHH npl-lBeJ\eHbi HH)!(e. flpIi 3TOM
Bce cpH3HqeCKHe napaMeTpbl B cpopMYJIe (1. 8) OTHeceHbl K cpe
HeH
TeMnepaType, paBHoH t ep = + (us + 0);
JIH npOBOJlOK, Tpy6 H lllapoB
3a onpeJ\eJlHlOlll.HH pa3M
p npHHHT HX J\HaMeTp, a J\JlH nJlHT - HX BbiCOTa.


<f>OPMYJlY (1. 8) MO)!(HO pa3BepHYTb H npeJ\cTaBHTb B pa3MepHoM
BHJ\e


a = C(
g.Pr )n. Aep . ( US-IJ ) n
" ep v 2n !-3
ep L n
floJ\cTaBJlHH B CPOPMYJlY (1. 9) J\JlH IWHKpeTHOrO cJlyqaH (Hanpl-lMep,
npOBOJlOKa B B03J\yxe) 3HaqeHHH C, n,
,g, Prep, I. ep , V,p H J\p.,
MO)!(HO nOJlyqHTb 60Jlee npoCTYlO CPOPMYJlY, YJ\06HYlO J\JlH npaKTl-lqe-
CKIiX pacqeToB. HanpnMep, J\JIH Tpy6, ccpep 1-1 BepTI-IKaJIbHbiX nJIHT npn
(Cr. Pr)ep = 5.10 2 -+- 2. 10 7 [2]
ex = 5,62. A 2 . ( us-; IJ ) "',
a npH (Cr. Pr),.p > 2 10 7


(1. 9)


(1. 10)


..


ex = A3 (us - 8)'1..
(Cr.Pr)ep = 10- 3 -+- 5.10 2
ex = 75A] ( L:
M ) ,


(1. 11)


.D.JIH npOBOJIOK npn


(1, 12)


fJ\e AI, A 2 H A3 J\JIH B03J\¥xa HMelOT CJIeJ\YlOlll.He 3Ha qeHH 51:
t ep DC A, A. A.
0 0,25 1.22 1.45
50 0,26 1.14 1,27
100 0,27 1,09 1,14
200 0,29 1.05 0,97
300 0,30 0,95 0,85
500 0:32 0,85 0,70
1000 0,35 0,70 0,48


JI!! I (Gr.Pr)ctJ I C I n
I I 1.10- 3 -5.10 2 I 1.18 1/8
2 5. 10- 2 _2. 107 0,54 1/4
3 I 2.107_1.1018 I 0,135 1/3
I


B cpOpMYJIaX (I. 10) H (I. 11) pa3MepHOCTb K03cpcpl-lUHeHTa TenJIOOT-
J\a'IH - B KKaA M- 2 IJac- 1 i!paa- l .
EOJIee nOJ\p06Hbie CBeJ
eHI-IH 0 3HaqeHHHX K03cpcpl-lUl-leHTOB TenJIO-
OTJ\aqH Te.n, HarpeBalOlIUI XCH I-IJII-I OXJI
)!(J\alOw.H XCH B pa3JII-I qHblX YCJIO-
BI-IHX, MO)!(HO HaHTH B yqe6HI-IKe M. A. MHxeeBa «OCHOBbi TenJIOnepeJ\aql-!».

 4. TenJloo6MeH paAHaUHeH
TenJIoo6MeH pa
HaUHeH I-IJII-I 1-13JIyqeHHeM npOHCXO
I-IT COrJIaCHO T3K
Ha3bIBaeMOMY 3aKOHY qeTBepTblX CTeneHei'i HJIlI 3aKOHY CTecpaHa-EoJIbU-
M3Ha. .D.JIH a6COJIlOTHO qepHbiX nOBepXHOCTeH, 06JIa
alOlll.I-IX MaKCI-IMaJIb-
HOM H3JIyqaTeJIbIIOH (a CJIe
OBaTeJIbHO, B cnJIY 3aKOHa KHpxrocpa [21.
H HaH60JIbilleH nOfJIOlll.aTeJIbHoM), cnoco6HoCTblO KOJIl-lqeCTBO TenJIa,
1-13JIyqaeMOrO eJ
I1Hlluei'1 nOBepxHocTH 3a e
HHHUY BpeMeHI-I, KOTopoe
0603Haql-lM q
, 6y
eT paBHO


q r = a . T4
, r .


(1. 13)




22


t1>U3uKo-MaTeMaTU'leCKUe OCHOBbl U3MepeHut'l TenA08blX 8eAU'tUH


KpaTKoe U3A03fCeI!Ue OCHOBl!blX nOHJlTut'l U 3aKiJHOB 0 renAoo6MeHe


23


3.L\eCb T - aOCOJllOTHa5J TeMnepaTypa H3JIyqmOlll.eH nOBepXHOCTH
B rpa.L\ycax KeJIbBHHa, paBHa5J t + 273,2°, eCJIH t - ee TeMnepaTypa,
Bblpa)!(eHHa5J B rpa.L\ycax IJ.eJIbCH5J I. BeJIHqHHa a r - a6COJllOTHa5J KOH-
CTaHTa T. e. K03cpcpHLl.HeHT H3JIyqeHH5J [I J. no nOCJIe.L\HHM .L\aHHbiM paBHbili
a r = 5,673.10- 12 8m,cM- 2 .epao- 4 .
.lI.JI5J y.L\06cTBa nHCbMa BMeCTO a nOJIb3YlOTC5J K03cpcpHLl.HeHTOM C r =
= 10 8 . a r H Bblpa)!(alOT ero B TeXHHqeCKOH CHCTeMe e.L\HHHLI.; nepecqeT
npHBO.L\HT K Ll.Hcppe
C r = 4,88 KKaA- I .ttQc- I 'M- 2 .epao- 4 .
113JIyqeHHe nOBepXHOCTeH, C KOTOpbIMH Mbl HMeeM .L\eJIO B TeXHHKe
H3MepeHHH, T. e. Bo06lll.e rOBOp5J HeqepHbiX nOBepXHOCTeH, C TOqHOCTblO,
.L\OCTaTOqHOH .L\JI5J npaKTHqeCKHX Ll.eJIeH, CJIe.L\yeT 3aKOHY, KOTOpbIH HMeeT
TY )!(e cpOPMY, qTO H 3aKOH CTecpaHa-EoJIbLl.MaHa (I. 6), a HMeHHO:
qe= a.p = c. c
o r (I. 14)
nOBepXHOCTH HJIH TeJIa :;noro p0.L\a Ha3bIBalOTcepblMH nOBepXHOCT5JMH;
pacnpe.L\eJIeHHe 3HeprHH H3JIyqeHH5J B HX cneKTpe nOJIyqaeTC5J H3 pacnpe-
.L\eJIeHH5J 3HeprHH B cneKTpe H3JIyqeHH5J qepHOrO TeJIa nOCpe.L\CTBOM YMeHb-
llleHH5J HHTeHCHBHOCTeH 3HeprHH Bcex .L\JIHH BOJIH B O.L\HOM H TOM )!(e
MaClllTa6e, qHCJIeHHO paBHOM .


e OKpy)!(alOlll.HMH ero TeJIaMH; 60JIee CJIO)!(Hble CJIyqaH paccMaTpHBalOTcfI
B pa3JIHqHbiX TpY.L\aX no TenJIo06MeHY, HanpHMep B yqe6HHKe
M. A. MHxeeBa [2 L
YpaBHeHHlO (1. 16) B TOM CJIyqae, KOr.L\a pa3HOCTb TeMnepaTYP
TeJIa H cpe.L\bl, T. e. AT = T - To = u - 6, HeBeJIHKa, MO)!(HO npH.L\aTb
60JIee npoCTYlO cpOPMY. .D.JI5J 3TOro HanHllleM npaBYlO ero qaCTb B 2 CJIe.L\YlO-
LII.eM BH.L\e: q = a [(To + AT)4 - T6] = a.t1T. (4T
 + 6To.AT +
+ 4To A T2 + A T 3). OpH MaJIOCTH BeJIHqHHbi AT Bblpa)!(eHHe B cK06-
Kax 6Y.L\eT He3HaqHTeJIbHO OTJIHqaTbC5J OT 4T
 H MO)!(HO 6Y.L\eT HanHcaTb:
3 1 ( To ) 3 t1 T
q_,y'l = 4. a . TO" t1T = 25' 100 . .


(1. 17)


113 ypaBHeHH5J (I. 17) CJI, e.L\yeT qTO nOTeplO TenJIa H3JIyqeHHeM
MO)!(HO npe.L\CTaBHTb B cpopMe, aHaJIOmqHOH (I. 4), a HMeHHO CJIe.L\YlOlll.HM
06pa30M:


q_, = (l./l' (us - 8),


(1. 18)


r.L\e (1../1 ____ «K03cpcpHLl.HeHT TenJIOOT.L\a'IH H3JIyqeHHeM» paBHblH
_
. C. ( U + 273,2 )

(X./I-25 100'


(1. 19)


CI
!=-.
CI,


(1. 15)


.D.JI5J ynpOlll.eHH5J MaTeMaTHqeCKOH TpaKToBKH npaKTHqeCKHX 3a.L\aq
C nOMOlll.blO K03cpcpHLl.HeHTa TenJIOOT.L\aqH (X 06blqHO CYMMapHo yqHTbI-
BalOT BJIH5JHHe Ha TenJIo06MeH KaK KOHBeKLl.HH, TaK H H3JIyqeHH5J.
B 3TOM cJIyqae H3 cpOPMYJI (1. 18), (I. 4) CJIe.L\yeT, qTO


BeJIHqHHY 3Toro OTHOllleHH5J e Ha3bIBalOT K03cpcpHLl.HeHTOM qepHOTbl H3JIY-
qeHH5J .L\aHHOH nOBepXHOCTH; nOCKOJIbKY a MeHbllle HJIH paBHa a" qHCJIO Ii
BCer.L\a MeHbllle e.L\HHHLI.bI HJIH paBHO e.L\HHHLl.e.
Mbi BH.L\eJIH Bblllle (B HaqaJIe 3TOH rJIaBbl), qTO BC5JKOe HCnYCKalOlll.ee
pa.L\HaLl.HlO TeJIO O.L\HOBpeMeHHO nOJIyqaeT pa.L\HaLl.HlO OT OKpy)!(alOlll.HX
ero TeJI; eCJIH a6COJIlOTHYlO Te
mepaTYPY 3TH X TeJI 0603HaqHTb 6YKBOH To
TO pa.L\HaLl.H5J TeJIa 6Y.L\eT YMeHbllleHa Ha BeJIHqHHY a T3 H Mbi nOJIyqHM
.L\JI5J nOTepH TenJIa C e.L\HHHLl.bl nOBepXHOCTH 3a e.L\HHHLI.Y BpeMeHH
q.//y'l = a.(p- T
) (1. 16)
3.L\eCb npe.L\nOJIaraeTC5J, qTO ra3, OMblBalOlll.HH TeJIa, np03paqeH .L\JI5J
pa.L\HaLI.HH.
B paCCMOTpeHHOM npOCTellllleM CJIyqae 06MeHa TenJIa pa.L\HaLl.HeH
Me)!(.L\y TeJIaMH pa3MepbI O.L\HOrO H3 TeJI BecbMa MaJIbi no cpaBHeHHIO


a. = a." + (X.Il'


(1. 20)


PaHce npe.L\nOJIaraJIOCb, qTO Bee TOqKH TenJIOOT.L\alOlll.E'H nORE'pX-
HOCTH S (cpHr. 8) .L\aHHOrO TeJIa (HJIH cHcTeMbI) O.L\HHaKOBO OT.L\alOT TenJIO.
B npaKTHKe B03MO)!(Hbi CJIyqaH, KOr.L\a HHTeHCHBHOCTb TenJIOOT.L\aqn
B pa3Hblx MeCTax HapY)!(HOH nOBepXHOCTH TeJIa pa3JIHqHa; 3TO paBHo-
CHJIbHO YTBep)!(.L\eHHlO, qTO (X 3aBHCHT OT KOOp.L\HHaT X s , Ys, Zs TOqeK
nOBepXHOCTH S. u
npHMepOM MO)!(eT CJIY)!(HTb TenJIOOT.L\aqa mpH30HTaJIbHOH nJIHTbi
B YCJIOBH5JX eCTeCTBeHHOH KOHBeKLl.HH, HJIJIlOCTpHpyeMa5J cpHr. 7: K03CP;
cpHLl.HeHT TenJIOOT.L\aqH KOHBeKLl.HeH B B
px
eH qaCTH nJIaCTHHKH (X It
ropa3.L\0 BbIllle, qeM B ee HH)!(HeH qaCTH (X"/(X,, = 0,5 - 0,6. u
.D.pyroH npHMep: np5JMOH KpyroBoH LI.HJIHH.L\p.oXJIa)!(.L\aeMbIH nOTO-
KOM B03.L\yxa, KOTOpWH HanpaBJIeH nepneH.L\HKYJI5JpHO KOCH LI.HJIHH.L\pa
H 06JIa.L\aeT nOCT05JHHOH CKOpOCTblO W (cpHr. 8). K03cpcpHLl.HeHT IiMeeT
pa3JIHqHble 3HaqeHH5J Ha 60KOBOH nOBepXHOCTH Ll.HJIHH.L\pa H Ha e
o TOp-
Ll.ax; 60JIee TOro: Ha nepe.L\HeH 60KOBOH nOBepxHocTH, 06palll.eHHOH K no-
TOKY, ex - HHoe. qeM Ha 3a):{HeiL
Bbl.L\eJIHM KaKOH-JIH60 3JIeMeHT dS HapY)!(HOH nOBepXHOCTH TeJIa
fI ooo3Ha'IIfM fI Q s KO.'1I1'IE'CTRO TE'nJI1'I, Tf'p5JPM()P jiM R TPqPHHP OP('J{OHP'IHuO
MaJIOrO BpeMeHH fI T: yqHTbIBa5J CYMMapHO nOTeplO TenJIa KOI-IBeKIJ.HeH,


I B Tex C1IY4aHx npaKTJfKH, Kor.na npHxo,'!HTCH HMeTb .liMO C BblCOKHMH TeMnepa-
TypaMlI, nopH.nKa 500 0 C Ii Bblllle, MO}KHO nOJlb30BaTbCH MeHee TOlJHOH UJfqJpOH J\JlH
nepexo.n a OT WKa.1b1 UeJlbCHH K llIKaJle KeJlbBHHa, a HMeHHO 273. Ha060poT, B 06JIaCTH
BeCbMa HJf3KHX TeMnepaTYP, nopH.nKa MHHYC 180 0 C Ii HH)I{e. CJleJ1yeT 6paTb 60Jlee TOlJHOe
3HalJelllie. a I1MeHHf\ 27:1,lfi + (),OI npH "....prp...m TPMTlpr:nVrf'I"X r
3W)('T
I'1 ) t -
= AT = TI - 1 2 = II - 12 ueT HY}K.nbI npHHHMaTb BO BHHMaHHe YKa3aHHbIe 3.neCb
pa3J1H4HH.




24


tl>U3uKo-MaTeMaTUfteCKUe OCHOBbl U3MepeHUil TenAOBblX 8eAU'/UH


p a .nHaL1.Heii H KOH,nYKL1.HeH (qepe3 nOrpaHHqHblH CJIOH, CTp. 18),
Mbl, aHaJIOfH
IHO cpopMYJIe (I. 5), MO)!(eM HanHcaTb, nOJlb3Y5JCb paBeH-
CTBOM (1. 20):
oQs=a..(us-t).dS.o't. (1. 21)
3,necb y)!(e B OTJIHqHe OT CPOPMYJIbl (1. 15) KO.3cpcpHIJ.HeHT T
nJIOOT,naqH-
CPYHKL1.H5J Koop,nl1HaT:


a = (1. (l s , Ys, 2S).


(1. 22)


B HeKoTopblX CJIyqa5JX a MO)!(eT 3aBHceTb eIIJ.e H OT BpeMeHH T; .3TO
Ha6Jl1o.n a eTC5J, Kor,na pe)!(HM oKpy)!(alOIll.eH cpe,nbl - nepeMeHHblH, Ha-
npHMep Kor,na TeJIO 06,nYBaeTC5J nopblBHCTblM BeTpOM. TaKHe CJIyqaH
B ,naJIbHeHWeM HaMH paCCMaTplmaTbC5J He 6y,nYT.
B orpOMHOM 60JIbWHHCTBe CJIyqaeB Ha npaKTHKe onpe,neJI5JlOT He «JIO-
KaJIbHbIH» KO.3cpcpHL1.HeHT TenJIOOT,naqH a (xs, Ys. zs), a ocpe,nHeHHblti
no nOBepXHOCTII S HJIH «cpe,nHHH» Ko.3<}JcpHIJ.HeHT TenJIOOT.naqH -;, BeJIH-
qHHa KOToporo onpe,neJI5JeTC5J paBeHCTBOM
_ I a (xS. YS. zs).dS
a cp = a. S (1. 23)


l-lT06bl H36e)!(3Tb rpOM03,nKOCTH B 0603HaqeHl15JX, OqeHb qaCTO ero
0603HaqalOT O,nHOH 6YKBOH a 6e3 3HaqKOB.
B 3aKJIlOqeHHe .3TOH rJIaBbl npHBe,neM HeKOTopble KOHKpeTHble L1.HcppO-
Bble ,naHHble OTHOCIITeJIbHO KO.3cpcpHIJ.HeHTOB, KOTopble BCTpeqalOTC5J Ha
npaKTIlKe (,no CHX nop HalliH paccy)!(,neHH5J HMeJIH 06IIJ.HH xapaKTep).
npe,nBapl1TeJIbHO paCCMOTpHM Bonpoc 06 e,nHHHL1.aX H3MepeHH5J TenJIO-
BblX BeJIHql1H.



 5. 0 Bbl60pe e)l.HHI1L1. H3MepeHHSI
npH BBe,neHHH BC5JKOH HonoH npoH3Bo,nHOH cpH3HlJeCKOH BeJIHqHHbl
He06xo,nHMO Bblpa3HTb ee pa3MepHocTb, Ha OCHOBaHIIH 3apaHee Bbl6paH-
HOH CHCTeMbl OCHOBHblX e,nHHHIJ.. B TenJIOTeXHHKe H TenJIocpH3HKe qaIll.e
Bcero npHMeH5JlOT «rexHHqecKYlO cHcTeMY e,nHHHL1.», B KOTOpOH OCHOB-
HblMH BeJIHqHHaMH CJIy)!(aT KHJIOrpaMM, MeTp, qac, rpa,nyc Me)!(,nYHapo,n-
HOH cTorpa,nycHoH WKaJIbl TeMneparyp, npaKTHqeCKH cOBna.nalOIIJ.eH
C TepMo.nHHaMHqeCKOH WKaJIOH.
3a e.nHHHL1.Y KOJIHqeCTBa Ten JI OTbl npHH5JT ,n)!(OYJIb, COrJIaCHO nOCJIe.n-
HeMY Me)!(,nYHapo,nHOMY COrJIaWeHHlO 1948 r. O,nHaKo, yqHTblBa5J Tpe-
60BaHH5J npaKTHKH, nOJIb3YlOTC5J nO-npe)!(HeMY KHJIOKaJIOpHeH, onpe-
.neJUISI ee KaK KOJIHqeCTBO TenJIOBOH .3HeprHH, He06xo.nHMge ,n,,'!5J nOBbl-
llIeHH5J TeMnepaTypbl o.nHoro KHJIOrpaMMa BO,nbl Ha O,nHH rpa,nyc.
TenJIOeMKOCTb BO,nbl II3MeH5JeTC5J C TeMnepaTypoH, nO.3ToMY ,nJI5J YTOq-
HeHH5J onpe,neJIeHH5J He06xo,nHMO YKa3aTb, npH K3KOH TeMnepaType
npoH3Bo,nHTC5J HarpeBaHHe; B COOTBeTCTBHH C .3THM pa3JIHqalOT ,nBe
KaJJOpHH: «n5JTHa,nL1.aTHrpa,nvcHYlO» H «,nBa)l.IJ.aTHrpa,nVCHVlO» - Ka1/ 15
H MlA:o, llpl1'-!eM Kall = 10 3 KKaIi. 4HCJIeHHOe COOTHoweHHe Me)!(,ny


KpaTKoe U3ACYJ/CeHU
 OCH08HbiX nOHJlTU/l u 3aKOHOB 0 TenAoo6MeHe


25


KaJIOpHeH H ,n)!(OYJIeM 3aBHCHT OT Toro, C KaKOH TOqHOCTblO y.naeTC5J
onpe,neJIHTb y,neJJbHYlO TenJIOeMKOCTb BO,nbl npH pa3HblX TeM
epaTypax.
Ocpe,nHeHHe pe3YJIbTaTOB Han60JIee ,nOCTOBepHbIX Ha6JIlO,neHI1H npHBo.nHT
K CJIe,nYIOIIJ.eMY COOTHoweHHlO:
I a6c. o [}fCoylib = 0,2390 Kall 15 = 10 7 sp2. (1 24)


npHHHMa5J BO BHHMaHHe HeH36e)!(Hble HeTOqHOCTH ,a3)!(e JIyqIllHX
TexHHqeCKHX H3MepeHHH, MO}KHO npeHe6peraTb pa3JIHqIIe:\1 Me)!(,ny IW.I1 15
H IW,120 H J\JI5J nepexo,na OT KIW.I1 K MeXaHHqeCKHM, a6COJIlOTHblM e,nHHH-
IJ.aM CqHTaTb:


1 KKa.l1 = 4183 a6c. OOIC }
I a6c. OOIC = 10 7 3P2 = 1 eamm.ceK = 0,239 IW/l


(1. 25)


E,nHHHIJ.bl CJIO)!(HblX cpH3HqeCKHX II TeXHHqeCKIIX BeJIHqHH BbI6H-
palOT TaK. qT06bl ypaBHeHH5J, CJIy)!(aIIJ.He ,nJI5J onpe,neJIeHH5J .3THX BeJIH-
4HH HMeJIl1 npoCTeHIllYlO CPOPMY. npH .3TOM ,nJI5J 0603HaqeHH5J e,nHHHIJ.
BeJI
qHH 6YKBbl, HX 03HalJalOIll.He, 3aKJJlOqalOT B KBa,npaTHble cK06KH HJIH
HHor)l.a 'hHIlIYT KypCHBOM. 0
CHMBOJIbl pa3MepHocTeH OCHOBHblX e,nHHHL1. B HallieH CHCTeMe 6y,nYT M,
'lac K2 2pao. CHMBOJI ,nJI5J e,nHl
aIJ.bl KOJIHqeCTBa TenJIa - KKa.l1.
'J1.JI
 pacnpoCTpaHeHH5J TenJIa KOH,nYKIJ.HeH BHYTPH TeJIa CYIIJ.eCTBeH-
Hoe 3HaqeHHe HMelOT cpH3l1qeCKHe CBOHCTBa BeIIJ.eCTBa .3TOrO TeJIa: ero
TenJIOnpOBo,nHOCTb A. y,neJIbHa5J TenJIOeMKOCTb Co H !nJ10THOCTb, HJJH
06'beMHblH Bec 1. Pa3MepHocTH CHI B TeXHHqeCKOH CHCTeMe e,nHHHIJ. -
CJIe,nYlOIIJ.He:


[cJ = KKa.l1 Kr l 2pao- l , [,J = K2 M- s .


(1. 26)


flpu.Mep 1. nOKa)!(eM, KaK onp
,neJIHTb pa3MepHocTb K0.3cpcpHIJ.HeHTa
TenJIOnpoBo,nHOCTH A B TeXHHqeCKOH CHCTeMe e,aHHHIJ.. COrJIaCHO ypaB-
HeHHlO (1. 1) HMeeM


zpaa 2
KKaIl = [I,] ,-'M 'lfac.
M


OTClO,na C"le,nyeT, lJTO
fA] = KKall. M- I .lfac- I 2pao- I .


(1. 27)


Bbl6paB 3a OCHOBHVlO cpH3HqecKYlO CHCTeMY e,nHHHIJ., r,ne e,nHHHIJ.eH
KOJ1HqeCTBa TenJ10Tbl HBJI5JeTC5J ,n)!(OYJIb - OOlC, paBHblH em.ceK, Mbl
HMeJIH 6w ,npyrylO e,nHHHIJ.Y ,nJI5J A, a HMeHHO
[A] = OOIC . CAt-I. ceK- i . 2pao- 1 =- em. CM- 1 . 2pao- 1 . (1. 28)


AHaJIOfHqHO H3 (1. 4) nOJIyqaeM pa3MepHocTb Ko.3<}JcpHIJ.HeHTOB renJIOOT-
,naqH:


[aJ = [a"J = [aAJ = KK.U.I1.M 1'lftK 1 '2puJ 1


(1. 29)





 .


26


fPU3ufCO-ltIaTeMaTU'IeCKUe OCH08bl U3lt1epeHuQ TenAOBblX BeAU'IUH


KpaTKoe U3A03ICeHUe OCH()BHbIX nOHJlTui1 U 3aKOHOB 0 TenAOo6lt1eHe


27


a H3 3aKOHa 'IeTBepTbiX CTeneHeH (I. 13) Ii (1. 14) pa3MepHocTb K03cp-
cpHI.I.lieHTOB H3J1Y'IeHIiH C H C,:
IC] = IC,] = KJ\.QA'M- 2 'IfQC- 1 .epao--. (I. 30)
O'IeBH.L\HO, 'ITO K03cpcpliUHeHT '1epHOTbl H3J1Y'leHIiH e (IiJ1H, no .L\pyroH
TepMIiH0J10rIiH, «CTeneHb '1epHOTbl» .L\aHHOH nOBepxHocTH) HMeeT HYJleBYIO
pa3MepHocTb.


MeTaJ1J1bl, Ha060poT, HMelOT BeCbMa BblCOKYIO TenJ1onp OBO .L\HOCTb;
3TO - «xopolllHe npOBO.L\HHKH TenJ1a».


A MeTanJlOB npH 20° C


Cepe6po


MeJ1b AJlIOMH- )!(eJle30
QHCT8S1 HHH O'-leHb CBHHeu
'-IHCToe


PTYTb


CT3J1b
yrJlepo.
.D.HCT3Sl


CT3J1b MeJ1b
851-I-T ToprOB."


KOHCT3HT8H


360


330 175


65


30


7


40-50


14.5 300


H HH}Ke 19,5


0.021


0.021


0.020


0,125


B0J10p0J1
0.15


B03J1YX
0.022


CnJ1aBbl HMelOT 60J1ee HH3KYIO TenJ1onpOBO.L\HOCTb, '1eM '1HCTble
MeTaJlJ1bl; A CHH)!(aeTCH .L\0 10.
TenJ1onp OBO .L\HOCTb PY.L\, MeTaJ1J1OKepaMHKH H aHaJ10rH'IHbIX MaTepHa-
J10B O'leHb MaJ10 IiCCJ1e.L\oBaHa; nO-BH.L\IiMOMY, OHa J1e)!(IiT Me
.L\Y 10 H 3.
MaccHBHbIe ropHbIe nopO.L\bl C nJ1OTHOCTblO nOpH.L\Ka 3500-2000 KFM- 3
(rpaHHTbI, .L\lia6a3bl, anaTHTbl, HOpHTbl H T. .L\.) IiMelOT CHJ1bHO K0J1e6-
J11OW.ylOcH TenJ1onpOBO.L\HOCTb B npe.L\eJ1ax npHMepHo OT 1 .L\0 3 (npH 6ec-
nopH.L\O'lHOM pacnOJlO)!(eHHH KpIiCTaJ1J1OB).
I1cKycCTI?eHHble KaMHH, r.L\e npe06J1a.L\aeT KpHCTaJ1J1H'IecKHH KOMno-
HEHT, KaK B MarHe3HTOBbIX, KOpYH.L\OBbIX H Kap60PYH.L\OBbIX KHpnH'IaX
Ii T. n., HMelOT npH KOMHaTHoH TeMnepaType BbICOKYIO TenJ10npoB O .L\HOCTb,
.L\OXO.L\Hlll.YIO B HeKoTopbIX CJ1Y'IaHX .L\O 10, I<OTopaH npH BblCOKIiX TeMne-
paTypax (1000-1400°) pe3Ko na.L\aeT no CJ1O)!(HOMY 3aKoHY, CHH)!(3HCb
J(O
3. .lI.pyrHe omeynopbl - .L\HHaC, waMOT H np.- HMelOT A nopHJ(Ka 0,8
H HH)!(e B 3aBHCliMOCTH OT CTeneHH nopHcToCTH.
TaKora )!(e nopH.L\Ka, a '1alll.e HH)!(e - nOpH.L\Ka 0,6-0,3 -IiMeIOT A
KepaMPI'leCKHe H CTpOHTeJ1bHbIe (cyxue) MaTepHaJ1bI .L\J1H CTeHOBblX
orpa)!(.L\eHH II.
TenJ1onp OBO .L\HOCTb HH)!(e 0,3-0,2 (npH t = 20° C) xapaKTepHa J(J1H
TeIVIOH30J1HUHOHHbIX MaTepliaJ10B - nJ10XIiX npOBO.L\HHKOB TenJ1a.
TenJ10H30J1HTOpbI cpe.L\HerO Ka'leCTBa HMelOT TenJ10npoBO.L\HOCTb no-
pH.L\Ka 0,1-0,2; TaKOBbI nJ10THble KapToHbl, B TOM '1HCJ1e ac6eCTOBblH,
cpaHepa, .L\peBeCHHa Ii T. .L\.
3cpcpeKTHBHble TenJlOH30_'lHTOpbl UMelOT TenJ10npOBO.L\HOCTb nopH.L\Ka
0,05-0,10, BbIcOK03QJcpeKTHBHble - 0,03-0,05. TaKoBbl np06Ka, pac-
nyweHHblH ac6ecT, CTeKJ1HHHaH H MIiHepaJ1bHaH BaTa, neHOnJ1aCTbI.
K03QJcpHUlieHT TenJ1OOT.L\a'lli, KaK Mbl rOBOpHJ1H BbIwe (n
 3 :;noH rJ1aBbl),
He HBJ1HeTCH KaKIiM-J1H60 cpH3H'IeCKHM CBOHCTBOM, a npe.L\CTaBJ1HeT C060H
CPYHKUHlO MHorHX napaMeTpOB; oc06eHHO CIiJ1bHO Ha HeM CKa3bIBaeTCH
y.n.eJlbHaH TenJ10eMKOCTb oKpy)!(alOlll.eH TeJ10 cpe.L\bI ()!(H.L\KOCTH HJ1H ra3a)
Ii CKOpOCTb ee .L\BH)!(eHHH. HH)!(e npIiBO.L\HM ,l,aHHble, xapaKTepH3Y IO lll.He
nOpH.L\OK 3TOH BeJ1H'IHHbl.



 6. 0 I.JHCJ1eHHbIX 3HaI.JeHHSIX K034!4mLI.HeHTOB TenJ10npOBoJI.HOCTH,
K034!4!HLI.HeHTOB TenJ100TJI.aI.JH H cTeneHeH l.JepHOT

DpH TeXHIi'leCKHX paC'leTaX, npH COCTaBJleHIiH nJlaHa 3KcnepHMeHToB
H npH npoeKTHpoBaHHIi npH60poB He06xo.L\IiMO pacnOJ1araTb 0pHeHTH-
pOBO'lHbIMIi 'lHCJ1eHHbIMH .L\aHHbIMH OTHOCHTeJ1bHO Tex BeJ1/1'lHH C KOTO-
pbIMH npIiXO.L\HTCH HMeTb .L\eJ1O; He06xo.L\HMO, BO BCHKOM cJ1Y'l;e, HMeTb
npe.L\CTaBJ1eHHe 0 nOpH.L\Ke 3TH X BeJ1H'lHH. B .L\aHHOM naparpacpe 6Y.L\YT
C006lll.eHbl HeKOTopbIe .L\aHHble 0 BeJ1H'lHHaX, C KOTOpblMIi Mbl BCTpeTIi-
J1HCb B npe.L\bl.L\YWHX naparpacpax.
K03qxpHUlieHT TenJ10npOBO.L\HOCTH I. 3aBliCHT OT CBoikTB .L\aHHoro
Belll.eCTBa, HO HMeeT BnOJ1He onpe.L\eJ1eHHOe 'lHCJ1eHHOe 3Ha'leHHe TOJ1bKO
.L\J1H He60J1bWOH rpynnbl XHMH'leCKH 'lHCTbIX Belll.eCTB; eCJ1H 3TO-
TBep.L\bIe TeJ1a (MeTaJlJ1bl, ropHble nOpO.L\bI, nJ1aCTMaCCbI H T. .L\.), TO Ha A
J(aHHoro Belll.eCTBa BJ1IiHeT He TOJ1bKO ero CTpYKTypa, KaK, HanpHMep,
.L\J1H KpIiCTaJ1J1H'leCKOrO H aMopcpHoro KBapua, HO elll.e MeXaHH'leCKaH
Ii TepMIi'leCKaH ero 06pa60TKa. D03TOMY K .L\aHHbIM OTHOCHTeJ1bHO J.,
npHBo.L\HMbIM B Y'le6HHKax H CnpaBO'lHHKaX, CJ1e.L\yeT OTHOCHTbCH KPH-
TH'IeCKH: TaK, .3arpH3HeHHe 'lHCTOrO Bew.ecTBa, HanpliMep, MeTaJ1J1a,
MO.L\H4JHKaUHH CTPYKTypbl H TOMY nO.L\06HbIe cpaKTopbl y)!(e H3MeHHIOT A.
Elll.e MeHee YCTOH'lH.Ba TenJ1onpOBO.L\HOCTb TeXHH'IeCKHX MaTepHaJ1OB,
o 'leM Mbl 6YJ(eM rOBopHTb HH)!(e B
 I rJ1. 15. HaliHH3weii TenJ10npo-
BO.L\HOCTblO 06J1a.L\aIOT ra3bI. TaK, Mbl IiMeeM: 1


KHCJlOPOJ1


A30T


A ra30B npH 20° C

'rJleKHCnOT3 reJlHA


)l(H.L\KOCTH IiMelOT 60J1ee BbICOKYIO TenJ1onpOBO.L\HOCTb; HaH60J1bWHM A
06J1a.L\aeT BO.L\a; TenJ1onpOBO.L\HOCTb HX K0J1e6J1eTCH B He60J1bWHX OTHO-
CHTeJ1bHO, npe.L\eJ1ax. '


A }KHJ1KOCTeH npH 20° C
BOJ13 neHT3H CnHpT TOJlyoJl P33J1HLJHble TeXHH'-IeClme
M3cna
0,51 0.10 0.17 0.13 0.10-0,15


YCJlOBHSl TenJlOOT.D.a'-lH


"It


I U6palHle IJHHMaHHe Hd 8HOM8JJbHO IJbICUKYIO TenJlOnpoBuJ\HU\:Ib BOP.O!-'0J\a,I1MeHHO
n03TOMY ero npHMeHSlIOT
JlSI OXJla}K.I\eHHH 3J1eKTpH4ecKHx Mallll!H.


CnOKOHHblH B03J1YX . . .
UHr:KYJlHllHII B03J1yxa H ra30B. . . . . . .
MacJla H ,ll,pyrue TeXHHQeCKHC }KHJ1KOCTH TOH }KC nJlOT-
HOCTH:
cllohoi:'IHble .


2-8
20-100


Jl,BH}KYlllHeCH


200 300
300-1000




28


tl>U3uKO-l>laTeMaTU'IeCKue OCHOBbl U3MepeHui1. TenJlOBblX BeJlU'ItlH


Ta6Atll{a 1 .
npH5J1HIKCHHble 3HalJeHHH K03i!Ji!JHQHeHToB lJepHOTbl H3J1YlJeHHH HeKoTopblX
TeXHHQeCKHX nOBepxHocTeH
MmpHan I IXAt-2

c
f:;aa-41 t °C


4CpHOC TeJlO .
JIaMnoBaH KonOTb. ca}f{a


>KCJle30, lJyrYH, CH,1bHO OImC.leH-
Hble
>KeJle3HI,!e OUHH!{QBaHlIbIe JlHCTbI
ceporo UBeTa .
Ccpe6po
AJlIOMHHHii Hc06pa60TaHHb!;i
nOJlHpOBaHlIblH
nOKpblTl:le SMaJleBI,IM Jlal<OM B
4 CJlOH
DOKpI,!THe 4CPHI,!M CnlIpTOlJbIM
.
aKOM B 4 CJlOH .
DOKpI,!THe uanOH-JlaKml
JIaTYHb, nOJlHpOBaHHaH nanoii
roVl .


OKHCJlCHHaH CBIfHUOBaH nOBcpx-
HOCTI,
KHpnHlJ cJla60 rnepoXOn3TI,!H .
fJla3ypoBaHHbIe n.mTKH
Ac6ecT


CH:K.
O rJlaJ1KOe .
360HHT rJla.'(Kl!H, lJCpHbIH
MeJl
BO,ll,a
PTYTb
JIe,ll, (BJla}f{HbIH)
PC3HHa (cepaH')
n.1aTHHa


TOJlCTblii CJlOH MaC.
a Ha n01Hpo-
BaHHOM }KeJle3e
C.1OH 0,12 MM
CJlOH 0,08 l>IM
UOH 0,029 MM
lJHC'Tor }f{rnr"'o
Heij3HnL6ep CBeTJlI,lH THH Y;I,Iii


1.00
OT 0,95
.'(00,97


0.91-0,92


0.28
0.03
0.071
0,052


0,91


0,77
.
0,94


0.26-0.30 I


0,273
0,95
0,875
OT 0,93
,11,0 0.95
0,94
0,94
0,81
0,90
0,18
0,97
0,86
OT 0,036
,11,00,19


0,82
0.75
0.44
0,35
n,Ofi8
0.30


4.88
OT 4,65
1\0 4,75


4.45
4.5


0,137
0,0145
0.035
0,0255


4.45


3.75
4,58


1,3-1.5


0.132
4,65
4,3
OT 4,55
J10 4,65
4.6
4,6
3,95
4,4
0.088
4.75
4,2
OT 0,0175
,11,0 0,093
4,0
3,65
2.15
1.7
0,028
0,146


JlI06aH
OT 20°
J10 350°


40°-250°


24°
20°
26°
23°


20°


20°
20°


20°


20°
20°
20°
OT 40°
J10 350°
20°
20°
20°
20°


0°
25°
OT 30°
Au 1200°


20°


KpaTKoe U3A03ICeHUe OCHOBHblX nOHRTuii U 3aICOHOB 0 TenAoo6MeHe


29


Bo;w:
cnoKoHHaH
J1BH}KYll.laHCH
6ypHO KHnHll.laH ......
)KHAKl!C MCTaJlJlI,! OpHCHTHpOBOlJHO


200-600
1000-3000
10 000
5000-10 000


K09<tJ4JHL\UeHT qepHOTbl H3J1YQeHuSi. 3Ta cpH3HqeCKaSl BeJIHqHHa
B oqeHb CHJIbHOH CTeneHH 3aBlICHT H OT xapaKTepa 06pa60TKH nOBepx-
HOCTH; Ha Hee CHJIbHO BJIHHIOT J\a>Ke CJIa6ble 3arpSl3HeHHSI nOBepxHocrn
(3anbIJIeHHOCTb, >KHpHble nHTHa, YBJIa>KHeHHe H T. J\.). KpoMe Toro,
H3JIyqeHHe Cepblx TeJI, a OHH Bcero Ba>KHee J\JIH TexHHKH, 3aBHCHT OT
TeMnepaTypbI. Ta6JI. 1 cOJ\ep>KHT HeKoTopbIe - opHeHTHpOBOqlIbie -
J\aHHble.
He06xoJ\HMO ew.e pa3 nOJ\qepKHYTb, qTO TOqHOCTb L\HcppOBbIX J\aHHbIX
Ta6JI. 1 He CJIeJ\yeT nepeOIJ.eHl1BaTb: OHH B OCHOBHOM npHrOJ\HbI J\JISI
npeJ\B3pHTeJIbHblX paCqeTOB. OTBeTCTBeHHbIe paCqeTbI, B KOTOpblX BeJIH-
qHHbl C H e HrpalOT Ba>KHYIO POJIb, J\OJI>KHbl COnpOBO>KJ\aTbCH HenocpeJ\-
cTBeHHblMH H3MepeHHHMH C He; HeJIb3H nOJIaraTbCSI Ha TaKHe Heonpe-
.n.eJIeHHble YKa3aHHH, KaK «CHJIbHO OKHCJIeHHaSl nOBepXHOCTb» H HM
nOJ\06Hble.
B HeKOTopblX JIHTepaTypHblX HCTOqHHKaX J\a>Ke nOCJIeJ\HHX JIeT
(1954-1956 rr.) J\JIH K03cpcpHIJ.HeHTa JIyqeHcnycKaTeJIbHOll cnoc06HoCTH
qepHOrO TeJIa B TeXHHqeCKHX eJ\HHHIJ.aX npHBoJ\HTCSI IJ.Hcppa 4,95-4,96;
no HOBeHlllHM J\aHHbIM 3Ta IJ.Hcppa .n.OJI>KHa 6bITb npH3HaHa MeHee TOqHOH,
qeM npHBoJ\HMaH HaMH B Ta6JI. 1 C, = 4,88. COrJIaCHO [20] H B COOT-
BeTCTBHH C peweHHSlMH X reHepaJIbHOll KOHcpepeHIJ.HH no MepaM H BecaM,
COcToSlBwellcH B 1954 r., HaHBepoHTHellwHM 3Ha qeHHeM J\JISI a, CJIe-
,!{yeT npHHHTb a, = 5,6728 (1 ::t 0,0006).10- 12 em'CM- 2 .epaa- 4 .
OpHHHMaSl em = 0,2389 lwll.ceK- 1 , T. e. em = 0,861 KKa.l2' 'iac- l ,
nOJIyqaeM B TeXHHqeCKHX e,!{HHHIJ.aX
C, = 10 8 .5,673.0,861. 10 4 . 1O
12 -= 4,88::::::-; 4,9.



 7. YpaBHeHue TenJlOnpOBo)l.HOCTU «I>YPbe
OpH BbIBo,!{e ypaBHeHHSI TenJIOnpoBo}J.HOCTH J\JIH npOCTOTbJ H3JIO>Ke-
HHSI npe}J.nOJIO>KHM, qTO TeMnepaTypHoe nOJle 3aBHCHT TOJIbKO OT O}J.HOll
Koop}J.HHaTbl x. 003TOMY Bce H30TepMHqeCKHe nOBepxHocrn 3J\ecb-
nJIOCKOCTH, nepneH}J.HKYJIHpHbIe K X-OCH.
OYCTb B HeKOTopblH MOMeHT BpeMeHII or BHYTPH TeJIa BbIJ\eJIeHbI }J.Be
H30TepMHqeCKHe nOBepXHOCTH F H F', HaXOJ\Hlll.HeCSI O}J.Ha OT }J.pyroH
Ha BeCbMa 6JIH3KOM paCCTOSlHHH Ax. BbI.n.eJIHM CHCTeMOll JIHHHll TenJIO-
Boro TOKa Ha nOBepxHoCTSlX F H F ' J\Ba OJ\HHaKOBbIX KycKa nOBepx-
Hocrn S (cpHf. 9) H paccMoTpHM H3MeHeHHe TenJIOBOrO COCTOSlHHSI nJIa-
CTHHKH C nJIOw.aJIhlO OrHOR::IHHH S "If TomnvmoH D. Y, np01wIIIPT(IIIf'P II TPtj'P-
HHe 6eCKOHeqHO M3J10rO npOMe>KYTKa BpeMeHH fI or. OpeJ\nOJIO)KHM elll.e,
'ITO B STOM 06'beMe V MorYT Haxo}J.HTbCSI HCTOqHHKH TenJI8, MOI1\HOCTIo




30


CPU3UKO-ItIaTeMaTu'teCKue OCHOBbt U3MepeHUa TenAOBbtx 8eAU'tUH


KpaTlcoe U3,10:JICeHUe OCHOBHblX nOHJ!TUU U 3aKOHOB 0 TCnAOo6MeHC


31


KOTOpblX B MOMeHT BpeMeHH T, OTHeCeHHYlO K e.L\I-IHl-Il.le 06'beMa, 0603Ha-
'II-lM W.
flpl-lMeHI-lM .L\Ba 3aKOHa: 3aKOH COXpaHeHI-IH 3Heprl-ll-l 1-1 3aKOH <I>ypbe.
KOJll-I'ieCrnO TeOJla, nOCTynalOw.ee B 06'beM V CJleBa 'Iepe3 nOBepXHOCTb F
3a BpeMH fiT, 0603Ha'IHM flQ, a KOJll:l'IeCTBO TenJla, nocTynalOw.ee H3
06'beMa V H YXO.L\Hw.ee HanpaBO 'Iepe3 nOBepXHOCTb F', 0603Ha'IHM fI Q'.
ECJlI-I 3a BpeMH fI T TeMnepaTypa u = u (x, T) 06'beMa V nOBblCI-IJlaCb
Ha flu rpa.L\YCOB, TO KOJlH'IeCTBO TenJla, nOrJlow.eHHoe 3TI-IM 06'beMOM,
paBHO C' I ' V flu; p
60Ta HCTO'IHHKOB
TenJia Bbl30BeT .L\OnOJlHHTeJlbHOe nOCTY-
nJleHHe 3HeprHI-I, paBHoe V. W' O't. B
CHJlY 3aKOHa coxpaHeHHH 3HeprHH KO-
J1H'IeCTBO 3HeprHH, nOCTymJBllIee CJleBa
B 06'beM V, nJilOC KOJlH'IeCTBO 3HeprHH,
Bbl.L\eJleHHOe HCTO'IHHKaMI-I, paBHO KO-
J1I-1'IeCTBY TenJla, npOllIe.L\llIerO 'Iepe3
npaBYIO ero CTOPOHY. nJilOC KOJlH'IeCTBO
TenJia. nor J1ow.eHHoe 06LeMOM. T. e.


II. yCTpeMI-lB b.x K nYJlIO, nOJlY'll:lM:
\ . <t> (x + t.x) - <t> (x) ael>
1m =-
l1x-?O t.x iJx '


a n03TOMY npe.L\bl.L\yw.ee ypaBHeHI-I:': npl-lMeT BII.L\:
iJ ( iJU ) , au
iJx A iJx -: W = q . (h .


(l 31)


t"S
:'MI
I
)---
/)
/


npl-l 60Jlee 06llI.eM npe.L\nOJlOllieHHH, 'ITO nOJle TeMnepaTYP He O.L\HO-
MepHoe, a 3aBHCHT OT Bcex Tpex .L\eKapTOBbiX Koop.L\I-IHaT, paccylli.L\e-
i-IHe, COBepllIeHHO nO.L\06HOe npe.L\bl.L\yw.eMY, npI-lBO.L\HT K ypaBHeHI-lIO:
d ( iJU ) iJ ( au ) iJ ( iJU ) au
iJx A iJx + ay A iJy + di' A az + W = q (h .


(1. 32)


oQ +
 .W.OT = c,Q' + cy. V.Qu.


(*)


Yl3 Hero nOJlY'IHTCH ypaBHeHHe TenJlonpOBO.L\HOCTH <I>ypbe, 1-13 KOTO-
poro 06bl'IHO I-ICXO.L\HT npH Bcex renJlOBblX paCIJeTaX H npH pa3pa-
60TKe MeTO.L\OB onpe.L\eJleHI-IH TenJlOBblX xapaKTepHCTI-lK MaTepHaJlOB:
eCJ1l-I A He 3aBI-ICHT OT TeMnepaTypbl. TO ero MOlliHO BbIHeCTH KaK
OOCTOHHHblH MHO>KHTeJlb 3a 3HaK 'IaCTHOH npOH3BO.L\HOH, H Mbi nOJlY'II-lM:


Ha OCHOBaHHH 3aKOHa <t>ypbe (1. 2)
J:
H onpe.L\eJleHHSI nOHSITHSI y.L\e.iIbHoro
TenJlOBOrO nOTOKa H rpa.L\HeHTa TeM-
el>Hr. 9. K BblBO.ny ypaBHeHHH <I>ypbe. nepaTypbl HMeeM:
e,Q = q,S'01: = -AS (

 )x,O't;


npl-l A, He


A 2 + iJu ]
''\1 u W = q.(h'
3aBHCSlw.eH OT TeMnepaTypbl u.


(1. 33)


o


oQ' = q' ,S'o't = -AS ( iJU ) ,o't.
. iJx x+t.x


3HaKOM 'fi;2u 3.L\eCb 0603Ha'IeH onepaTop JIanJiaca OT CPYHKUI-IH U, KOTO-
pblH .L\J1H .L\eKapTOBbIX Koop.L\I-IHaT onpe.L\eJlHeTCH CPOPMYJlOH
iJ 2 u iJ 2 u iJ 2 u
fi/ U = iJx 2 + ' iJy2 + iJz2 . (1. 34)


flmtoMY paBeHcTBo (*) MOllieT 6blTb npe.L\CTaBJleHO cJle.L\YlOw.HM 06pa-
30M (y'IHTblBaSl, 'ITO V = S .b.x):
- A. S . ( iJ iJtI ) . o't + S . l1x. W . OT = - A. S . ( iJu ) . OT + cy. S . b.x. au.
x iJx X+l1x


B TOM cJJY'Iae, Kor.L\a B TeJle HeT I-ICTO'IHI-IKOB TeOJla, W = 0, ypaB-
HeHHe (1. 33) npl-lMeT 60Jlee npoCToH BII.L\
: = a'v 2u . (1. 35)


TaK KaK U - CPYHKUI-ISI X H 't, a A Bo06w.e 3aBI-ICHT OT U, TO npo-
1-13Be.L\eHHe (A

 ) eCTb CPYHKUHSI x H T; 0603Ha'IHM ero (A :
 ) = <I> (x, T).
113 npe.L\bl.L\yw.ero paBeHCTBa, pa3.L\eJlHB ero Ha S, Ax.o't, nOJJY(IHM
el> (x +
x, 't) - el> (x, 't) +
U
l:1x W =cY'a:t.
Pa3J10>KI-IB pa3HOCTb B J1eBOH 'IaCTI-I 3Toro paBeHcTBa B PS!:.L\ no CTene-
HSiM Ax,
,t, ( + A
 iJ«tI i) 2 «t1 2 1
'i-' X """",)-c1>(x)
 oX .
X+ iJx l - . (Ax) .
+...


BYKBOH a npHHSlTo 0603Ha'IaTb BeJll-I'Il-lHY
A
a=-,
C"f
KOTOPYIO Ha3bIB81OT TeMnepaTyponpOBO.L\HOCTblO MaTepl-laJia. Ee CP1-l31-1-
'IeCKI-IH CMblCJI 6Y.L\eT 06'bHCHeH HI-Illie - B
 2 rJl. 8.
.lI.aHHblH HaMH BbIBO.L\ ypaBHeHHH TenJlonpOBO.L\HOCTH <I>ypbe OTJlH-
'IaeTCSI OT npHBO.L\I-IMOrO B orpoMHoM 60JlbllII-IHCTBe PYKOBO.L\CTB - CM.,
HanpHMep, [2] - B TOM OTHOllIeHHH, 'ITO B HeM Y'Il-lTbiBaeTCSI HenOCTOHH-
crno K03qxlmu.HeHTa TenJlonpOBO.L\HOCTII A: onblTbl nOKa3aJlH, 'ITO K03cpqm-
IIHl'HT A .L\J1H BCl'X M;JH'pltaJJOB B 60JJbUll'rf HJlH Ml'HblIIl'H CTf'nf'HH <!
HnWHT
OT TeMnepaTypbl, 1-1 3TO 06CTOHTeJJbCTBo. KaK Mbl YBH.L\HM .L\aJlbllIe-


(1. 36)




32 tl>u3uKO-ltIaTeltlaTU'IeCKUe OCItOBbl U3lt1CpeHuQ TenAOBblX BeAU'IUH


B fJ1. 6, 8 H .L\p., HMeeT cyw.ecTBeHHeHwee 3Ha'-leHHe .L\J15J npaBHJ1bHOH
pa3pa60TKH MeTO.L\HKH H3MepeHH5J TenJ10Bb1X xapaKTepHCTHK A, a, C
MaTepHaJ10B.
I1HTerpHpoBaHHe ypaBHeHH5J (1. 32), T. e. nOJ1Y'-leHHe ero 06lll.ero
peWeHH5J - 06lll.ero HHTerpaJ1a - B BH.L\e 5JBHOH CPYHKLl.HH 01' KOOP.L\H-
Hal', BpeMeHH H npOH3B0J1bHbIX nOCT05JHHbIX ('-IHCJ10 KOTOpblX MO)!(eT
6blTb He TOJ1bKO KOHe'-lHbIM, HO H 6eCKOHe'-lHO 60J1bWHM), npe.L\CTaBJ15JeT
C060H TPY.L\HYIO MaTeMaTH'-IeCKYIO np06J1eMY, .L\a)!(e eCJ1H C'-IHTaTb A, C II a
nOCT05JHHbIMH; eCJ1H me 01' :noro .L\OnYlll.eHH5J OTKa3a1':bC5J, TO peweHHe
ypaBHeHH5J <I>ypbe nOJ1Y'-laeTC5J B cpopMe, HenpHrO.L\HOH .L\J15J npaKTH'-Ie-
CKHX npHJ10)!(eHHH, 3a HCKJ1IO'-IeHHeM HeKOTopblX '-IaCTHblX CJ1Y'-laeB,
KOTopble H 6Y.L\YT paCCMOTpeHbI .L\8J1bwe H KOTopbIe Bce OTHOC51TC5J K CTa-
Ll.HOHapHOMY TenJ10BOMY p e)!(11 MY . Kor.L\a TeMnepaTypHoe nOJ1e CTaLl.HO-
HapHoe. ECJ1H HX HCKJ1IO'-IHTb, TO CJ1e.L\yeT CKa3aTb, '-11'0 BC5J COBpeMeHHa5J
TeOpH5J TenJ10npOBO.L\HOCTH, Bce TenJ10Bble paC'-IeTbI HeCTaLl.HOHapHblX
TenJ10Bb1X pe)!(HMOB nOCTpoeHbl Ha ypaBHeHHH (1. 33).


,


.


rJlABA 2


YPA.BHEHI1E <l>YPbE
AJUI CTA.L1.110HAPHOrO n0J151 TEMnEPA.TYP TEJ1A.
6E3 I1CT04HI1KOB TEnJ1A.


.D.J15J ,!Toro n0J151
l: = 0, H60 11 - TOJ1bKO CPYHKLl.H5J KoopnHHaT
u = t = t (x, y, Z), n ypaBHeHHe (1. 32), r.L\e CJ1e.L\yeT C'-IHTaTb W = 0,
npllMeT BH.L\


a ( at ) a ( A
 )
 .!!..- ( A i!!... ) = °
ax A ax + ay dy t- oz az .


(2. I)



 t. CTaLl.HOHapHblH TenJIOBOH nOTOK '-Iepe3 nJ10cKYIO CTeHKY


OCTaHOBHMC5J Ha Tex >Ke 0603Ha'-leHH5Jx. KOTOpblMH Mbl n0J1b30Ba-
JIHCb paHee -- B
 I r J1. I. HO paccMoTpHM 60J1ee 06lll.HH CJ1Y'-laH,
a HMeHiIO npeJl.n0J10mHM, lITO I.. - He nOCT05JHHa5J BeJ1H'-IHHa, a CPYHKUH5J
TeMnepaTypbI:


).=f(t).
YpaBlleHile (2. I) npHMer, B CHJ1Y YCJIOBH5J (2.2), BH.L\
:x (A
:
 ) = :x [f (t).
: 1 = 0;


(2, 2)


OTCIO.L\a C JIe.L\yeT, '-11'0


dl
f (I). dx = c 1 ,


r.L\e C 1 - nOCT05JHHaH
[1oCJ1e I1merpHpOBaHlUl Me>K.L\y npe.L\e.naMH t H t \. r.L\e t -- TeMne-
paTypa B CTeHKe Ha paCCI05JHl1H x 01' HallaJ1a KOOpJl.HHaT 0
cpHr. 10).
nOJ1Y'-lHM:


/,
J f(t)dt=C 1 X+C 2 ,


r.L\e C 2 - BTOpa5J nOCT05JHHa5J HHTerpHpOBaHlUI.
[10CT05JHH3H C, HMeeT npOCTOH Q:>H3H'-IeCKllii CMblC.n. TaK KaK OHa paBH3
dl
J... dx -= -J. grdu t = q B CH.ny UCHUHlIUIU .Wh.UlId \1 J). .D.JI\-\ UIIlJC-
3 KOHJlpaTbeB
763




34


cPU3UfCO-ltIaTeMaTU'IeCKUe OCHOBbt U3lt1epeHUU TenA08blX 8eAU'IUH


J'paBHeHue cPYPbe iJAR CTa14UOHapH020 noAR TeltlnepaTyp TeAa


35


):(eJIeHlHl C 2 OTHeCeM nOCJIe):(Hee ypaBHemle K Ha'laJIY KOOp):(l-IHaT x = 0,
TOr):(a t = t 1 H Mbl nOJIY'll1M C 2 = O. CJIe):(OBaTeJIbHO, TeMnepaTypHOe
nOJIe onpe):(eJIHeTCH ypaBHeHlleM


I,
qx -= S f (t) dt.
I
B TOM 'laCTHOM CJIY'lae, Kor):(a A = f (t) CBO):(HTCH K nocToHHHOH,
ypaBHeHHe (2. 3) 06panncfJ B ypaBHeHHe npHMoH JIHHHH:
qx = 'qt] - t). (2.4)


npH'leM 3TO paBeHcTBo onpaB):(blBaeTCfJ
B llmpoKoM HHTepBaJIe TeMnepaTYP -
OT MHHYC 100° C ):(0 npH6JIH3HTeJIbHO'
800° C, a HHor):(a H Bblllle; npH 3TOM

 - 'lHCJIO nOJIO)!(HTeJIbHoe. B 3TOM
cJIYGae HHTerpaJI B npaBOIl 'laCTH (2.3)
6epeTcH 6e3 Tpy):(a, H Mbl nOJIY'laeM
( il -!- i )
qx. = 1..0 (11 - t) 1 +

 .


Pacnpe):(eJIeHHe TeMneparyp B nJIOCKOH CTeHKe H306pa3HTCfJ napa60-
JIOH C BbmYKJIOCTblO, 06pallI.emlOH B CropOHY nOJIO)!(HTeJIbHbIX op):(HHaT
(T. e. +t), KaK npe):(CTaBJIeHO Ha cpl-lr. 10.
HeKoTopble MaTepl-laJIbl (B TOM 'll-lCJIe Bce KpHCTaJIJIbl) 06JIa):(alOT
npOTI-IBOnOJIO)!(HbIM CBOHCTBOM: ):(JIH HHX A y6bIBaeT C B03paCTaHl-leM
TeMnepaTYP H 'laCTO no CJIO)!(HOMY 3aKoHY (nanpHMep, ):(JIH MarHe3H-
TOBblX Kl-lpmI'leij). Tor):(a KpHBaH (2. 3) 6y):(eT BOrHYTaH.
ECJII-I OrpaHH'll-lTbCH He60JIblllHMH HHTepBaJIaMH TeMnepaTYP t I , 1 2 .
TO B 3TI-IX npe):(eJIax B Ka'leCTBe ):(OCTaTO'lHOrO )J.JIH IJ.eJIeH npaKTI-IKI1 npH-
6JII-I)!(eHI-IH MO)!(HO npHHHMaTb ), = const, JI1-I60, Kor):(a Tpe6yeTcH
66JIblllaH TO'lHOCTb,
 = const, npH'leM B03MO)!(Hbl ):(Ba CJIY'laH:
 > 0
1-1
 < O. .
OTHeceM ypaBHeHHe (2.6) K TeMnepaType t 2 , Kor):(a x = X, 1-1 BBe):(eM
TO 3Ha'leHHe 1.., KOTopoe COOTBeTCTByeT TeMnepaType cpe)J.HeH apHcpMe-
TlI'leCKOH Me)Kj\Y t 1 , H 1 2 , 0603Ha'il-lB .


q


<1>Hr. 10. TeMnepaTypHoe o.nHOMep-
Hoe nOJle nJIocKoil CTeHKf!; AB-
Ter"mepaTypHa!'! Kpf!BaH; A - qJYHK-
Uf!H TeMnepaTypbl (B03paCTalOU.laH).


r)J.e


1 _ il+i2
ap- 2 .


(2.3)


Tor):(a ypaBHeHl-le (2.6) npl-lMeT TOT )!(e BI-I):(, (1.1) HJII-I (1. 2), KOTOpblH
cOOTBeTcTByeT npe):(nOJlO)!(eHI-IIO A = const, HO A B HeM HY)!(HO 3aMe-
HI-ITb I.. ap COrJIaCHO (2. 7). 3TI-IM co06pa)!(eHHeM 'IaCTO nOJIb3YlOTCfJ
npH TenJIOBblX paC'leTaX CTaIJ.I-IOHapHblx TenJlOBblX pe)!(HMOB H npH
IIcnbITaHHH MaTepHaJIOB Ha TenJIOnpoBo):(HOCTb (CM. rJI. VI).
llpu.Mep 2. Tpe6yeTcH onpe):(eJIHTb y):(eJIbHblH Ten"'lOBOH nOTOK 'lep
3
[1JIOCKYlO cTeHKY TepMoCTaTa - HllI.I-IKa, H30JIHpOBaHHoro np06KoH,
BHYTpl-l l<OToporo no):():(ep)!(HBaeTCH nOCTOHHHaH TeM
epaTypa. TeMne:
paTypa Ha rOpH'leH nOBepXHOCTI-I H30JIHIJ.HH t 1 = 30 C, Ha XOJIO):(HOH
t 2 = _20° C. TenJIOnpoBo):(HOCTb np06KH 6blJIa onpe)J.eJIeHa H3 cne-
IJ.1I3JIbHbIX OnbITOB. npl1'leM HaH):(eHo:
)'0 = 0,04 KKa/l M- 1 'iac- I cpaa- I ,

 = 4,5.10- 8 cpaa- I . TOJIllI.I-IHa 1-130"'lHIJ.HH 10 CM.
COrJIaCHO npe):(bl):(YIIJ.eH TeoplIH HaXO):(I1M:
i l + t 2 _ 50' A a p = 0,04 (l + 4 5.10- 8 .5) = 0,0436;
2 - ,


-x


nOJIO)!(lIB B HeM x = X, COOTBeT-
l'TBeHHO 'leMY 6y):(eT t = 1 2 , npH):(eM
K HaH):(eHHOMY paHee ypaBHeHl1lO (1. 2).
. MHOrO'lHCJIeHHblMH OnbITaMH YCTa-
HOBJIeHO, 'lTO ):(JIH pH):(a TeXHH'leCKHX
MaTepHaJIOB-):(H3JIeKTpHKoB, nJIOXO npo-
BO):(HllI.HX TenJIO, TenJIOnpoBo):(HOCTb I..
HBJIHeTCH JIHHeHHOH cpYHKIJ.l-leH TeM-
nepaTypbl:
'1..= f (I) = 1..0 (1 +
t), (2.5)


- 0 0436 30 - (- 20) =.208 KKa/l M- 2 'iac- 1 .
q-, 0.1 '


(2. 6)


ECJIH 6bl Mbl He Y'lJIH 3aBHCI-IMOCTb A OT TeMnepaTypbl 1-1 OTHeCJIH I..
u 454
K TeMnepaType 30° C, TO Mbl npeYBeJIH'lHJII-I 6bI TenJIOBOH nOTOK B 436 =
= 1,04 pa3a: olllH6Ka 6blJIa 6bl He3Ha'iI-lTeJIbHoH.
lJpu.Mep 3. CTeHKa H3 Kl-lpnl-l'la TOJIIIJ.HHOH 40 CM HMeeT Ha rOpH'leH
cropoHe TeMnepaTYPY t 1 = 900°, Ha XOJIO):(HOH t 2 = 100°. Onpe):(eJIHM
TenJIOBOH nOTOK, eCJIH H3BecTHo, 'lTO )J.JIH npHMeHeHHoro 3):(eCb Kl-lpnl-l'la
A = 1,0 + 10- 8 . t.
I1MeeM


500
Aap = 1,0 + 1000 = 1,5;


[103TOMY


f..ap = 1..0 (1 +
I ap),


q = 1 5. 900 - 100 = 3000 TeXH. e)J..
, 04
ECJII-I 6bl Mbl npeHe6perJIH ;aBHCHMOCTblO I.. OT t H B
JIH 6bl paC'IeT
no ero 3Ha'leH1-l1O. 1-13MepeHHOMY npH KOMHaTHOH TeMnepaType (KaK
3TO HHor):(a H ):(eJIalOT), T. e. no A = 1,02, TO Mbl nOJIY'II-IJIH 6bl 3aHH-
)!(eHHYlO npOTI-IB )J.eHCTBHTeJIbHOH BeJIH'lHHY y):(eJIbHOrO TenJIOBOrO nOTOKa
1 02
B- 1 ' - , nO'ITH B 1,5 pa3a.

 1
OTClO)J.a BHJI.HO, 'lTO, CMOTpH no 06CTOHT
JIbCTBaM, 3aBHCHMOCTblO I\.
nT t MOiKlIO 1I110r)J.a npene6pe ' IL, a HlIorj],a 3TO DC'1£'T l{ 1IC'110nYCTHMblM
OIllH6KaM.


(2. 7)


"*
.,




36


tl>U3uKO-ltIaTeMaTU'leCKue OCHOBbl U3MepeHur1 TenAOBblX BeAll'lUH


JlpaBHeHlle tl>YPbe aAR CTa/{UOHapHOZO nOA.'l Te'''tlepaTyp Te1a


37


x t, - t
y- 1\- t 2 '


6J1H3Klie H30TepMli4eCKHe nOBepXHOCTI1 F Ii F'. paJ\IiYCbl KOTOpblX paBHbl
r Ii r + dr (qmr. 14). TeMnepaTypIJoe nOJle He 3aBliCliT OT Z Ii n03TOMY
,'1.Jl5I BbI4HCJleHIi51 Q* B03bMeM 3J1eMeHT dF UliJlHH.lI.pH4eCKOH nOBepx-
IJOCTIi F, CTopOHa KOToporo, napaJlJleJlbHa51 OCH OZ. paBHa .lI.JlHHe Z


(2 8)


x


OTKJ10HeHHe pacnpe1l.eJ1eHIiH TeMnepaTYP OT np5lMOH J1HHIiH MO}KHO
HaHTIi nOcpe.ll.CTBOM q,OPMYJ1bl (n04TH 04eBH.lI.Holi):
I +
 1\ + t 2
2
I + P t} + t .
2


Oll1li6Ka B oueHKe paCCT05lHH5I x, Ha KOTOpOM Ha6J1IO.lI.aeTCH 3a.ll.aHna51
TeMnepaTypa t, J\aHa BTOpbIM MHO}KIiTeJ1eM (.lI.P06blO) B npaBOH 4aCTH
(2. 8).



 2. CTaLl.I-IOHapHbIH TenJ10BOH nOTOK lJepe3 L\1-IJ1UH.II.PI-IlJecKYIO cTeHKY
PaccMoTpHM cTaUHoHapHoe TeMnepaTypHoe nOJ1e Tpy6bI, ,aJ1HHa KOTO-
pOH paBHa Z (q;lir. II), paJ\liycbl - BHYTpeHHIiHIi BHewHIiH - R \ Ii R 2
a .lI.liaMeTpbl D 1 Ii D 2 . OpH MaTeMaJli4eCKOM onlicaHli1i TeMnepaTypHoro
nOJ1H Tpy6bI y,a06HO H36paTb L\HJ1IiHJ\pIi4eCKlie KOOp.ll.liHaTbI r, cp. z
(q;lir. 12).
z - ECJlIi YCJlOBIiH OT.lI.a41i TenJ13 no
HapY}KHOH 60KOBOt'I nOBepxHoCTIi


Tpy6bl nOBclOJ\Y O.ll.liHaKOBbI Ii eCJlIi Tpy6a HaCTOJ1bKO ,aJ1IiHHa5l, 4TO
BJlli5lHHeM TOpUOB Ha ee TeMnepaTypHoe nOJ1e MO}KHO npeHe6pe4b, TO
TeMnepaTypHoe nOJle 6Y.lI.eT 3aBliceTb TOJIbKO OT O.ll.Holi Koop,aHHaTbI r -
paCCT05lHliH KaKOH-J11i60 T04I<H M TPy6bJ OT OCIi L\1iJ1HH,apa Oz. KOTOpylO
MbI npliMeM 3a OCb UlfJIHH,apIi4eCKHX KOOp.ll.HHaT (q:mr. 13); 3.l1.eCb npe,a-
CTaBJ1eHO nonepe4Hoe ce4eHlie Tpy6b1, npoxoJ\5Iw.ee 4epe3 T04KY M.
Cne.ll.OBaTeJlbHO, t - CPYHKL\HH TOJIbKO r, a 1i30TepMH4ecKlie nOBepx-
HOCTIi - L\1iJ1HH,aPbl. HaH.lI.eM Bblpa}KeHHe ,aJ151 nOJ1HOrO TenJ10BOrO no-
TOKa Q*, npoxo,a5JllJ.ero 4epe3 Tpy6y B ee pa.ll.HaJ1bHOM HanpaBJleHli1i
OT BHYTpeqHeH nOBepxHocTIi K HapY}KHOiL OH OJ\IiH Ii TOT }Ke J\JlH J11060ii
WIOT£'pMJI'I£'CKOJI noo('p,,"onJl F, n3 KOTOpOJI J1£'H<IIT TO'IJ<3 .'1 (r, cp, Z),
TaK KaK TenJ10BOH nOTOK CTaLl.HOHapHbIH. PaCCMOTpHM .lI.Be 6eCKOHe4HO


cDHL 11. OTceK UHJIHHJ1pa (Tpy6bl)
.nJlHHOH Z.


UH.lIliH.lI.pa «(jmr. 15); nJ1ow.a,ab 3Toro 3J1eMeHTa dF = Z. r. dcp. OH npo-
Hli3bIBaeTC5I TenJ10BbIM nOTOKOM, paBHbIM dQ*; nOJ1HbIH TenJ10BOH nOTOK
Q';' = SF dQ*, OplfMeHIiM 3aKOH <I>ypbe K 3J1eMeHTapHOMY TenJ10-
BOMY nOTOKY dQ*; HanpaBJ1eIme
HOpMaJ11i K nOBepXHOCTIi F B T04Ke
M COBnaJ\aeT C pa.ll.IiYCOM; 3TO H


fl,
<!JHr. 13. nonepe4Hoe ce4e-
HHe Tpy6b1.


1\1


z


y


:£


<t>HL 12. CHCTeMa l1,HJIHHJ1PHlJCCKHX
KOOp.n HHaT .


o


<!JHL 15. Bbl.neJleHHe 3J1eMeHTa dF
H301epIVIIIlJeCKOH nOBepxHocTH B UH
JllIUJ1pe HJJH Tpy6e.


cDllL 14. M30TepMH4ecKHe no.
BepxHocTH B UHJIHHJ1pe F H F'.


o


<!JilL 16. 3JIeMeHTapHblii Ten-
JlOIJOH nOTOK dQ lJepe3 3J1e-
MeHT nOlJepXHOCTH IlHJJHHJ].pa.


6y,aeT nanpaB.lIeIIlie y,aeJ1bHOrO renJlOBOrO nOTOK3 B M,
OCHOBaHli1i (I. 3), 3aMeHliB n 4epe3 r, nOJIY4liM
d
q = -A. grad t = -A'lif'


Ii }Iii




38


cjJU3U1W-MaTeMaTU'IeCKUe OCHOBbl U3MepeHUil Ten/lOBbIX Be,ZU'lUli


YpaBHeHue CPYPbe OAR. CTal{UOHapHOZO nOAR. TeMnepaTyp TeAa


39


nOTOK 'Iepe3 nOBepXHOCTb dF 6Y.L\eT paBeH (qmr. 16):
dQ* = q.dF = - 'A..!!!....Z .r.d([)'
dr . ,
nOJ1HblH nOTOK Q* nOJ1Y'IHM, nepe6paB Bce 3J1eMeHTbl dF, T. e. H3MeHHH m
OT 0 .L\O 2'1t: T


Y.L\eJ1bHble TenJ10BbIe nOTOKH Ha HapY)!(HOfI H BHYTpeHHeH nOBepx-
HOCTHX TPy6bl pa3J1H'IHbI BCJ1e.L\CTBHe KPHBH3Hbi H30TepMH'IeCKHX nOBepx-
HOCTei!:


TenJ10BOH nOTOK 'Iepe3 IJ.HJ1HH.L\pH'IecKYIO CTeHKY npHHHTO Ha3bIBaTb pac-
XO.aHJJJ.liMCH (<j:mr. 16).

 3. CTauHoHapHblif TenJ10BOH nOTOK lJepe3 rnapoBytO CTeHKY
COBeprneHHo aHaJ10rHIJHbIM 06pa30M BbIBOlI.HTCH ypaBHeHHH .L\J1SI
nepe.L\a'IH TenJ1a 'Iepe3 TBep.L\YIO CTeHKY, OrpaHH'IeHHYIO .L\BYMH KOHIJ.eH-
TpH'IeCKHMH rnapoBblMH nOBepxHOCTHl\HI, pa.L\Hycbl H COOTBeTCTBeHHO .L\Ha-
MeTpbl KOTOpbIX paBHbl RI' R 2 H DI' D 2 . .lI.J1H nOJilloro TenJ10BOrO nOTOKa,
npoHH3bIBalOlll.erO 06e IloBepxHocTH, nOJ1Y'IHM lblpa)!(eHHe
Q* = - 41t'Ar 2 :
 . (2. 14)



B ypaBHeHHH (2. 14) A - Bo06III.e
CPYHKIJ.HH TeMnepaTypbI. TeMnepa-
TypHoe nOJ1e 3aBHCHT TOJ1bKO 01'
pa.L\Hyca-BeKTopa r TO'IKH M
(cpHr. 17), eCJIH npe.L\Il0J10)!(HTb, 'ITO
YCJ10BHH TenJ100T.L\a'IH Ha Hapy)!(-
HOI
I rnapoBoH nOBepxHocTH nOBclO.L\Y
OLI.liHaKOBbl, BCJ1eJI.CTBHe 'Iero Ii TeM-
nepaTypbI Bcex ee TO'IeK OJI.HH H Te y/
}Ke H paBHbI f 2 . To )!(e caMoe OTHO-
CHTCH H K BHYTpeHHeH wapoBof\
nOBepxHocTH, TeMnepaTYPY KOTO-
poi'! 0603Ha'IHM fl'
B rnapOBOH CTeHKe TenJ10BOH nOTOK-TP.K)!(e P<'CXOJI.Hlll.liHCH, KaK 31'0
HMeJIO MeCTO .L\JIH UHJ1HHJI.pWIecKoi'! CTeHlm; TeMnepaTypHoe nOJ1e-
O.L\HOMepHoe BO Bcex Tpex 3JI.eCb paCCMaTpliBaeMbIX npoCTeiiwHX CJlY-
'IaHX - IlJ10CK.oii, UHJ1HHJI.pH'IeCKOii, rnap03011 CTeHKH.
YpaBHeHHe TeMnepaTypHoro nOJ1H nOJ1YIIliTCH nYTeM HHTerpHpOBaHHH
JI.ml)(pepeHIJ.HaJ1bHoro ypaBHeHHH (2. 14) B npeLI.eJ1ax 01' f .L\O f I :


Q'
q B1lymp = nD) ;


Q'
qllQP = nD 2 .


'1'=2"

 . dt
Q* = -Z 'A.r. - d

dr .'
'I'



a OTCIO.L\a CJIeJI.yeT


Q* dt

 = -21t'Ar-
Z dr


(2. 9)


3.aeCb A, KaK H B npe.L\bl.L\Ylll.eM r J1Y'Iae nJ10CKOI
1 CTeHKH, Bo06lll.e
3aBHCHT 01' TeMnepaTypbl f - CM. (2. 2). 1-'13 npe.L\bl.L\Ylll.ero ypaBHeHHH
nOJ1Y'IHM:


d( ;J


Q* I
'z' 27t = 'Adf


r


R;


OTKy.aa


Q* i
- 2nZ . In ( ;, ) = S f (t) df + C I ,
i.


r.ae C) - nOC10HHHaH.
nOJ1ara
 3.L\eCb r = R l' 'IeMY nYCTb rOOTBeTCTByeT TeMnepaTVpa Ha
BHYTpeHHeH nOBepXHOCTl1 f = 11. YBH.aHM. 'ITO C I = O. J
I1TaK, paCnpe.L\eJ1eHHe TeMnepaTYP B IJ.liJ1l1H.L\pH'IeCKOii CTeHKe .L\af-IO
ypaBHeHHeM
J' [It)dt
 ,
'z ln(
,) 1
I
I


(2. 13)


J


<Df!!'. 17. CHCTeMa ccpepf!'IeCKf!X KOOp-

 -.
J].f!HaT; OM = r - paJ].f!yc-neKTop TO'!-
Kf! M lllapoBoro CJlOH.


I,
S f (f) df = Q* ( -2... - -2...\ ; .
4n Rt r
i
Dpe.L\noJ10)!(liB, 'ITO ). He 3aBHCliT 01' TeMnepaTypbI, H OTHOCH ypaBHeHHe
(2. 15) K r = R2' KOr.L\a f = f 2 , nOJlY'IaeM Bblpa)!(eHlie .L\J1H nOJ1HOrO
TenJ10BOrO nOTOKa 'Iepe3 rnapoBYIO cTeIIKY:
Q* = 2n.A.(t] - t 2 ) (2. 16)
I I
Dl - D



(2. 10)


rJ1.



)., = f (f)


B TOM CJ1Y'Iae, KOr.L\a MO)!(HO npeHe6pe'Ib 3aBliCHMOCTblO
ncpaTypbl, cpopMYJ1a npliHliMaeT npoCToii BH.L\:
Q* ( r )
1 1 -1=-ln -
'2nZ.A R,'


'A 01' TeM.


(2. 11)


0603HaIIHB 1 2 TeMnepaTYPY
nOJ1Y'IHM J1.JlH nOTepH TeriJ1a C
e.L\liHHIJ.Y BpeMeHH Bblpa)!(eHHe
'-- Q*
Q--z=


fIpH A = const.


Ha HapY)!(HOH nOBepXHOCTH Tpy6bI,
norOHHoii eJ1.HHHUbl J1.J1HHbl TPy6bl 3a
27tA
D . (t 1 - f 2)
In ( D: ) .


(2 12)


.


(2. 15)




40


C/JU3UKo-..
!aTeJlWTU'leCKUe OCHOBbl U3MepeHU!i TenAOBblX ReAU'lllH


JlpaBHeHue C/JYPbe aAR CTat{UOHapHOZO nOAR Te}.mepaTyp Te1a


41



 4. 0606meHI1e npe}l.bl)l.yml1X (jJOPMYJl (I. 2), (2. 12), (2. 16)
3TH cpO pM y.1Jb1 YJJ.06Hbl no CBoeH npOCTOTe, H nO:H0:\1Y OHH HaX0JJ.51T
WHpOKoe npHMeHellHe lIa npaKTHKe; OHH Bbl BeJJ.eIl bl B npe)J,nOJlOmeHHH,
lJTO A He 3aBHCHT OT TeMnepaTypbl; O)J,HaKO II B 06meM CJlVlJae, Kor)J,a
A - cpYHKLl.H5I TeMnepaTypbl, paClJeTHble C
OPMYJlbl cOXpaII5IIOT TY me
qJOPMY, eCJlH TOJlbKO B HHX Ha Meno A nO)l.ClaBHTL cpe)J,Hee ero 3Ha-
lJeHHe A cn' OOKa)l(eM, KaK 31'0 3Ha4eHHe CJleJJ.yeT HaXO)J,HTb.
OYCTb onblTHblM H.1JH TeopeTH4eCKHM nYTf'M Hail)J,eHa 3aBI1CHMOCTb ).
01' TeMnepaTypbl )l.Jl5I 1'01'0 MaTepHaJla, H3 KOToporo H3rOTOBJleHa pac-
CMaTpHBaeMa51 neHKa, T. e. f (I) B (2. 2) - H3BeCTHa51 cjJYHKLl.H5I. 3aMemiM
I,
BO Bcex (
OpMYJlaX, KY.'I.a OH BXO)J,HT, HHTerpaJl .f f (t) dl npoH3Be)J,e-
I
HHeM H3 pa3HocTH npe)J,eJlOB Ha cpe)J,Hee 3Ha4eHHe nOll,HHl'erpaJlbHOH
(I}YHKLl.HH COrJlaCHO TeopeMe 0 cpe)J,HeM 3HalJeHHH I1IITerpaJla; Tor)J,a


TeflJlOBOH nOTOK, npoxo)J,51Il1,Hi\ OT FI K F2' 6Y)J,eT )J,<'H q:opMYJlaMH:
S
I Acp (t 1 - t 2) X )J,Jl5I nJIOCKOfO CJl051
: ,,,(t, - t,) 2';; . ""ftM",p"qeCKOrO CftOM
Q I In


 D,
I Acp U J - 1 2 )
:
 " wapOBoro CJl051
D, D 2


opOCaeTC5I B rJla3a 3HaJlOnHI Me)I{;J,Y HHMI1: TenJlOBOii nOTOK BblpameH
B BH)J,e npOl13Be)J,eHH5I Tpex MHOmHTeJlelI, nepBblH H3 KOTOpblX - TenJlO-
npoBo;J,HOCTb, 1'. e. CBOIICTBO Beme-
CTBa TeJla, Bl'opOH-TeMnepaTypHblH
Hanop, TpeTHH - IIMeeT pa3Mep-
HOCTb )J,JlHHbl, onpe)J,eJl5leTC5I reOl\1eT-
pHlJeCKHMH CBoHcTBaMH H30TepMH-
qeCKHX nOBepxHOCTeH H 3aBHCHl' 01'
I1X cjJOpMbl. EMY r1pHcBOeHO Ha3Ba-
HHE' - K03qx)JHLl.HeHT cpOpMbl cTaUHo-
HapHoro nOTOKa.
31'0 CBOHCTBO 0606maeTc5I Ha .1JIO-
60e cl'aUHoHapHoe nOJle TeMnep3TYP,
I-Ia cpHr. 18 nOKa3aHbi )J,Ba KycKa
AB H CD H30TepMHlJeCKHX nOBepx-
HOCTeil FI H F 2 C TeMnepaTypaMH II
H 1 2 , 3TH nOBepxHOCTH Bbl)J,eJleHbl H3 CHneMbl H30TepMHlJeCKHX no-
BepXHOCTeil BHYTPH KaKOrO-JlH60 TBep)J,oro TeJla, orpalIH4eHlIOfO
nOBepxHocTblO S. J1HHHH TOKa 01' nOBepXHocTH F I K F 2 HopMa.1JbHbl
K H30TepMaM, n03TOMY YTe4KH TenJia B 60KOBble CTOpOHbl AC H
BD HCK.1JlOlJeHbl. OpH 3THX YCJlOBH5IX TenJlOBOH nOTOK Q*, npo-
XO.'l.51mHH 01' FI K F 2 B HanpaBJleHHH na)J,eHH5I TeMnepaTYP (II > 1 2 ),
Bblpa3HTC5I KaK


I,
.rt(t)dl = (/ 1 - t)f(B),
I
l')J,e II
 0
 I, a
e)J,OBaTe.'1bHO, f (
) - BeJlJ1llI1iI3 IW3cjJcpHUHeHTa
TenJlOnpOBO)J,HOCTH )J,Jl51 TeMnepaTypbl, Jle)l(3ILl.eH ME'mJJ.Y i l H I; eCJlII
1 = 1 2 . 0603HaLJHM era A cp; aHa Bhl4HCJlHTC5I no qJOpMYJle
I,
J f (t)dt
I.
t l - 1 2


f(
) =, Acp =


(2 17)


ECJlH f (I) - JlHHeHHa51 qIYHKUH5! [eM. 2. 5) J. 10 H3 noc.'1eJ].lIeH tPop-
MYJlhl CJleJ].yeT, lJTO


I,Cp=


I,
"0 S (I +
t) dt
I. = 1..0 ( 1 +
. r d 2 - 12 ) -= "aI"
t 1 - t 2


t -'-t u
T. e. Acp HymHo OTIIeCTH K TeMnepaType
 = I Jp - CpeJ].HeH
apIlcpMeTl-lLJeCKOii MemJ].y II H 1 2 . 0.!"\HaKO 31'0 6YJ].eT 3aKOHHO TOJlbKO B
npeJ]:nOJlOmeHHH
 = const (He 3aBHCHT 01' TeMnepaTYPhl), 41'0 HHOfJ].a
Ha npaKTHKe H He HMeeT Mena.
BbIBeJ].eHHhle 3J].eCb CpOpMy.1Jbl H CJ].e.1JaHHhle 3aMelJaHH5I HMelOT cyme-
CTBeJIHoe 3Ha 1 leHI1e J].Jl5I TenJlOBhlX p3C4eTOB 11 JJ.Jl5I npaBHJlbHOrO npHMe-
HeHH5I MeTOJ].OB H3MepeHH5I, J].Jl5I ycneulHoro nonpoeHIHI H 31{CnJlyaTa-
Ll.HH npHGopoB, KaK 31'0 6YJ].eT nOKa3aHO B rJl. 6.

 5. l(03(jJ(jJI1L1.l1eHT (jJOpMbl CTau,110HapHOro nOTOKa
C06epeM BOE'.'I.HHO (IJOpMy.1Jbl, nOJlYlJeHHhle J].Jl5I Tpex nponeHwHx
'P 0 p\1 C.r10R 1\13TepIla.'13, Orpalllf'lE'IIIJOro '{oYI\H1 1I10TrpMII'I(,CKIIMJI nonrpx-
HOCTRMH FIH F2' KOTOphlM cooTBeTcTBYlOTTeMnepaTyphl tlH 1 2 (cpHr. 16);


.


fz


q:ML 18. K onpeJ1eJleHMIO nOHHTHH
«K03cpCPMuMeuT qJ0PMbl»; CTp
KH

YKa3bIBalOT HanpaBJIeUHe JIHHHM TOKa.


Q';' = Acp (t I -./ 2 ) L *.


(2. 18)


L * H eCTb K03qJcjJHLl.HeHT CIJOpMbl cTaLl.HOHapHoro nOTOKa; ero BbllJHCJle-
HHe B 60Jlee CJlOmHblX CJlY4a5lX, HemeJ1H nponeilwHe, HaMI1 paccMoTpeH-
Hble, 51BJl5IeTC5I J].OBOJlbHO cJlomHol1 MaTeMaTHlJeCKuH 3aJ].alJeil; OJ].HaKO L *
TaKme MomeT GblTb nOJlVlJeH H nOJl)'3KcnepHMeHTaJlbHbIM nYTeM. OH
HaXOJ].HT npHMeHeHHe B TenJlOBblX pac4eTax H B HeKoTopblX MeTOJ].ax
onpeJ].e.rIeJIH5I K03ltcjJHLl.lleHTa TenJlOnpoBoJ].HOCTH A npOHTeJlbHhlX H Ten-
JlOH30Jl5lUHOHHhlX M3TepHaJlOB.
flpu.Mep 4. Onpe)l.eJlHM MOIlJ,HOCTb 3J1eKTpHlJeCKOrO HarpeBaTeJl5l,
3aJlOmeHHoro BHYTPb meJle3HoII Tpy6hl J].JlHHoll 3 M, eCJlH Ha TPy6y MOH-
Tllponalla TCnJIOOafl 1130JlflIlIIll II] fTI'I<.'1STililOfi naTl,I, Tn.'1I1\I1Hnij 1()()
111,
npUlJeM Ha nOBepxHocTH Tpy6hl nOJ\J].epmHBaeTC5I TeMnepaTypa 200 0 C,




42


C/JU3UKO-.MaTe.MaTUfteCKue OCHOBbl U3ltlepeHUa TenAOBblX BeAUftUH


a Ha HapymHoi1 nOBepXHOCTH H30JISllI.HH TeMnepaTypa 40° C. HapymHblll
,AHaMeTp me.1Je3HOll Tpy6bI (OH me BHYTpeHHHll ,AHaMeTp H30JlSlLl.HH)
paBeH 50 MM. TenJIOnpOBO,AHOCTb CTeKJISlHHOll BaTbi 3aMeTHO 3aBHCHT
OT TeMnepaTypbI, H 3TO HymHo Y4HTbIBaTb; ,AJISI TOll BaTbI, KOTopaSl 3,AeCb
npHMeHeHa,


A = 0,042 (1 + 2,6.10- 8 t).


COrJIaCHO o6meH TeopHH 3,AeCb 6Y,AeT
Acp = A ap = 0,042 (1 + 2,6.10- 3 .


200 + 40 ) = ° 05 5 '
2 "
K03c1Jc1J H Ll.HeHT c1JOPMbl CTaLl.HOHapHoro nOTOKa L * = 21t: so = 11,7;
In 50
Q* = 0,055. (200-40) . 11,7 = 103 K1W/l t.lQC- I =


TenJIOBOll nOTOK
= 0,12 Kern.
npeHe6peraSl
25-30 % .


3aBHCHMOCTbIO A


OT


t, C,AeJIaeM ollm6KY nopSl,AKa



 6. CTaLl.lfOHapHblH TenJIOBOH nOTOK lIepe3 CJImKHyID nJIOcKYIO CTeHKY.
TenJIOBOe conpOTHBJIeHHe
YpaBHeHHIO nepe,Aa4H CTaLl.HOHapHoro TenJIOBOrp nOTOKa 4epe3 nJIO-
CKYIO cTeHKY (I. 2) npH,AalOT cj:0PMY, n03BOJISlIOllI.YlO HarJISI,AHO HCTOJI-
KOBaTb 3TOT npou.ecc H npoBecTH aHaJIOrHIO Mem,AY TenJIOBblM nOTOKOM
If 3JIeKTpH4ecKHM TOKOM, XOTSI H 4HCTO c1JopMaJIbHYlO, HO Y,A06HYIO ,AJISI
npaKTH4ecKHx paC4eTOB H BOllJe,AllJYIO BO Bce06mee ynoTpe6JIeHHe. Ha-
nHllJeM ypaBHeHHe (1. 2) B BH,Ae
q= t I P i 2 (2. 19)
r,Ae 6YKBOH P 0603Ha4eHa ,Ap06b:
o
P=T'


(2. 20)


npH4eM
 - TOJIllI.HHa CTeHKH (paHbllJe Mbl nHCaJIH X). cI>opMYJIa (2. 19)
COBepllJeHHO aHaJlOrH4Ha 3aKoHY OMa - c1JopMYJIe
. VI - V 2 .
1= R '
B KOTOpOll U 1 H U 2 - nOTeHLl.HaJlbl B ,ABYX T04Kax O,AHopO)l.HOrO npOBO,A-
HHKa, 3J1eKTpH4eCKoe conpOTHBJIeHHe KOToporo Mem,AY HHMH paBHO R.
TenJIOBaSl BeJIH4HHa P nO,A06.HO R npOnOpLl.HOHaJIbHa ,AJIHHe npOBO,AHHKa
I
TenJIa, T. e. TOJlmHHe
 cTeHKH, H npOnOpLl.HOHaJIbHa T - Ten.1JOBoMY
conpOTHBJIeHHIO BemeCTBa CTeHKH.
PaCCMOTpnM Tenepb CJIOIKHYIO nJIOcKYIO CTeHKY (HJIH CJlOmHblH CJIOll) ,
C()CT()R1L1.YIO In n nJIOTIIO nplfJI('rmollUlx J\P) r K J\pyry CTeHOK pa3IIoii
TC>,IIllI.HHbl, fl3 MaTepllaJJOB C pa3HbiMU K03cpcpHl-!.HeHTaMH renJIonpo-


,



PQBHeHUe C/JYPbe
AH cTaquoHapHozo nOAH Te.MnepaTYP TeAa


43


BO,AHOCTH. 0603Ha4HM 0/ TOJllll.HHY H A, TenJIOnpOBO,AHOCTb i-Toro
CJ1 OSI , P; ero T
nJlOBOe conpOTHBJIeHHe. TaK KaK KacaHHe ,ABYX coce,A-
HHX CJ10eB - l-Toro H (i -t I )-ro . a6COJIIOTHO nJIOTHOe, a TenJIOBbIe
nOTOKll Ha rpalmLl.e HX pa3,AeJ1a O,AHHaK?Bbl, TO HMeeM:
A ( dt ) / /_ A .t/+ ( I :1t ) J
I. dx i - .+, dx HI'
3,AeCb t" t/ +, - TeMnepaTypa Ha rpaHHu.e i-Toro H (i + I )-ro CJ10Sl.
B CHJlY (2. 21) Tel\mepaTypH
SI KpHBaSl npe,ACTaBllTC5I J10MaHOH, KaK
3TO nOKa3aHO Ha c1JHr. 19. B ,AaJIb-
Hei1llJHx HallJHX paccYiK,AeHHSlX 6y-

eM npeHe6peraTb 3aBllCHMOCTbIO
), OT TeMnepaTypbl; n03TOMY JIH-
HHSI Ha c1JtJr. 19 COCTaBJleHa H3
npSlMo.1JllHellHblx oTpe3KoB. B pa-
BeHCTBe
t/- t'+ 1
q= I HJIHqP I =t , -tt+-lo
Pi


(2. 21)


r,Ae


-L


i.


t n ..


P _ 0;
I-T;'


(2. 22)


npl111a,AHM 3Hat.IKY i pSl,A u.eJlbiX
3Ha4eHlfM OT I ,AO n; nOJlY4HM pSl,A
paBeHcTB:


<1>Hr 19. nepeJ1alJa TenJIa Qepe3 CJIO}K.
HYIO nJIOCKYIO cTeHKY (<<CJIO}KHbIH CJIOH»):
ti. t 2 . . ii' in + 1 - TeMnepaTypHaH
KpUBaH.


t l -t 2 =qP h
t 2 - t 3 = q P 2,


t n - J - t n = qPn-h
in - t nH = qPn.
CJ10}I{l1B HX H 3aMeHHB ,AJISI e,AHH006pa3HSI 0603Ha4eHHH t n +, 4epe3
'2, nOJIY[IHM:


,=n
lJ- t 2=P!P"
/-1


0603Ha4HM CHMBOJIOM P 8 CYMMY BCeX TenJIOBblX COnpOTHBJleHHH, «npeO,AO-
JIeBaeMblX» TenJ10Bb1M nOTOKOM npH ero Te4eHHH OT ropSl4eH BHYTpeHHei'l
I10BepXHOCTll (CJ1eBa) K XOJIO,AHOll HapymHoH (cnpaBa):
Ps =
 PI' (2.23)
Torlla Y,AeJIbHbIH nOTOK TenJIa 4epe3 CJ10mHYIO, cocTaBHYIO cTeHKY npe,A-
cniBHTcSI npoCToH c1JOPMYJIOH Toro me BH,Aa, K3K (2. 19):
'.-'. 2
q=p;-' ( .24)




44


(/JU3UKO-MaTeMaTUJ{eCKue OCHOBbl 1l3.lIepeHUii Ten,1OBblX Be/lUJ{UH


P 9 - 3KBHBa.1JeHTHOe Ten.nOBOe COIl_pOTlm.1JeHHe, T. e. Ten.nOBOe conpo-
THB.neHHe TaKOrO (PHKTHBHOrO Bo06pamaeMOrO npOCTOrO O.ll.HOpO.ll.HOrO
CJlOR, TO.nw.IfHa KOTOpOrO B =

i - CYMMe TO.nW.HH C.nOeB, COCTaB-
.n 51 IOW.H X .lI.aHHblU pea.n bHblH C.nOH.
AHa.nOrH4HO ). BBO.ll.RT TaKiKe VC.nOBHblli «3KBHBa.1JeHTHbIii K03(jJ(PH-
UHeHT Ten.nOnpOUO;(HOCTH» ).
; nIIWYT


q = 1..9' II , 1 2 .
o


(2. 25)


OTCIO;(a H H3 npe)l.bl.ll.YU
HX q-OP:\1Y.n BblTeKaeT, liTO
A=

9 \'--'
'

AI


(2. 26)


r.ll.e


o=
ai'


::\.lI..lI.HTHBHOCTb - HaH60.1Jee uemroe B npaKTH4eCKOM OHroweIllllt
CBOHCTBO Ten.nOBbIX conpOTHB.neHHH, ynpou
alOIlI.ee paC4eTbI.


* *


*


cDopMy.ne (2. 18) .lI..nR K03q)(jJl1UHeIHa qJOpMbl cTauHoHapnoro nOTOKa
HHor)J.a npH)J.alOT BH.lI., HeCIWJlbKO nOXOIKUH Ha (2. 19), BBO;],R YC.nOBHYIO
Be.nH4HHY


I
R = AL * ,
KOTOpOH, KaK 11 P, npHcBaHBalOT Ha3BaHHe «Ten.nOBoe conpOTlm.neHHe».
Tor.ll.a ypaBHeHl1e (2. 18) npuHHMaeT BH.lI.:
Q '!' = 1 1 - 1 2
R .
Pa:MepHOCTb Be.nH l IHHbl R OT.n114aeTCR OT pa3MepIlOCTH P, TaK KaK
B .neBOI1 4aCTI1
oc.ne.ll.Her<: ypaBHeHI1R CTOliT no.nHblrl Ten.nOBOrl nOTO/{ Q'\
a He Y.lI.e.nbHbllI Ten.nOBOH nOTOK q, KaK B ypaBHeHHII (2. 19).
B HeKoTopblX c.nY4aRx Y.lI.aeTCR HaUTH aHa.nHTlIl/eCKoe Bblpa.iKellHe
)J..nR R, 4aw.e Bcero npI16.'lHmeHHoe. HanpHMep, ec.n11 nOBepXHOCTb FI _
wap C .lI.l1aMeTpOM D, a F 2 - n.nOCKOCTb, TO


I ( D ) I
R ::::: 21tD 1 + 4Z T


np:t YCJlOBl1l1, 4TO wap pacno.nOlKeH 6.1J113KO K n.nOCI<OCTH. Hero ueHTp
B paCCTOHHHll Z OT Hee.

 7. TenJlonepe)l.a4a OT oJl,Hoii CpeJl,bl K Jl,pyroii 'lepe3 nJlocKYIO cTeHKy
PaccMoTpHM BaiKHblH npaKT114eCKHI
i c.nY4aii cTauHoHapHoro ren.no-
Boro pemHMa, npe.ll.CTaB.neHHblH CXeMaTI14eCKH Ha cjJllr. 20, KOr.ll.a TBep)J.aR
(npocT3R 11.'111 C."I01KIHHI) ('T(,I1K1J paJ1('.THl(,T 10(' CP(''J,LI, /1\I1)J.Klle I1JIII I dJU
06pa3Hble, IH II. TeMnepaTypbl KOTOpblX CYTb 6' H 6". Ha nOBepxHocTHX


JlpaBHeH.Ue (/JYPbe a.1fJ. CTa1luOHapHOZO nO/lJl. TeMnepaTYP TeAa


45


A B H CD, OT.lI.eJl5l1ow.I1X CTeHKY OT Cpe.ll.bl I H cpe)J.bl II, Ten.n006MeH
cOBepwaeTcR KOHBeKTHBHO-KOH.lI.YKTHBHbIM. nYTeM. 0603Ha4HM ex' K03cjJ-
IpHUlfeHT Ten.nOOT.lI.a4H Mem;1Y Cpe.ll.OH I H nOBepxHocTblO AB, ex"-
Me)l(:
Y Cpe.ll.OH II H nOBepxHocTblO CD.. TaK KaK Ten.nOBOH pemllM CTa-
UIiOHapHblrl, TO 01lHH H TOT me Y.lI.e.nbHblH Ten.nOBOH nOTOK q npOXO.ll.llT
l\epe3 Bce 4aCTH CHCTeMbI. nO.nb3YRCb 3aKOHOM HblOTOHa (I. 14) H BblBe-
J],eHhbIMH B
 6 ypaBHeHHRMII, no.nY4HM:
L' I
u -l]=q.--;;;-;


t I - t 2 = q' p 3;
tJ" I
t 2 -u = q'7'






t


:r


(J'


-.!L



I


n


<!JHr. 20. K onpeJ1eoleHI1IO nOHHTHH K03<pqm1lMeHTa TenJIOnepeJ1a4M k.
C.nomHB HX HaH.lI.eM:
8'-
"=q.(-b-


"




P 9 ) .


(2 27)


3TO ypaBlleHHe npHHRTO nHC3Tb B cjJopMe
q = k(6' -!J");


(2. 28)


k - Be.ni1'-IHHa, xapaKTepH3YIOIlI.aR HHTeIlCHBHOCTb Ten.noo6MeHa Mem.ll.Y
cpen.aMH. OT.lI.e.neHHbIMH TBepn.oii CTeHKoii, Ha3bIBaeTCR K03cjJcjJHUHeHTOM
Ten.nonepe.ll.a4H [II. OH aHa.norH4eH K03cjJqmuHeHTY Ten.nOOT.lI.a411 H
I1MeeT TY >Ke pa3MepHOCTb; B TeXHll4eCKlIX e.ll.llHHUaX
r k I = KKO/l M- 2 40C- I cpaa- 1 .
I
Be.nH4HHY - MomHO TaKiKe VC.nOBHO Ha3bIBaTb "nOBepXHOCTHbIM"
a .
Ten.nOBbIM COnpOTlm.neHHeM: 0603Ha411M
P n =
, 1-' n = .-!., l
 n =
 . (:l. 2Y)
a a a




46


c[)U3UKO-MaTeMaTU'IeCKue OCHOBbl U3MepeHUa TenAOBblX BeAU'IUH


J'paBHeHue c[)ypbe aAJl cTalluoHapHozo nOAlI TeMnepaTYP TeAa


47


Tor)l.a <POPMYJlY (2. 27) MO)l{HO npeJ\cTaBHTb B BH.lI.e
6'-6"
q=-
P CYM '


(2. 30)


BaTbC5I TeMnepaTypa t' = 18° C, 4T06bI 3KcnepHMeHTaTopbI He CTpaJ\aJlH
OT XOJl0.ll.a (<pHr. 22). ·
BeJlH4HHY ex' MO)l{HO OIJ.eHHTb IJ.H<ppOH 8, ex" -::::: 200; TeMnepaTypa
BOJ\bI t" = 4° C. HaXO.ll.HM TenJlOBOe conpOTHBJleHHe CJI05I H30JI
UHH PI'
TenJIOBOe conpOTHBJIeHHe CTaJIH P 2, C4HTa5I TOJllll.HHY CTaJIbHOH CTeHKH
0,1 I 40
8
 = 10 eM, OIJ.eHHM B P2 = 40 = 400 ' npHHHMa5I A 2 = .
no (2. 30) H (2. 31) nOJIY4HM
Q* t' - t"
-=q=. "
S Pn+Pn+PI t- P 2


r.ll.e P CYM - cYMMapHoe Ten.1JOBOe conpOTHBJIeHHe MeiK)l.Y_ Cpe.ll.aMH I H II:


04eBH.lI.HO TaK)I{e, 4TO


P CYM = P
 + Pa t- P
.


(2.31)


1
k= I I 8, '
- + -+
-
at a"
 AI


(2. 32)


3



 8. TenJlonepe.ll.aqa Qepe3 HenJlOCKYW cTeHKy
nYCTb Cpe.ll.bI I H II OT.lI.eJleHbI .lI.Pyr aT .lI.pyra IJ.HJIHH.lI.pH4eCKOH HJlH
wapOBOH CTeHKoi'r.. B 3TOM CJIY4ae y)l{e HeT B03MOIKHOC';H TaK npOCTO,
KaK 3TO 6blJI0 BbH10JlHeHO .lI..1J5I nJIOCKOH CTeHKH, BbIpa3HTb TenJIOnepe-
)l.a4Y: XOT5I H Y.ll.aeTC5I BBeCTH HeKOTopbIe BeJIH4HHbI, 06JIa.ll.aIOllI.He a.ll.J\H-
THBHOCTbIO, Bce )l{e HX CTpYKTypa
CJIO)l{Ha, 4TO orpaHH4HBaeT HX npaKTH-
4eCKoe npHMeHeHHe.
ECJIH CTeHKa HMeeT CJIO)l{HbIe 04ep-
TaHH5I, TO peweHHe 3a.ll.a4H B 06weM
= BH.lI.e )1.0 CHX nap He )l.aHO J\atKe J\JI5I
Taro CJIY4a5I, KorJ\a CTeHKa - O.ll.HOpOJ(-
_
 Ha5I. ECJIH orpaHH4HBaIOWHe ee no-
BepXHOCTH COBna.ll.aIOT C H30TepMH4ec-
KHMH, 3a.ll.a4a CBO)l.HTC5I K HaXOIK.lI.e-
HHIO K03<p<PHI-lHeHTa <pOpMbI (CM.
 5).
B TOM CJIY4ae, eCJIH pa.ll.HYCbI KPH-
BH3HbI orpaHH4HBaIOWHX nOBepXHO-
CTeH 60JIbWe no cpaBHeHHIO C 06weii
TO.1JWHHOH CTeHKH npHMepHo B weCTb H 60Jlee pa3, MO)l{HO C .lI.OCTa-
TOL/HbIM npH6J1H)I{eHHeM npHMeH5ITb <POPMYJlbI nJIOCKOH CTeHKH (<pHr. 21).
flpu.Mep 5. Pacc4HTaeM OTenJIeHHe 6aTHc<pepbI. TaK KaK ee .lI.HaMeTp
(nop 5I .lI. Ka J\BYX MeTpoB) BeCbMa BeJlHK no cpaBHeHHIO C TOJIllI.HHOi'r CTe-
HOK H C TOJIllI.HHOH H30.1J5IIJ.HH, TO paC4eT C BnOJlHe J\OCTaT04HOH T04-
HOCTbIO MO)l{HO BeCTH no <PoPMYJIaM nJlOCKOH CTeHKH (2. 22) - (2. 32).
B 6aTHc<pepe HaXOJ\5ITC5I .lI.Ba 4eJIOBeKa B CH.lI.5I4eM nOJlOlKeHHH H B 06bI4HOH
O.ll.e, iK.lI.e Cpe.ll.Hee TenJIOBOe cOnpOTHB.1JeHHe KOTOpOH paBHO
O,17-
0,18 ,M! 'tae 2paa ICKa/l- I . B 3THX YCJIOBH5IX TenJIOBbI.lI.eJleHHe Ka)l{.lI.OrO
H3 HHX npH6JIH3HTeJIbHO paBHO MOWHOCTH 100-BaTTHoH 3JIeKTpH4ecKoi'!
JIaMnbI HaKa.1JHBaHH5I ::::::: 86 K/W/l 'tae-I. Y4HTbIBa5I, 4ro Bce )l{e OHH COBep-
III a lOT HeKOTopbIe J\BH)I{eHH5I, OIJ.eHHBaeM: Q* = 2.100 = 200 KKa/l 'tae-I.
OnpeJ\eJIHM He06xo.ll.HMYIO TOJllll.HHY 8 H30JI5ILlHH, nOJlara5I, 4TO npHMe-
HeHa BbICOI<OK3'leCTn('I1n3H 3KCn3I1311TI13H npo6Ka C J... = 0,03G (33BII
CHMOCTbIO OT t npeHe6peraeM) H 4ro B 6aTHc<Pepe )l.OJI)I{Ha nOMepiKH-


,

 ===


<DHL 21. nepeJ1alJa TenJla OT CpeJ1bl J
1< cpe.ne J J lJepe3 HenJlOCKYIO cTeHKY
MaJIoii KpHBH3H
I.


II.1J1I


200
41t


14
O,I25--t-0.005 + 0.0025+P]


HJIH


0,1275 + PI = 0,281t',


oTKyJ\a


5 r.1
PI = 0,7 = 3,035


<DHr. 22. 1130JIHpoBaHHe 6aTH-
cqJepbl:


I - MeT8J1n11'-1eCK8H 060nO'-lKa; 2 - "30.
T. e. 8 I :::::; 0,026 M = 26 ,MM: TOJIWHHa JlAUHA; 3 - OKHO.
COBCeM HeBeJIHKa.
3.l1.eCb MbI npeHe6perJIH nOTepei'! TenJIa 4epe3 OKHa 6aTHc<pepbI, C4H-
Ta5I, 4TO aHa KOMneHcHpyeTC5I TenJIOBbIJ\eJIeHHeM npO)l{eKTOpa J\JI5I OCBe-
weHH5I MOpCKHX rJly6HH.


* *


*


B J\aJIbHeHIJ.IeM H:3y4aIOTC5I pa3HbIe CJIY4aH He
TaIJ.HOHapHbIX TeMne-
paTypHbIX nOJlei'!; KpaiiH5I5I CJIOIKHOCTb MaTeMaTH4ecKoli CTOpOHbI 3a.ll.a4
3Toro pO.ll.a BbIHY)l{J\aeT npH HX peIlleHHH C.lI.eJlaTb )l.Ba J\onYlll.eHH5I.
Ope.ll.nOJlaraIOT, 4TO Bce TenJlOBbIe xapaKTepHCTHKH MaTepHaJIOB,
H3 KOTOpbIX COCT05IT TeJla paccMaTpHBaeMoli CHCTeMbI, He 3aBHC5IT aT
TeMnepaTypbI, T. e. CYTb a6COJIIOTHbIe KOHCTaHTbI. u u
TenJIo06MeH Me)l{.lI.Y nOBepxHoCTbIO CHCTeMbI H OKpY)l{aIOllI.eH cpeJ\oH
C .lI.OcTaT04Hoi'! T04HOCTbIO MO)l{eT 6bITb onHcaH C nOMoWbIO 3aKOHa oXJla-
}!{.lI.eHH5I HbIOToHa.
y13 BeCbMa 60JlbWOrO KO.1JH4eCTBa BonpocoB, CIO.lI.a OTHOC5IWHXC5I,
BbI6paHbl Te, KOTopbIe JIe)l{aT B OCHOBe MeTO.ll.O.B H3MepeHH5I Ba)l{HbIX J\Jl5I
npaKTHKH TenJlOBbIX BeJlH4HH H npH60pOB H HaX0.ll.5IT npHMeHeHHe B Ten-
JlOBbIX paC4eTax.
3a.ll.a4H 6Y.lI.YT peWaTbC5I B nOp5I)l.Ke HX B03paCTaJow.eii CJlOIKHOCTH.


.




3AeMeHTapHaJl TeOpUJI Wtepl{Uu teA U CUC7'e,M 6e3 UCTO'lHUKOB TenJW 49


.


r.nABA 3


(IIJIH TeJIa) U, He COBna,AaeT C KpHBOH ABCD; 3TH KpHBble Mary!
HHor,Aa nepeceKaTbCH B HeKOTopblX TOlJKax. TaK, Ha cpHr. 24 B TOlJKe C
TeMnepaTypa Cpe,Abl ,AOCTHrJIa MaKcHMYMa, a TeMnepaTypa CHCTeMbl Bce
eIll,e npo,AOJl)l{aeT nO,AHHMaTbCH, ,AOCTHraH CBoero MaKcHMYMa B TOlJKe
e 3HalJHTeJIbHO n03)1{e, KOr,Aa TeMnepaTypa Cpe,Abl y)l{e ,AaBHO HalJaJIa
na,AaTb. 5IBJIeHHe 3Toro OTCTaBaHHH TeMnepaTypbl U TeJIa HJIH ClfCTeMbl
OT TeMnepaTypbl 8 Cpe,Abl Ha3bIBalOT TenJIOBOH HJIH TepMHlJeCKOH IIHep-
uHeH (HHepUHoHHOCTblO).
BblBe,AeM OCHOBHoe ypaBHeHHe 3J1eMeHTapHoli TeopHH TeIIJIOBOH
HHepuHII. flu
PaccMoTpHM H3MeHeHHe d Q .
TenJlOCO,Aep)l{aHHH Q CHCTeMbl I c
3a 6eCKOHelJHO MaJIblll npoMe-
IKYTOK BpeMeHH d7:, B TelJeHHe
KOToporo ee TeMnepaTypa
nycTb II3MeHHeTCH C U ,AO
ll-du; OlJeBH,AHO


.


3J1EMEHTAPHA5I TEOPH5I TEnJ10BOfi HHEPLl.HH TEJI H CHCTEM'
6E3 BHYTPEHHHX HCT04HHKOB TEnJ1A


C HBJleHHeM TenJlOBOH HHCpll.HH npHXO,AHTCH BCTpeqaTbCH B BeCbMa
pa3H006pa3IIblX 06JIaCTHX lf3MeplfTeJlbHOil TeXHlfKli, If era
Ce06Il1.HOCTb
3aCTaBJIHeT Y,AeJilfTb eMY oc06eHHoe BHHM3Ime. KpaihIHH CJlO)l{HOCTb
3a,AalJlf [4] 3aCTaBJIHeT HalJlfHaTb C Half60Jlee npocToH ee nOCTaHOBKH
C TeM, LIT06bl BbI5ICHlfTb OCHOBHble
lJepTbl HBJleHHH.
Y npOIueHHe 6Y,AeT COCTOHTb B
npe,AnOJlO)l{eHlflf, lJTO nOJle TeMne-
paTYP ClfCTeMbl paBHOMeplloe, T. e.
lJTO


r.Qe Ul' U2, .., TeMnepaTypbl OT-
O .'],eJIbHblX TOLle'<.ClfCTeMbl MI
XI' Yl'
2,), M 2 (X2' Y2. 22), . . .-cplfr. 23.
TeMncpaTYPY HapY)I{HoII BHeWHeii
Cpe,Abl 0003HalJlfM 8; npe,Ano.1JO)l{lfM,
4TO aHa O,AHHaKOBa BO Bcex ee
T04Kax; B 4aCTHOM CJIY4ae b MO)l{eT
6bITb nOCTOHIIHOii, a Bo06w.e 3TO-
<PYHKlI.lfH BpeMeHlf. K03cpcplfll.HeHT Ten.1J00T,Aa4lf ex, Ha rpaHlfll.e S TeJla
If Cpe,Abl, 6Y,AeM ClJlfTaTb TaK)I{e: a) O,AlfHaKOBbIM BO Bcex T04Kax HapY)I{HOH
nOBepxHocTH S If 6) nOCTOHHHblM no BpeMeHlf, T. e.


8


C0


.M,


..


<!JHL 23. TeJlo (If JIM CHCTeMa) F, Haxo-
.nHll.leeCH B cpeJ1e E paBHOMepHOH Tellme.
paTypbl ti; nO.He TeMnepaTYP TeJIa F-
paBHOMepHoe.


dQ=-C.du;


.II
a


U J = U 2 = lis = .. = u, (*)


3HaK MHHYC COOTBeTCTBye'i'
y6blJIH BHYTpeHHeii 3HeprHH
CHCTCMbI. nOCKOJIbKY TenJIO-
OT,Aa4a He COnpOBO)l{,AaeTCH
H3MeHeHHHMH B arperaTHOM
COCTOHHHH TeJI, BXO,AHIlI,IIX B
CHCTeMY, H cpellbl, KOJlHlJeCTBO
d Q TenJI0'30H 3HeprHH, nOTe-
pHHHoe CIICTeMOH, B CIIJIY 3aKOHa coxpaHeHIIH 3HeprHH, paBHO KOJIII-
4eCTBY Ten.1Ja, no.1JYlJeHHOMY Cpe,AOH II npowellweMY CKB03b HapY)I{-
HYIO nOBepXHOCTb CIICTeMbl; Ha OCHOBaHIIH 3aKOHa HblOTOHa HMeeM:


-r


dT


-T


<!JHL 24. fpaljJHlJeCKaH xapaKTepMcTHKa HBJIe-
HHH TenJlOBOH MHepuHH: ABCD - KpMBaH
H3MeHeHHH TeMnepaTypbl 6 cpeJI.b1, abed - KPM-
BaH H3MeHeHMH TeMnepaTypbI U TeJIa.


dQ = ex.S. (u - 8) d7:.
1-13 cpaBHeHHH llBYX nOCJlellHHX CPOPMYJI nOJIYlJaeTCH OCHOBHoe ,AII<pcpe-
peHqHaJIbHOe ypaBHelme, CBH3bIBalOIlI,ee li II 8; Mbl era HanHweM B cpopMe
!!!!:. + mu - m8 = 0 (3. 1 )
d-r '


H


ex He 3aBHCHT 01 X s , Ys. 2s }
ex He 3aBHCHT OT BpeMeHH 'to


r,Ae 6YKBOH m 0603Ha4eHa BeJIHlJHHa, CYIlI,eCTBeHHO nOJIOIKHTeJIbHaH,
paBHaH


(*"')


.


as
m=C'
YpaBHeHHe (3. 1) coxpaHHT TOT )l{e 81Il!., eCJlII CHCTeMa B TelJeHHe
BpeMeHII d7: nOJIY4aeT TenJlO aT cpe,AbI, lJTO COOTBeTCTByeT (<pHr. 24)
TOlIKe B Ha TeMnepaTYPHoH KpIIBOH Cpel!.bI.
n CI!JlY l:,U.CJldIlIlLIX Hc:lMIl LlLIwe ,U.ulIYlllClIllii 'IlIl:JIU T1I - neJIiI'I1U13
nocToHHHaH, a n03ToMY ypaBIIcHHe (3. 1), eCJlH B HeM ClJHTaTb B 3allaU-
1 KOHllpaTbeB 2763


(3.2)



 1. BblBOll OCHOBHoro ypaBHeH"SI
DYCTb fJ - cpYH, KlI.HH 3a,AaHHaH HJI" aHaJIHTHlJeCKH HJlH rpacpH4e-
CKH, Hanp"Mep, TaK, KaK 3TO npellCTaBJleHO JlHHHeii ABCD lIa cpHr. 24.
TeopH 51 nOKa3bIBaeT II OnblT nO.QTBep)l{l!.aeT, lITO CHCTeMa
 MrHOBeHlIO
p£'arupYCT 113 113MCIICIIIIC TCMnCpaT} pLI Cp£'1hl, a C 3an03131I11CM: I<pl!
BaH abed ,tfJHr. 24), H306pa)l{alOU
aH H3MeHeHHe TeMnepaTypbl CHCTeMbl




50


C/JU3UKO-,IWTeMaTUljeCKUe OCHOBbl U3MepeHUa TenAOBblx BeAUltUH


8AeMeHTapHaJl TeOpWl UHep/iUU Ten U cUCTeM 6e3 UCTOltHUKOB TetlAa


51


HOll cpYHKUHei% BpeMeHH, npe.lJ,CTaBJISleT COOOH JIHHeHHOe .lJ,Hcp(pepeH-
UHaJIbHO
 ypaBHeHHe O'-leHb npOCTOrO BH.lJ,a, 06
Hll HHTerpaJi KOTO-
poro Hall.lJ,eTCSI CJIe.lJ,YIOIUHM 06pa30M
0603HalIHM fJ, paCCMaTpHBaeMY
 KaK cpYHKUIfIO 't:
fJ = F ('t). (3. 3)
nG.1IO}KHM u = V'W, r.lJ,e V H W - HeH3BeCTHbIe nOKa cpYHKUHlI 't;
no nO.lJ,CTaHOBKe B ypaBHeHHe (3. I) nOJIYlIHM
( dv ) dw
w, £h+m.v +v'(h-m.F('t} =0.
BbI6epeM CPYHKUHIO v = V ('t) TaK, lIT06bl cYMMa B cKooKax OOpaTHJIaCb
B HYJIb:


ypaBHeHHe K Ha'-laJIbHoMY MOMeHTY BpeMeHH 'to. npH'-IeM
TeMnepaTypbI CHCTeMbI H Cpe.lJ,bI B 3TOT MOMNIT '-Iepe3 U o H
Go = 81,
,o = F ('to). U o = u h=,o'


06031Ia'IHM
8 0 :


(3. 4)


HeonpeJIe.1JeHHbIH HHTerpaJi 3a.\1eHHM onpe.lJ,eJIeHHbIM,
B npe.lJ,eJlax OT '0 JIO 'to nOJIYlIHM


B3HB ero


U o = De -m,.


"


,
-om l'-'ol + -m, S m' F (
 ) d
u = uoe tne. e . 'to
'0


dv
- + mv = 0
d, '


.llaJlee, npnMeHIIM K HHTerpaJlY B opaBOH '-IaCTH nOCJle.lJ,Hero paneH'
CTI33 q OPMYJIY HHTerpHpOBaHHH no lIaCTHM; nOJIY1IHM:
m.S em'.F ('t}.d't = s' P ('t}.d(e m .') = [F ('t}.e m .']' - f em.'.F' ('t}.d't,

o

o
o


HJIH, '-ITO TO me:


d(In v +m't) = O.
Tor.lJ,a .lJ,JISI W nOJIY'-IHM JIemo HHTerpHpyeMoe
dw m
£h '"'" v. F ('t).
113 npe.lJ,WeCTBYIO
ero eMy ypamreHHSI CJIe;I,yeT, lITO In v + m't =
= const, T. e. ve m ' = const H v = C1e- m \ rJIe C 1 - nOCTOflImaSl. nO-
3TOMY ypanHeHHe .lJ,JISI Onpe.lJ,eJIeHHSI W npH06peTaeT cpOPMY
dw mm,
(J.t = C;' e . F('t) ,


ypaBHeIme:


nocJle '-Iero 4-0pMYJIa .lJ,JISI U npHMeT cJle.lJ,YIO
Hll nH.lJ,:
U = U o .e- m ('-'oj + e- m .'. { F ('t) .em" -- F ('to)' em.,o - f em.;; .F' (:) d't } .
B CHJIY (3. 3) H (3. 4) 3aMeHHM 3.lJ,eCb F ('t) H F ('to) '-I€'pe3 8 H 8 0 ; TOr.lJ,a
npHJ].eM K BblpameHHIO .lJ,JISI pa3HocTH TeMnepaTYP CHCTeMbI H cpe.lJ,bI:


,
U - e = (u
 - Go) e- m ('-'0) - e- m ' X em'p' ('t) d't.
;;0


(3.5)


OTKY.lJ,a


3TOT BH.lJ, HaH60Jlee Y.lJ,06eH .lJ,JIH npaKTH'leCKHX npHJIOmeHHll. nepexO.lJ,HM
K '-I a CTHbIM , HaH60JIee BamHbIM, CJIYlIaSlM.
,


m S m' F
W = c} e ('t}d-r:+C 2 ,



 2. nepBblif THm-l'-lHbIif cJIY'-Iaif npOSIBJIeHlUI TenJIOBOif HHepu,HH:
npocToe OXJIa
JIeHHe HJIH HarpeBaHHe
Ha npaKTIiKe lIaCTO npHxO.lJ,HTCSI BCTpeqaTbCSI co CJlYlIaeM, Kor.na
TeMnepaTypa 0 Cpe.lJ,bI - nOCTOSlHHaSl, a BHeceHHoe B Hee TeJIO HMeeT
B HaqaJIbHbIH MOMeHT BpeMeHH TeMnepaTYPY U o , 3aMeTHO OT Hee OTJIH-
'-IalO
YlOcSI. OnbIT nOKa3bIBaeT, lITO B 3TOM cJlyqae TeMnepaTypa TeJIa
aCHMnTOTHqeCKH npH6.nHmaeTCH K T€'Mn€'paType Cpe.lJ,bl, TaK qTO MbI
nOJIYlIaeM BCer.lJ,a THnHlIHbIe 3KcnepHMeHTaJlbHbie KpHBb1e, npe.lJ,CTaBJleH-
Hble Ha cpHr. 25. 3TO - CJIyqaii TaK Ha3bIBaeMoro «npoCToro»
xJIamJIe-
HHH HJIH HarpeBaHHSI.
DpHMepoB npoueccoB 3Toro po.na B npaKTHKe H3MepeHl-IH H B npH60po-
CTpoeHHH - O'-leHb MHoro: nHpoMeTp, KOTOpblH HMeeT KOMHaTHYIO TeM-
lIepdT)PY H DBC)J.CIl B I UIHI'IYIU He'lL C I10CTOHIlIIOtl TCMncp;nypoii;
l<aTaTepMOMeTp, npHMeHSleMbIH B KalIeCTBe aH€'MOH€'Tpa: 3.lIeKTpOH3Me-
4*


r.ne C 2 - HOBaSl nOCTOHHHaH.
OKOH'-IaTeJIbHO HaXOJIUM B CHJIY Toro, lITO u = v. W:
U = C1e- m ,( ;: S em' F ('t) d't + C 2 );


0603HalIHB C } C 2 = D , r n e D
I-'. - BOBaSl npOH3BOJlbHaH nOCTOSlHHaSl,
nO.1JyqaeM:


u =- e- m , (D + m S em' F ('t) d-r:).
3TO RhIpa}l{f"PHE' 1IE'.TIP('()()()p
'lIl() npf'1"T:1BIfTh B If II ()i, r!JopMr. np('>J{;J,£'
Bcero, onpe.lJ,eJll-IM npOH3BOJIbHYIO nOCTOSlHHYIO D, OTIIOCSI nOCJIeJIHee




52


cPU3UKo..ltaTeMaTU'leCfCUe OCHOBb! U3MepeHut1 TenAOtiblX BeAU'lUI-l


pHTeJIbHbIH npl160p, BHeCeHHbIH B rOpSl43H Llex 11 He cHa6>KeHHb!ll TenJIO-
BOH 3aWI1TOH; MHKpOKaJIOpl1MeTp CBeHTOCJ1aBCKOro [5], [6] H T. ]1,.
I13JIO>KeHHaSi B
 1 ,nOH rJIaBbI TeOpl151 ,'(aeT ypaBHeHl1e Kpl1Boi'! OXJIa-
>K]1,
HHSI I1JIH HarpeBaHI151; 113 ypaBHeHI1S1 (3. 5), r]1,e CJIe]1,yeT nOJIOIKI1Tb
8 .
- F ('t) = t = const, (3.6)


Mbl nOJIY4aeM


(3.7)


u - 8 = (u o - t) e- m «-
o),


TaK KaK


F' (1') = 0,


u.,Bt


u,B I


u.


B.con$!


-


B.const


U.


T.


To


-T


-T


<I>Hr. 25. nepBblii THnHlJHb1ii cJIY4ai'I TenJIOBOii HHepUMH - npoCToe OXJla}KJ1eHHe HJIM
HarpeBaHMe TeJla: TeMnepaTypa CpeJ1b! 6 He 3aBHCHT OT BpeMeHM 'to


]1,PYrHMH CJ10BaMI1: pa3HOCTb TeMnepaTYP TeJIa 11 Cpe.ll.bI npl1 ero npOCTOM
OXJIa>K]1,eHlJH I1JII1 AarpeBaHl111 113MeHSleTCSI no 3KcnOHeHLll1aJIbHOMY
3aKOHY.
BMeCTO K03

HLlHeHTa m, onpe]1,eJISIIOIll,era xapaKTep 3KcnmreHTbI,
4aCTO BBO.ll.S1T 06paTHYlO Be.Jl114HHY
I C
e = m = Sa . (3. 8)


aHa HMeeT pa3MepHOCTb BpeMeHH, TOr]1,a KaK m HMeeT pa3MepHOCTb
I
[m] = ell. BpeM. = (e]1,. BpeM,)-I.
<])opMYJIa (3. 7) MomeT 6bITb rpa1m4eCKH H306pa>KeHa eIll,e npOIll,e:
npoJIorapl1£pMl1pOBaB ee, nOJIY4aeM:
In I u - 81 = - + = const. (3. 9)


3]1,eCb In - 3HaK HaTypaJIbHOra JIOrapl1
Ma; e - OCHOBarme HaTY-
paJIbHblX
JIOrapl1<pMoB (<<3llJIepOBO 411CJ10»), - TpaHCLleH.lI.eHTHOe 4HCJ10,
npH6JIHmeHHO paBHoe 2,718. LLBe BepTI1KaJIbHbIe 4epTbI (II) - CHMBOJI
a6COJIIOTHOrO 3Ha4eHHSI.
nT('J()
;:t RH
Hn, QTO
;:tRH(,HMnrTh In 11/ - 8' OT Rpf'Mf'HH H
nfip;:t-
>KaeTCSI B ]1,eKapTOBbIX KOOp.ll.HH3TaX npSlMoH JIHHl1eH C OTpHLl3TeJIbHbIM
yrJ10BbIM. K03<p<pI1Lll1eHTOM (1160 e > 0, TaK K3K m > 0) -
11r. 26.


3AeMeHTapHaJl TeOpUJl UHepltUU TeA U CUCTeM 6e3 UCTO'lHUKOB TenAa


53


3TOT pe3YJ1bTaT n0J1Y4eH 3]1,eCb 411CTO TeOpeTI14eCKHM nyreM KaK
CJIe]1,CTBHe nepeBO.ll.a Ha S13bIK MaTeMaTI1KH HeKOTopbIX ynP?IlI,eHHbIX
l!m3H4eCKHX npe]1,nOCbIJ10K 0 TenJIoo6MeHe Mem]1,y reJ10M H cpe]1,OH. B pSl]1,e
CJIY4aeB OH BnOJ1He nO.ll.TBep>K.lI.aeTCSI onbITOM.


* *


*


npe>K]1,e 4eM nepeXO.ll.l1Tb K paCCMOTpeHl11O ]1,BYX .lI.pyrHx npOCTbIX
eJlY4aeB, C]1,eJIaeM CJIe]1,YlOw ee 3aMe4aHl1e.
113 ypaBHeHI1S1 (3. 5), npl1MeHHB K I1HrerpaJIY B era npaBoH 4aCTH
0606Il1,eHHYIO TeopeMY 0 Cpe.ll.HeM 3Ha4eHI1H HHTerpaJIa, nOJIY4I1M:
< < tn (u-t)
.f e mz F' (z) dz = F' (
) f e rnz dz,
'to 'to


r]1,e
 3aKJII04eHO Mem]1,Y 'to H 1':
'to <
 < 'to
3.l1.eCb MbI n0J1b3yeMcSI 0606-
IlI,eHHOH TeopeMoH 0 cpe]1,HeM
3Ha4eHHI1 I1HTerpaJIa, 3aKJI104alO-
IlI,eHCSI B CJ1e]1,YIOIlI,eM. nYCTb
nO]1,I1HTerpaJIbHaSi <PYHKLlHSI MO-
meT 6bITb npe.ll.CTaBJIeHa KaK
np0l13Be.ll.eHI1e ]1,BYX
YHKLlHH-
f(x) H qJ (x), npl14eM nYCTb qJ (x)
MOHOTOHHO B03paCTaeT I1JII1 y6bI-
BaeT B I1HTepBaJIe (a, b), B npe-
]1,eJIax KOToporo 6epeTcSI I1HTer-
paJI. Tor.ll.a I1HTerpaJI OT
YHKLlI1I1 f (x) qJ (x) paBeH
b b
J f (x) , (x) dx = f (
) ,f CfJ (x) dx,
a


o


'"


.--"


<I>Hr. 26. fpaqJHK npOCToro OXJIa}K.neHHH
TeJIa B nOJlYJlorapmlJMHlJecKMX KOOpJ\HHaTax
npeJ\CTaBJIHeT c06010 npHMYIO JIMHHIO, co-
CTaBJIHlOll.lYIO yrOJI
 C OCblO a6CUHCC (OCI:
BpeMeH); 6 = const; tg
 = m.


a


r.ll.e
 -- 4HCJIO B HHTepBaJIe (a, b).
3aMeHI1B 3.l1.eCb a H b 4epe3 'to 11 1', a x 4epe3 z H nOJIaraSi qJ (z) =
= e mz , nOJIY411M npe]1,bl]1,YIlI,YIO
OPMYJ1Y.
n03TOMY
OPMYJIY (3. 5) o6Il1,eH TeopHH MOIKHO HanHcaTb eIll,e B BII]1,e:
I - e- m «-<0)
u - 8 = (u o - 8 0 ) e -m «-<0) - F' (
)


m


OTCIO]1,a CJ1e.ll.yeT, 4TO eCJ1H TOJIbKO npOH3BO]1,HaSi :
 = F' (1') He
npl1llIlMaeT 6eCKOHe4HbIX 3Ha4eHHH - a TaKHe 3Ha4eHI1S1 He HMelOT
H3H-
4eCKoro CMblCJIa, - TO cOrJIaCHO 3JIeMeHTapHOH TeopnH OTCTaBaHHe u OT
8 BCer]1,a OCTaeTCSI KOHe4HolI l3eJII14HHOH, KOTopaSi C Te4eHlleM BpeMeHH,
T. e. no Mepe YBeJ1H4eHHSI l' - To (3TO BJIe4eT 3a C060H YCTpeMJIeHHe
K HWHO BblpameHH5I e- m (, - <0»). BbIpa311TcSI npOCTOH CPOpMYJ10H:
u - 8 -- - eF' (
). (3. 9)




54


CPU3UKO-,MUTeMaTU<teClwe OCHORbl U3AlepeHUU TenAOBblX BeAU'IUH


3T0 paBeHCTBO nOKa3bIBaeT, '-ITO .lJ.J15I .lJ.3HHOH CI1CTeMbI 11 .lJ.JI5I .lJ.aHHbIX
YCJ10BI1H TenJ100T.lJ.a'-lI1, '-IeM 11 Onpe.lJ.eJI5IeTC5I e, TenJ10B35I I1HepUH5I ee
33BHCI1T - B KOHe'-lHOM C'-IeTe - OT CKOpOCTH 113MeHeHH5I TeMnepaTYPbI
Cpe.lJ.bI.
3aMeTI1M eIll,e CJ1e.lJ.YIOIlI,ee.
B TOM CJlY'-Iae, eCJ1H KpHBa5I 113MeHeHI15I TeMnepETypbI TeJ1a HMeeT
MaKCI1MYM HJ111 MHHI1MYM (O.lJ.I1H I1J1H HeCKOJ1bKO 11J111 6eCKOHe'IHOe MHO-
!l.6
t


Uc


-T


6 0
I 110
I ' I
to 6) to e) -T


<!JHr. 27 I3Topoii T1fnH4HbIii cJlYlJait TenJIOBOii HHepUHII - HarpeBaHHe HJIII OXJla}KJ1eHHe
TCJla B cpeJ1e, TeMnepaTypa KOTOpOH H3MeHHeTCH c nOCToHHHOii CKOpOCTblO:
a, 6 - TeMoepSTYps cpellbl B03paCTseT, fl,;: - TeMOepaTYps cpellbl y6blBseT.


)!(eCTBO). TO 3TI1 MaKCI1MYMbl (MI1HHMYMbl) COBna.lJ.aIOT C TO'-lK3MH nepe-
Ce'-leHH5I TeMnepaTypHblX Kpl1BblX (3. 3) H (3. 5).
4T06bl B 3TOM y6e.lJ.HTbC5I, .lJ.OCTaTO'-lHO npl1paBH5ITb HYJ110 npOH3-
du
BOJ].HYIO lh 11 cpaBHHTb nOJIY'-Iemroe paBeHCTBO C TeM, K KOTOPOMY npH-
BOJ].HT YCJl0BI1e u = 8.
3TO 06CT05ITeJ1 bCT130 X3paKTepHO 1IJ15I p3BHOMepHoro noml TeMne-
paTYP TeJ1a; eCJ1H OHO He 6Y.lJ.eT 06Hapy)!(eHO npl1 nOCTpOeHl111 Kpl1BbIX
(:i 1) 11 (:1 S) "'1{('nprll
fP"TWlb"hIM nYWM. T. e, eC.'l1l TO'II<II nep(,C("I(,.
!
I1H Kpl1BbIX H I1X MaKCI1MYMbl 11 MHHI1MYMbI OKa)!(YTC5I CMeIll,
HH\;>IMli


3AeMeHTapHaR TeopUJt UHep/{uu TeA U CUCTeM 6e3 UCTO'lHUKOB Tenl1a


55


no OTHOllleHHIO ,npyr K .lJ.pyry, TO T3l<oe CMeIll,eHHe 6YJJ;e'f CJly)!(HTb "PU-
3HaKOM HepaBHOMepHOCTI1 TeMnepaTypHoro nOJIll TeJ1n. LJ:J151 HJ1J1IOCTpa

U,HH (£j:mr. 24, a H 6 II qmr. 27) nepBafl H3 HHX cooTBeTcTByeT CJlY'-IalO
Hep3BHoMepHoro TeMnepaTypHoro nOJ15I TeJ1a, BTopaH n0J1Y'-leH3 K3K rp3-
cpH'-IeCK35I HHTepnpeTau,l15I CPOPMYJ1, BbIBe.lJ.eHHbIX npH .lJ.OnYIll,eHHH (**).

 3. BTOPOH Tl1nl1'IHbIH CJIY'-laH npOHBJIeHIUI TenJIOBOH I1Hepu,HI1

HarpeBaHl1e I1JII1 oxaa*.lJ.eHHe TCJIa 13 cpelIe, TeMnepaTypa KOTOpOH
113MeH5IeTCH 130 BpeMeHH C nocToHHHOH CKOpOCTbW
nYCTb TeMnepaTypa Cpe.lJ.bl 113MeHHeTCH co BpeMeHeM JII-lHellHO, T. e.
e = b (T - to) - Bo (3. 10)


UJ1H, '-ITO TO )!(e,


!!!!.. = b = F' (t) =- canst.
d't


(3. 11)


BbIpameHue (3. 5) 06wero uHTerpa.1Ja OCHOBHoro .lJ. u cpcpepeHu,l1aJIbHOrO
ypaBHeHU5I (3. 1) 13 .lJ.aHHOM cJ1Y'Iae npHMeT BU.lJ.:
u - B = -be + (u o - Bo + be) e- m (-c--c.). (3. 12)
.
fp3cpl1'IeCKUe npe.lJ.CTaBJ1eHHH pa3HOBH.lJ.HOCTell peml1MOB 3Toro pO.lJ.3
.lJ.aHbI H3 cpl1r. 27, a, 6, e, 2. vb Hee BI1.lJ.HO, '-ITO B03MO)!(HbI cJ1Y'Ial1, KOr.lJ.3
Kpl1BbIe (a) 11 (u) nepeCeK3IOTC5I, HO OHH MorYT nepeceKaTbC5I He 60J1ee
'IeM 13 O.lJ.HOll TO'IKe.
nYCTb BpeM5I 't B03paCTaeT; BTOpoe CJlaraeMOe B (3. 12), CO.lJ.epm3wee
3KcnmreHTY e- m (-c - -co) 13 Ka'-leCTBe MHO)!(I1TeJ1H. CT3HOBI1TCH npeHe6pe-
)!(HMO MaJ1bIM no cp3BHeHHIO C nepBbIM, H Mbl npI1XO.lJ.HM K 33KJ1IO'IeHI1IO,
'ITO pa3HocTb TeMnepaTYP TeJ13 H Cpe.lJ.bl cTpeMHTC5I CTaTb nOCT05IHHOH,
T. e.


u - B = -be


(3. 13)


npl1 60J1bIHI'IX 't - 'to.
npou,ecc, 3.lJ.eCb paccMoTpeHHbIfi. pemc BCTpetIaeTC5I H3 npaKTI1Ke,
'IeM np e .lJ.bI.lJ.YWl1ll, 11 B J1a60paTopHH .lJ.J15I CBoero oCYIll,eCTBJ1eHI15I Tpe6yeT
npHMeHeHHH 60J1ee lllHpoKoro aCCOpTI1MeHTa npHeMoB; HBJ1eHl1e me
npOCToro OXJ1a)!(.lJ.eHH5I 'IaCTO npol1CxoJ].I1T B npHpO.lJ.HWX YCJ10BHHX 6e3
BMelllaTeJ1bCTBa 3Kcnepl1MeHTaTopa.
npHMepoM npou,ecca, KOTOpblH MOIKHO C 1I0B0J1bHO rpy6bIM npH6J1H-
}KeHHeM yno,nool1Tb BTOPOMY cJ1Y'IalO TenJ10BOH: I1Hepu,I1H, MO)!(eT CJlYc
,({HTb npou,ecc OXJ1am.lJ.eHHH MeTe030H.lJ.3 npH ero nO.lJ.'beMe.

 4. HarJIH,nHoe HCTOJIKOBaHlte nocToHHHOH TenJIOBOH ItHepu,1t1t
OCHOBbIBa5ICb H3 nOJ1Y'IeHHbIX BbIBOlIax, MO)!(HO .lJ.aTb .lJ.Ba npocTbIX
H HarJ15I.lJ.HbIX HCTOJ1KOBaHH5I nocToHHHOlI e, KOTOPYIO Ha3bIB31OT no-
CTOHHHOH TenJ10BOH (TepMH'IeCKoiI) l-lHepu,HI1, 3 HHor.lJ.a nOCTOHHHOH
BpeMeHiL
nYCTb 1];aHTjnp Te'ln j
I\I[PV111TPP TPVInpp
lTYPY 110' B MOMeHT r:peMeHH 't n
norpy)!(eHO B Cpe.lJ.Y C nOCTOHHHOH TeMnepaTypOH f:t; ero Te!\HlepaTypa




56


C/JU3U1W-MaTe.t.laTU'IeCKUe OCHOBbl U3.t.lepeHUii TenAOBblX BeAU'IUH


6Y,AeT CTpeMHTbCSI CTaTb paBHOll TeMnepaType Cpe,Abl 6; BbI6epeM TaKoH
MOMeHT BpeMeHH 't, (IT06bI 6bIJIO 't 1 - 'to = e; H3 ypaBHeHHSI (3. 7)
CJIe,AyeT, '11'0 ,AJISI 3TOro MOMeHTa pa3HocTb TeMnepaTYP TeJIa H Cpe,AbI
CTaHeT paBHoH U - 8 = e- 1 (u o - 8), T. e. paBHoi\ J... =0,368 3Ha-
e
qeHHSI, KOTOpylO OHa HMeeT B HaqaJIbHbIH MOMeHT 'to - MOMeHT norpy-
)KeHHSI TeJIa B cpe,Ay (cpHr. 28).
BTopoe HarJISI,AHOe HCTOJIKOBaHHe - CJIe,AYIOIIl.ee.
DYCTb TeJIO norpY/KeHo B cpe,Ay, TeMnepaTypa KOTOpOM 8 JIHHeMHO
H3MeHSleTCSI C TeqeHHeM BpeMeHH 't, H paccMoTpHM MOMeHTbI BpeMeHH,


u.8t


6=cO.


to 1',


-1'


<DHr. 28. DepBaH HarJlH.nHaH HHTepnpeTa-
UHH nOCTOHHHoi'I TenJIOBOii HHepUUH E:
npOMe}KYToK BpeMeHH E Bb16paH TaK, lJTO
u 1 - 6
----.. paBHO e- 1
 0,368; 6 = const.
U o - u


-t
<DHr. 29. BTopaH HarJIH.nHaH HHTep.
npeTauHH nOCTOHHHOM TenJlOBoii
HHepUHH E: E - CKOJIbKO BpeMeHH
TOMY Ha3a.n cpe.na .nOCTHrJIa TOM
TeMnepaTypbl, KOTOpylO HMeeT TeJIO
B .naHHblH MOMeHT; E = hI .


,AOCTaTOqHO ,Aa.1JeKHe 01' HaqaJIbHoro. PaCCMOTpHM pa3HocTb TeMnepaTYP
8 - u Cpe,Abl H TeJIa B KaKoM-HH6Y,Ab H3 3THX MOMeHTOB BpeMeHH 't;
Ha cpHr. 29, r,Ae H306pa)KeHbI 06e npSlMbIe (0) H (u), pa3HOCTb 8 - U
npe,ACTaBHTCSI oTpe3KoM Op,AHHaTbI, cooTBeTcTBYIOrn:ei-i MOMeHTY 't. DpoBe-
.'"(eM qepe3 TOqKY f npSlMoM (u) npSlMYIO, napaJIJIeJIbHYIO OCH a6CIl.HCC,A0 ne-
peCeqeHHSI ee B h C npSlMoH (8) H HaH,AeM ,AJIHHY OTpe3Ka hf kf . ctg khf;
HO ctg khf paBeH 06paTHoH Be.Jll1qHHe yrJIOBOrO K03cpcpHIl.HeHTa npSlMblx
I
(6) H (u), T. e. Ha OCHOBaHI1H <PoPMy.1JbI (3. II) BeJIl1qHHe m ; TaK KaK no
- - IbEI
(3. 13) kf = I be I, TO nOJIyqHM hf = IbT = e. CJIOBeCHOe BbIpa)Ke-
HHe 3TOrO BbIBO,Aa 6Y,AeT CJIe,AYIOIIl.ee: nOCTaBHM BOnpOC, 3a CKOJIbKO
BpeMeHH ,AO ,AaHHOrO MOMeHT(l Cpe,Aa I1MeJIa TY )Ke TeMnepaTYPY,
KOTOpylO HMeeT CHCTeMa B 3TOT MOMeHT; 3TO BpeMSI HMeHHO H paBHO
nOCTOSlHHOH TenJIOBOH HHepIl.HH e.
DepBoe Onpe,AeJIeHHe nOCTOSlHHOM Ten.1JOBOll HHepIl.mI SlBJISleTCSI o6IIl.e-
npHHSlTbIM B npH60pOCTpoeHHH; ero ,AalOT 6e30rOBOpOqHO; H3 npe,AbI,AY-
merI Teop"" B",Allu, IIpll hdhHX ,Aunyw.eHHSI}" UHU I1MeeT 4->H.oIJ1LleCKHH
CMbICJI H HBJI HeTCH TeXHHqeCKH npHeMJIeMbIM.


3.11eMeHTap'taR TeopuR UHepl{UU TeA U CUCTeM 6e3 UCTO'lHUKOB TenAa


57



 5. TpeTI1H THnl1lJHblH CJIyqaH npOSlBJI u eHI1S1 TenJIOBOH I1Hepll,HI1:
CI1CTeMa - B cpe)J.e, TeMnepaTypa KOTOpOH 113MeHSleTCSI co BpeMeHeM
nepHO)l.HqeCKI1 no KOCHHYCOI1)J.aJIbHoMY UJII1 CI1HycOH)l.aJIbHoMY 3aKOHY
31'0 - npoCTellllIHll CJIyqall nepHo,Al1'IeCKOro H3MeHeHHSI TeMnepa-
TYPbI cpe,AbI:


( 2'1t't )
6 = F ('t) = 6 m + A cas r- .


(3. 14)


Am - Cpe,AHee 3HaqeHHe TeMnepaTypbI Cpe,AbI,
KOJIO
I1CXO,ASlT ee KOJIe6aHHSI; T - nepHO,A KOJIe6aHHII.
BBe,AeM ,AJISI npocToTbI BbIKJIa,AOK eIIl.e BeJIHqHHY
2'1t
y=oo.


KOToporo npo-


(3. 15)


npllMeHHM ,AJISI OTblCKaHHSI pa3HOCTI1 U - 8 06mylO CPOPMYJIY (3. 5);
TaK KaK


F' ('t) = -Aoo sin (00 't),


TO




u - 6 = (u o - Ao) e- m (
-
.) + Awe- n " .\ em
 sin (oo't)d'!:.

.


MHTerpaJI B npaBOll qaCTH 3Toro paBeHcTBa 6epeTCSI B KOHeqHOM BH,Ae
no H3BecTHoH <PoPMYJIe I1HTerpaJIbHOrO I1CqHCJIeHHSI:
S e ax sin (bx - c) dx = a 2
xb' la sin (bx + c) - b cas (bx + c) + const].
Dpl1MeHSISI ee, nOJIY'lHM


<
S em

em
 sin (oo'!:) d'!: = m 2 + w 2
'0


't=1:
1m sin (w't) - 00 cas (oo'!:)] _ .
't-"t'o


'It
nJISI ynpOw.eHHSI BBe,AeM yroJI
, JIelKaIUHH Me)K,AY ° H "2' onpe-
,AeJISI SI ero paBeHcTBoM
tg
 = : =
 e,
 = arc tg c;e ) . (3. 16)


11 BeJIH'lHHY


A*=


Ao,
y m 2 + w'


= A sin
.


(3 17)


Tor,Aa BbIpalKeHlIe ,AJISI u- 6 npe06pa3yeTCSI K BH,AY
U - 6 = (uo - 8 0 ) e-m(
-
.) + A*e- m < l em
 sin (oo't) cas
 -
-em
cas (oo't) sin
 _ (em'. sin (oo'!:o) cas
 _em
. cas (oo'!:) sin 13)]






1f.T1H
fJ - A = (uo - Ao)e-m(
-<.) + A* [sin (oo'!: -
) - e-m(
-
.) sin (oo't --
)] ,




C/JU3UKO-MDreMarU'leCKUe OCHOBbl U3MepeHUa renAOBblX BeAU'lUH


3AeMeHrapHDJl TeOpUJl UHepl{UU TeA U CUCTeM 6es UCrO'lHUKOB ren/la


59


58


u - 8 = [Uo - tift - A* sin (O)
O -
)] e- m (

..) + A* sin (w't' -
) (3. 18)
Ha <J:)Hr. 30 H306pa>KeHO H3MeHeHHe TeMnepaTYP U H 8 B6J1H3H
Ha4aJlbHOrO MOMeHTa BpeMeHH. no Mepe YBeJlH4eHHH BpeMeHH nepBoe
CJlaraeMOe B npaBoH 4aCTH nOCJlellHerO paBeHcTBa y6bIBaeT H CKOpO
J\eJlaeTCH HI-I'ITO>KHO MaJlbIM no cpaBHeHHIO co BTOpblM, Tal< 4TO H3Me-
HeHHe TeMnepaTypHOH pa3HOCTH U - e J\aeTCH npOCTOH cl-OPMYJlOH


rlle 6YKBOH B 0603Ha4eHa aMnJIHTYlla KOJle6aHHH TeMnepaTypLJ CHCTeMbl
OEOJlO em; OHa paBHa


8=Acos
.


(3.21)


T. e.


Ha cpHr. 31 H306pa>KeHbI KOJle6aHHH TeMnepaTYP Cpellbl H CHCTeMbl
J\JlH YllaJleHHbIx OT Ha4aJla MOMeHTOB BpeMeHH; aMnJlHTYJ\a KOJle6aHHii
T


U - 8 = A* sin (w't' -
),


(3. 19)


U,e


'"
;:'j


I T
I
_
- I
I I
1(8)
(u)


!
A


A


<!:>nr. 31. KOJIe6aHHH TeMnepaTYP CpeJ1bJ H Te.na .nJlH .naJlbHHX
MOMeHTOB BpeMeHH; TeMnepaTypa cpeJ1b1 0 H3MeHHeTCH no 3aKOHY
rapMOHHlJeCKHX KOJIe6aHHH; TeMnepaTypa U TeJla - TaK }Ke.


Tn


TeMnepaTypbI CHCTeMbI B COS
 pa3 MeHbllle aMnJlHTYJ\bl KO.1Je6aImH TeM-
nepaTypbI cpeJJ,bI; OTCTaBaHHe no cpa3e llaHO Be.1JH4HHOH
, KOTopaH
3aBliCliT OT nepHo,'J.a KOJle6aHHii T H OT nOCT05lHHOH TenJlOBOH HHepUHH
CHCTeMbI e.


-7:
<!JHr. 30. Tpe-rnii THnHlJHbIii cJIYlJai\ TenJIOB0,!t HHepUlH-l - TeMnepaTypa CpeJ1bl 0 H3Me-
HHeTCH no 3aKOHY rapMOHH4eCKHX KOJle6aHHH; H3MelleHHe TeMnepaTypbl TeJlB U B6JIH3H
lIalJaJlbHOrO MOMeHTa BpeMeHH 'to.


T. e. OHa KOJle6J1eTCH nepHOllH4eCKH no 3aKOHY npocroH CHHYCOHJ\bI,
aMnJIHTYll a A* KOTOpOH YMeHbllleHa B MaCIIITa6e sin
 no cpaBHeHHIO
C aMnJlHTY1l0H A KOJle6aImH TeMnepaTypbf CpellbI OKOJlO rpellHerO 3Ha-
'-lep.H5I 8m; 3TH KOJle6aHHH CJ\BHHYTbf no cpa3e OTHOCHTeJlbHO KOJle6a-
mli) ij Ha BeJlH4HHY
.
EOJlee Har
HJ\Hoe npeJ\CTaBJleHHe 0 KOJle6aHH5IX U nOJlY4HM, eCJm
cpaBHHM 1<0"1eoaHH5I 06eHx TeMnepaTYP 8 H U OKOJlO (J . LLJHI 3TOro
B nocJlellH
ii cpopMYJle 3aMeHHM 84epe3 ero I3bIpa>KeHHe m (3. 14), a A*
'-lepe3 A SIn
; TOflla nO.1JY4HM
U - em - A cas (w't) = A sin
 sin (w't' -
) =
= A(cos w't' + sin
 sin w't cas
 - sin 2
 cos w't');
npocTOe npe06pa30BaHHe npHBo.JHT I{ BbIpa>KeIIHIO
U - 8m = B cas ( ;- 't -
) ,



 6. CJleACTBHH 3J1eMeHTapHoH TeopHH TenJlOBOH HHepQHH
y13 aHaJlH3a nOJlY4eHHbIx B npellbIJ\Ylll.HX
 2-5 cpopMYJI (3. 7),
(3. 9), (3. 13), (3. 16), (3. 20), (3. 21) BlIllHO, KaKYIO Ba>KHYIO pOJlb BO
Bcex THnH4HbiX C.1JY4a5lX HrpaeT nOCT05lHHa51 TenJlOBOIi HHepQHH e.
B TOM CJJyqae, Korlla TeMnepaTypa cpeJJ,bl nOCT05lHHaH, OHa BCeueJlO
onpeJJ,eJI5IeT 6bIeTpOTY npH6JIH>KeHH5I CHCTeMbI K TenJlOBOMY paBHOBeCHIO
CO cpeJJ,OH; B JJ,BYX JJ,Pymx CJIY'-la5lX napaMeTp, Bblpa>KalOlll.HH TenJlOBYIO
HHepUHOHHOCTb, no HCTe4eHHH HeKOToporo BpeMeHH CTaHOBUTCH npHMO
npanopUHOHaJIbHbIM 6. HTaK


(3.10)


B I cJlYlJae, KOrJ1a 0 = const, HMeeM E;
dO
BO II cJlYlJae, KorJ1a "'{j;- = const. HMeeM bE:
B 111 CJlYlJae, Kor.n:a 6 KOJle6J1eTCH no cHHycOHJ1a,
blloMY 3BKOHY OKOJlO
"It
tt m C nepHOIlOM T. IIMeeM E. T'




3AeMeHTGpH.aJ! reOpUR UHepl4UU reA U cUcreM 6e3 ucrOIlHUKOB ren.1a


61


60


<PU3UKO-ltIGreMarUlleCKue OCHOBbl U3MepeHUU renAOBblX BeAUIIUH


A Boo6ll1.e u -
 = -eF' (E) (CM. 3. 9). P' m 3aBHCHT' OT 3aKOHa
H3MeHeHHH TeMnepaTypbI cpe)J.bl 6 co BpeMeHeM, a OTCTaBaHHe TeMne-
paTypbl CHCTeMbl OT TeMnepaTypbl cpe)J.bl -)J.JIH .,'11060ro MOMeHTa Bpe-
MeHH - nponopllHOHaJlbHO e - BeJlHqHHe, He 3aBHCHlll.ei-i HH OT Bpe-
MeHH, HH OT 3aKOHa H3MeHeHHH 6.
C
PaccMoTpHM nO)J.p06Hee BeJlHqHHY e. COrJlaCHO (3. 8) e = S.a .
T. e. onpe)J.eJlHeTCH KaK qaCTHOe OT )J.eJleHHH )J.BYX BeJlHlIHH: nepBaH,
KOTOpylO Mbl )J.JlH KpaTKOCTH 0603HaqHM
C
<l> = S' (3.22)


xapaKTepHa )J.JlH caMoii CHCTeMbl H onpe)J.eJlHeTCH TOJlbKO ee cBoiicTBaMH,
He3aBHCHMO OT BHeWHHX YCJlOBHii; BTopaH - ex. - 3aBHCHT OT Toro,
KaKOBbl YCJlOBHH TenJlo06MeHa CHCTeMbl C OKpY}KalOlll.eii cpe)J.oii: O)J.Ha
H Ta }Ke CHCTeMa MO}KeT HMeTb COBepweHHO pa3J1HqHYIO TepMHqecKYIO
HHepllHIO B 3aBHCHMOCTH OT ex..
hOT cpaKT HMeeT 60JlbWOe 3Ha'IeHHe B npH-
60poCTpoeHHH, B npaKTHKe TepMoperYJlHpOBaHHH H B TeMnepaTypHblX
H3MepeHHHX.
Bblpa}KeHHe «IiHepTHblii TepMOMeTp» He HMeeT onpe)J.eJleHHOrO CMbICJla,
eCJlH He YKa3bIBaeTCH O)J.HOBpeMeHHO nopH)J.OK K03cpcpHllHeHTa TenJlOOT-
)J.aqH cpe)J.bI, )J.JlH H3Mepel-llIH TeMnepaTYPbl KOTOpoii OH npe)J.Ha3HaqeH,
HJlH He )J.aHO npHMeqaHHe, paBHOCHJlbHOe 3TOMY YKa3aHHIO (HanpHMep,
«)J.JlH HaCbllll.eHHoro napa», «}KHD.KOCTH», «ra3a» H T. n.).
I1TaK, )J.JIH e 'HMeeM:


H. A. 5lpblweBa [7 J. Pe3IOMHpYH, CJle)J.yeT CKa3aTb, 'ITO 3Ta TeopHH )J.aeT
lleHH
e YKa3aHHH npH KOHCTpYHpOBaHHH npH60poB H npH TenJlOB
X
paCqeTaX H Ha'IHHaeT nOJlyqaTb Bce 60Jlee
HpoKoe npHMeHeHHe )J.a}Ke
B 06J1aCTHX, )J.aJleKHX OT Te
JlOBbIX H3MepeH
H. npHBO)J.HMble HH}Ke npH-
Mepbl CJlY}KaT KOHKpeTHOH HJlJlIOCTpallHeH ee npHMeHeHHH.
npe}K)J.e 'IeM K HltM nepeXO)J.HTb, BBe)J.eM Ba}KHOe B npaKTHqeCKOM
OTHoweHHH nOHHTHe 0 «BpeMeHH YCTaHOBJleHHH CHCTeMbl».
npe)J.nOJlO}KHM, 'ITO )J.aHHaH CHCTeMa ()J.JlH KOTOpoii, CJle)J.OBaTeJlbHO,
nOCTOHHHaH <l> H3BeCTHa) norpY}KeHa B )J.aHHYIO cpe)J.Y (T
K qTO H3Be:TeH
TaK)I{e H K03cpcpHllHeHT TenJlOOT)J.a'IH ex. Me}K)J.Y CHCTeMOlI H CpeD.OH) H
B Hei-i OXJla}K)J.aeTCH liJlH HarpeBaeTCH, CTpeMHCb K Ter.mepaType cpe)J.bl a,
KOTOpaH nOCTOHHHa BO BpeMeHH. 3TO 3HaqHT, qTO paCCMaTpHBaeTCH nep-
Bblii, npoCTeiiwHll, CJlY'Iaii TenJlOBOii HHepllHH. Tor)J.a no)J. «BpCMeHeM
YCTaHOBJleHHH Z CHCTeMbl» nOHHMalOT TO BpeMH, no HCreqeHHH KOTopor

pa3 H OCTb I u - (J I TeMnepaTYP CHCTeMbl H cpe)J.bl CTaHeT MeHbwe 3a)J.aHHOH
BeJlHqHHbl6. (l-IanpHMep, 0,1 rpa)J.yca). 4acTo noD. 6. nOHHMalOT TY He60Jlb

wylO pa3HocTb TeMnepaTYP, KOTopaH HaXO)J.HTCH H'a npe)J.eJle TOqHOCTH
H3MepeHHii, OCYllI.eCTBJlHeMOll nocpe)J.cTBoM HaXO)J.Hlll.erOCH B HaweM pac-
nOpH}KeHHH KOHTpOJlbHO-H3MCpHTeJlbHOrO npH60pa. 3TO BpeMH Z onpe-
D.eJlHeTCH Bbl'IHCJleImeM, eCJlH H3BeCTHO e, )J.JIH qero B paBeHcTBe (3. 7)
CJle)J.yeT nOJlO}KHTb T - To = Z, lu - 61 = 6., a Uo - (J CqHTaTb 3a)J.aH-
HbIM; Tor)J.a )J.JlH Z nOJlY'IHM
Z=e.ln( IUo
el ) (3.25)


<I>
e== -;-_


(3. 23)


npH


e = const.


<l> - «cpaKTop CHCTeMbl» - MO}KeT 6bITb BblqliCJleH, eCJlH H3BeCTHbI
TenJlOeMKOCTH C; OT)J.eJlbHbIX 'IaCTeH I, II, .., N, H3 KOTOpblX COCTOHT
CHCTeMa


.\'
C

 C; -= C] +C 2 +... +C",
i=1


(3. 24)


flpUMep 6. B Jla60paTopHbIX YCJlOBHHX HCCJle)J.yeTcH TeMnepaTypHoe
nOJle B03)J.YWHOll KaMepbl, r)J.e nOMelll.eHbl TOqHbIe Mepbl, H3MeHeHHe )J.JlHH
KOTOpblX KOHTpOJlHpyeTcH H 3aBHCHT OT TeMnepaTypbI. .D.JlH H3MepeHHH
TeMnepaTYP npHMeHeHa CHCTeMa )J.HcpcpepeHllHaJlbHblX TepMonap C 06ll1.HM
cBo6o)J.HblM cnaeM, KOTOpblii )J.OJl}KeH coxpaHHTb CBOIO TeMnepaTYPY no-
CTOHHHOii C TOqHOCTblO)J.O 0,05 rpaD.yca. 4T06bl 06eCneqHTb 3TO nOCTOS!H-
CTBO B TeqeHHe 24 qac., cnaii nOMelll.aeM B MaccHBHblii MeTaJlJlw!eCKHii
6J10K-llHJlHH)J.P, BblCOTa KOToporo paBHa OCHOBaHHIO. B 6.rIoKe, KpoMe
cnaS! TepMonapbI, HaXO)J.HTCH TOqHblii C )J.eJleHHS!MH Ha 0,02 HJlH 0,01
rpa)J.yca PTYTHblii CTeKJlHHHblii TepMOMeTp, n03BOJlHIOllI.Hii C TOqHOCTblO
)J.O 0,02-0,04 rpaD.yca KOHTpOJlHpOBaTb nOCTOHHCTBO TeMnepaTypbI cnaH
(cpHr. 32). ECJlH 6J10K )J.OCTaTOqHO MaCCHBeH, MO}KHO O}KH)J.aTb, qTO Ha
ero renJlOBOM pe}KHMe He 6Y)J.YT 3aMeTHO OTpa}KaTbCS! KOJle6aHHH TeM-
nepaTypbl B03)J.yxa Jla60paTopHH: OH 6Y)J.eT pearHpOBaTb TOJlbKO Ha ee
cpe)J.HIOIO TeMnepaTYPY.
nOCTaBHM ce6e 3a)J.aqy nO)J.06paTb pa3Mepbl 6J10Ka TaK, 'IT06bl KOJIe-
6aHHH ero TeMnepaTypbl He BbIXO)J.HJlH 3a npe)J.eJlbl -+ 0,025°; Tor)J.a Bblwe-
I1m:ldBJIeUUUe ll-'cGuBdIlue UUl:IUUUCTB3 TeMneprlTypLI (,Bo6()J.I1 1ro corm
TepMonap 6Y)J.eT Y)J.oBJleTBOpeHo. Ko.TJe6aHHH TeMDepaTYP
 B03)J.yxa


H nJlOlll.a)J.b S ee HapY}KHOii nOBepxHocTH, 'Iepe3 KOTOpylO cOBepwaeTcH
TenJl006MeH CHCTeMbl C BHeWHeii cpe)J.oi't; ex HaXO)J.HTCH 3hcnepHMeH-
TaJlbIlO HJlH no cpopMYJlaM THna (I. 10), (I. 11) HJlH (I. 12), eCJlH HapY}K-
HaS! nOBepXHCCTb HMeeT npOCTYIO cpOPMY - nJIOCKYlO, qHJlHH)J.pH'IeCKYIO,
wapoBYIO [2].
113J1o}KeHHaH Bblwe TeOpHS! OXBaTbIBaeT TOJlbKO OCHOBHbIe qepTbl
HBJleHHS! TenJlOBOH HHepllHH (HJlH, KaK elll.e rOBopS!T, OTCTaBaHHS!, 3ana-
3)J.blBaHHH), nOTOMY qTO OHa OCHOBaHa Ha )J.onYllI.eHHHX (*) H (**), KOTO-
pble He Bcer)J.a onpaB)J.blBalOTCH B )J.eiiCTBHTeJlbHOCTH; B 3THX cJlyqaS!x
ee MO}KHO paCCMaTpHBaTb KaK nepBoe npH6J1lI}KeHHe. npH Ma;TIbix 3Ha-
tJeHHHX K03cpcpHllHeHTa TenJlOOT)J.atJH - nopS!)J.Ka 2 -7- 50 - TeMnepa-
TypbI B CIICTCMC ycneBaJOT BLlpaBHHTLCJI, Il Tor)J.a TeOpllJI C xopull1ci't
TOqHOCTbIO onHCblBaeT S!BJleHHe, qTO H 6bIJlO nO)J.TBep}K)J.eHO OnbITaMH
.




62


CPU3UKO-MGTel>WTU'leCKUe OCHOBbl U3MepeHutl TenAOBblX BeAU'lUH


JIa60paTopHH nYCTb He BbIXO}!.51T 3a npe)J.eJlbl :!: 0,5°; nepHO)J. HX nYCTb
paBeH T = 30 MHH, = 0,5 'lac.
B KaqeCTBe MaTepl-laJia D.Jl5I H3rOTOBJleHH5I- UHJlHHD.pa B03bMe!\1 MeD.b
HJlH 6pOH3Y. OpH 20° YD.PJlblla51 TenJlOeMKOCTb MeD.H C200 = 0,092, nJlOT-
HOCTb 8600; n03TOMY q = 791. PellleHHe 3aD.aqH CBeD.eTC5I I< onpeD.e-
JIeHHIO paD.Hyca R UHJlHHD.pa (BJlH5IHHeM He60JlblllHX oTBepcTHH )J.JI5I
npOBOJlOqeK TepMonapbl H D.Jl5I Tep:'IOMeTpa npeHe6peraeM).
<DopMYJla (3. 22) B D.aHHOM qaCTHOM CJlyqae npHMeT BH)J.:
V 2
R3 I
<D= sC'[ = 2.rr;.I(2 + 2.
.R.2.R .c'y = 3' R.c.y.


LIJl5I paCtleTa HaM He06xoD.l-r-
Mbl ewe CPOPMYJlbl (3. 23), (3. 21)
H (3.16). <DopMYJla (3 21) n03-
BOJl5leT HaHTH
. 00 YCJlOBH5IM
3KcnepHMeHTa HaH60Jl blllee OT-
KJlOHeHHe TeMnepaTypbl CpeD.bl -
B03JJ.yxa - OT cpeD.HerO 3Haqe-
HH5I 8m paBHO (8 - 8m)max =
= A = 0,5.
COrJlaCHO HaUJeMY Tpe60Ba-
Hl-lIO, Mal<CHMaJi blloe OTKJlOHeHHe
TeMnepaTypbl 6J10Ka OT 8m D.OMKHO
6blTb (u - 8)max = B = 0,025.
I
OTclO)J.a no (3. 21) cos
 = 20 .
<l>HL 32. MeTaJlJlH4eCKHH 6J10K .nJlH CBO- 3Ha51
, no cpopMYJle (3. 16)
60J1HbIX cnaeB TepMonapbl:. onpeD.eJl HeM 8, npHqeM, no-
1- l.llfnlfHllpHqeCKIfH 6.'OK; 2 - TOqlfblH PTYTHblH CKOJlbKY COS
 MaJl, MO}/{HO cqH-
CTeKnBHHblH TepMoMeTp; 3 - TepM03neKTpollbl Tep- 1
Monapbl; 4 - MBcno ifnI{ ..eTBnn BYllB; .
 - HO"'''H TaTb tg

 COS (.! ; nOJlyqHM:
H3 TenJlOH30nsuU1oHHoro M3TepH8J1a. t'
8 = 2 T tg R = 0,5 .20 =
 .
1t t' 2rr; 1t


3


4


HaKOHeu, cpopMYJla (3. 23) n03BOJlHT HaHTH II HCKOMoe R, npH 3TOM
HY}/{HO 3HaTb IX. EY)J.eM CqHTaTb, qTO B03)J.yX B nOMeweHHH cnOKOHHblH
H 6J10K npe)J.oxpaHeH C nOMOWblO KapTOHHoro 3KpaHa OT cJlyqaHHblX
BbIHY,K)J.eHHbIX nOTOKOB B03)J.yxa. ECJlH 6.aoK HHKeJlHpOBaH HJlH nOJlH-
pOBaH, TO cr HeBeJ1HI<O, a CJle)J.OBaTeJlbHO, M8J10 H IX A . B 3THX YCJlOBH5IX
3HaLJeHHe K03cpcpHI!.HeHTa TenJlOOT)J.aqH IX He npeB30H)J.eT 5: IX = 5.
00 (3. 23) HaXO)J.HM <D = -{- Rq = IX 8 = 2; , oTKY)J.a CJle)J.yeT, qTO
24 _
R = 791 M
 3.10 ? M = 3 CM.
CJIe)J.OBaTeJlbHO, Y)j(e D.OBOJIbHO MaJleHbKUH 6J10K HCnOJlHHT' CBoe Ha-
3HaqeHUe; C 3anaCOM MO}/{HO npHH5ITb D = 2R = 8 CM.
31Ul IIp!IMCP IIUKaJLlUael, KaK U4.eHL llpuC1LIM llpHCMuM MwhHO 1CpMO-
CT3TlIpOBaTb cnaH TepMOnapbl.


.


3AeMeHTapHGll TeopUJ! UHep14UU TeA U CUCTeM 6es UCTOllHUKOB TenAG


63


llpU.Mep 7. OYCTb npH H36paHHoH B npeD.blD.yweM npHMepe 3aWHTe
cBo60D.HOr9 cna51 TepMonapbl pe)J(HM KOMHaTbI He Bbl)J.ep)J(aH, TaK qTO
u

TeMnepaTypa B03)J.yxa B HeH HaqaJla B03paCTaTb CO CKOpOCTblO

= b = I 2pao !lac-I. ECJlH TaKoe B03pacTaHHe 3aT5IHYJIOCb, TO HaM
He y)J.aCTC5I y}/{e TepMOCTaTHpOBaTb CB060D.HbIH cnaH TepMonapbJ: ero
TeMnepaTypa CTaHeT paCTH C TOH }/{e CKOpOCTblO I rpaD.. 'lac. -1, T. e.6Y)J.eT
nOBbllllaTbC5I npHMepHO Ha 1,7 COTblX rpaD.yca B MHHYTY. 3Ta CKOpOCTb
H3MCHCHH5I TeMnepaTypbl 6J10Ka (D.Jl5I )J.aJlCKHX OT HaqaJla MOMeHTOB
BpCMemJ) HC 3aBHCI-IT OT ero nOCT05lHHOH HHepUHH 8; HO OTCTaBaHHe no
TCMncpaTYpc, onpCJl.eJl5lCMOC CPOPMYJlOH (3. 13), 3aBHCHT H OT 8 H OT b.
005lCHHM 3TO CJlCD.YIOWHM pacqCTOM, paCCMOTpCB, qTO 6YD.eT qCpe3
_ 2,5 qaca noCJIc HaCTynJleHH5I pC}/{HMa JlHHCflHOro B03paCTaHH5I TCMne-
4.10- 3
paTypbl 6.noKa. .lJ..n51 Halllero 6J10Ka <D =
 791 = 10,5 (rexH. e)J..),
105
8 = -----5- = 2, I; n03ToMY no (3. 13) U
 8 = -2, I 0. ECJlH B Ha qaJle
pCllil-lMa TCMncpaTypa B03D.yxa 8 6blJla 20°, TO qepC3 2,5 qaca OHa 6Y)J.eT
paBHa 22,5°; B 3TOT MOMeHT TCMncpaTypa 6JIOKa U 6Y)J.eT paBHa u =
= 22,5 - 2,1 = 20,4°: Tpc60BaHHe, C$OPMYJlHpOBaHHoe B npHMepe 6,
He 6Y)J.eT C06J1IOD.eHO.
fJpu.Mep 8. 06pa3uoBa51 JlaTYHHaH lllKaJla, HMelOIlI.a51 CPOPMY CTep}/{H5I
KBa)J.paTHoro CeqeHH5I co CTOpOHOH B 14 MM, )J.JIHHOH I M, xpaHHTC5I
npH TeMnepaType 20° C. OepeHeceM 3TY lllKaJlY B B03)J.YlllHbJH repMocTaT,
rD.e nOJUJ.ep}/{HBaeTC5I aBTOMaTHqeCKH TeMnepaTypa 30° C H r)J.e npoH3-
BO)J.HTC5I cpaBHeHHe C 06pa3uoBoH lllKaJlOH pa60qHX lllKaJI H Mep, K03cpcpH-
UIICHT pacrrmpeHH5I BCWeCTBa KOTOpblX He H3BeCTeH. JIHHeHHblH TepMH-
qecKl-lii K03cpcpHUHeHT pacLllHpeHH5I JlaTYHH 1I3BecreH H npH 20° k =
= 17,5. 10- 1 2pao- l .
OOCTaBHM ce6e 3aD.aqy onpe)J.eJlHTb, CKOJlbKO BpeMeR-H HY}/{HO Bbl)J.ep-
}/{aTb UJKaJlY B KOMnapaTope)J.o HaLJaJla KOMnapHpOBaHH5I, eCJIH Tpe6yeTc5I
06eCneqHTb H3MepcHHe )J.JlHH C TOqHOCTblO D.O 10 MIC = 10- 2 MM.
3aD.aqa CBOD.HTC5I. K onpe)J.eJleHHIO BpeMeHH YCTaHOBJleHH5I Z TeMne-
paT,ypbl U UJKaJlbl, eCJIH TeMnepaTypa B03)J.yxa
 = const = 30° C H eCJlH
HaqaJlbHa51 TeMnepaTypa Uo = 20° C. LIaJlee He06xoD.HMO oueHHTb,
KaKoMY H3MeHeHHIO t::,. t TeMnepaTypbl UJKaJlbl cooTBeTcTByeT H3MeHeHHe
ee )J.JlHHbl B 10 MIC. ECJlH 1-)J.JlHHa ee npH r C, a 10 - npH O°C, TO k =
dl 1 M M 10 °
= lod!
 ['M' OTKY)J.a t::,.t = Tk. = 106.17,5 10-6 = -0,57 , CJle-
)J.OBaTeJlbHO, KaK TOJlbKO pa3HOCTb TeMnepaTYP UJKaJlbl H B03)J.yxa
CTaHeT MeHbUJe 3TOH BeJlHqHHbl, oUJH6Ka OTCqeTa, BbI3BaHHa51 HenOJlHblM
paBeHCTBOM HX reMnepaTYP, 6YD.eT MeHbUJe 10 MIC. He06xo)J.HMOe )J.J151
::)Toro BpeM5I HaH)J.eTC5I no (3. 25). .
CnepBa onpeD.eJl5leM e no (3. 23). I1MeeM: )J.Jl5I )J.JIHHHorO CTep}/{H5I,
nepHMeTp nOnepe'lHOrO CeqeHH5I KOToporo paBeH p, a nJlOIlI.a)J.b a,
.h l' 10 P
'V = S'c,'Y:=:::;1P'c.y = T C '1.


\


.




3AeMeHTap'iafl TeOpUfl UHepl{UU TeA U CUCTeM 6e3 UCTO'lHUKOB TenAG


65


li4


tPU3UKo-.UGTeJ.IaTU'IeCKue OCHOBbl U3AlepeHuii TenAOBblX BeAU'IUH


BeJIHlIJWY IX OueHJlM UJlcppOH 6. Tor)J.a <D = ..!.i.. 10- 3 .791 = 2 76
4 ' ,
2,76 ° 46 I'
JI e =
 = , lIac. Y'ICKOMOe BpeM51 BbJ)J.ep)KJlBaHJl51 lllKaJIbl paBHO
Z = 0,46 In ( 0

7 ) =0,46.2,862= 1,32 lIac., T. e. BeCbMa 3HallJlTeJIbHO.
He MeHblllYIO pOJIb HrpalOT JI B03MO)KHble KOJIe6aHH51 TeMnepaTYPbI
B03)J.yxa B B03)J.YlllHbIX KOMnapaTopax, oc06eHHO eCJIH cpaBHHBaeMble
MepbI HMelOT pa3JIHlIHbIe nOCT051HHble TepMH-
lIeCKOH HHepUJlJI. C aHaJIOrJ\lIHbIM 06CT051TeJIb-
CTBOM MbI BCTpeliaeMc51 JI B rpaBJlMeTpJlJl. Bbl-
WeJl3JIO)KeHHa51 TeOpJl51 n03BOJI51eT BbI51CHJlTb
BJlJl51HJle HenOCT051HCTBa TeMnepaTypHoro pe-
)KJlMa KaMep JI renJIOBoii JlHepUJIJI 06'beKTOB
Ha TOliHOCTb H3MepeHJlii.


TenJIOBa51 HHepUH51 npJl06peTaeT oc060e
3HalleHJle B TepMoperYJIJlpOBaHHH JI B TeMne-
paTypHbIX Jl3MepeHJl51X; He YlIJlTbIBa51 ee.
MO)KHO BnaCTb B rpy6b1e 01llJl6KJI. OpJlBO)J.JlMbIe
HJI)Ke npJlMepbl, OTHo'tmll,JleC51 K H3MepeHJl51M,
C KOTOpbIMJI npJlXOAJlTC51 HMeTb .lI.eJlO B caMOH

 06bIliHOH npaKTJlKe, nOCJIY)KaT KOHKpeTHOH
JlJlJI IOCTpaUJlei! npJlMeHeHJl51 BbIWeJl3J10)KeHHOH
TeOpJlJl. XOT51 TeOpJlSl JI 3J1eMeHTapHaSl, OHa
)J.aeT YKa3aHJl51 OTHOCJlTeJlbHO TeXHJlKJI 3Kcne-
pJlMeHTa JI n03BOJl51eT OueHJlTb nOp51.lI.OK
oum60K, 06YCJlOBJleHHbiX OTCTaBaHJleM rep-
MOMeTpa JlJlJI nJlpOMeTpa OT Jl3Mep51eMOH TeM-
nepaTypbl.
npu.Mep 9. Onpe)J.eJlJlM TenJIOBYIO JlHep-
UJlIO 06blKHoBeHHoro pTYTHoro CTeKJI51HHOrO
TepMoMeTpa B pa3JIHlIHbIX YCJlOBJl51X ero npJl-
MeHeHJl51.
C TOliHOCTblO, .nocTaToliHoH )J.Jl51 Tex HJI lIe-
CKJlX paclieToB, pe3epByap TepMoMeTpa MO)KHO
npJlH51Tb 3a UJlJIJlHIlP C )J.BYM51 nOJIywapJlSIMJI no KOHuaM; BbICOTa ero
paBHa Z, JI IlJlaMeTp nonepeliHoro CelleHJl51 D. KaK nOKa3aHO Ha cpJlI'. 33.
Z JI D - HapY)KHble pa3l'v1epbl - HaXO)J.51TCSI nYTeM o6Mepa. OYCTb
HaH)J.eHo Z = 12 MM, D = 2R = 5 MM.
CorJIaCHO 06Il1.eii TeOpJlJl, He06xo)J.JlMO npe}K)J.e Bcero onpe)J.eJIJlTb
KOHcTaHTY cI> - eM. (3. 22) JI (3. 23), nOToMY liTO JlMeHHO 3TOH BeJlJl-
lIJiHOH JI K03cpcpJlUJleHTOM 1'enJlOOT)J.allJl IX onpe)J.eJl51eTCSI BeJlJlllJlHa OTCTa-
B81l1lH TepMOMeTpa BO Bcex nmll'lIlLIX CJlyqaHX. TenJlUeMKOCTb repMU-
npJleMHJlKa C CJlaraeTC51 Jl3 TenJlOeMKOCTJI CTeKJla C 1 H TenJlOeMKOCTH


IHl 1


In
.3


z


.....


-

 "2 D


D


<1>Hr. 33. TepM04YBCTBif
TeJlbHaH 4aCTb }KHJ1KOCT-
HOro CTeKJlHHHOrO TepMo-
MeTpa:


I - KanHnnHp; 2 - TepMoMeT-
pW..lecK8S1 >KH.nKOCTb B K3nHn.
.'Hpe; 3 - TepMoMeTpH
ecKaH
>KHIlKOCTb 0 pe3epoyape; 4 -
CTeKIlO pe3epoyapa.


PTYTJI C 2 . 0603HallJlM YIleJIbHbIe TenJIOeMKOCTJI JI nJIOTHOCTJI 3TJlX )J.BYX
BemeeTB C 1 , 'II (CTeKJlO) JI C2, '12 (pTYTb). VIMeeM no (3. 24)
C= V 1 c 1 11 + V 2 C 212,


r)J.e VI - 06'beM, 3aH51TblH eTeKJlOM, V 2 - 06'beM, 3aH51TblH PTYTblO.
OpeHe6pera51 Jl3MeHeHJleM BeJIJllIJlHbl C"( C TeMnepaTYPoH, JlMeeM )J.JlfI
06bIlIHbiX TepMOMeTpJllleCKJlX CTeKOJI
C III = 0,186.2,59 = 0,48 Kal!,cM- 3 'cpaa- 1 ,


IlJl 51 pT.YTJI


C 2 12 = 0.033.13,6 = 0,45 Kal!.cM- 3 'cpaa- l .


2


*


3TJI BeJlJl'IHHbl HaCTOJlbKO 6J1J13KJI .lI.Pyr K )J.Pyry, a TenJlOeM'{OCn.
CTeKJIa pe3epByapa HaCTOJI bKO HeBeJlJlKa CpaBHJlTeJlbHO C TenJIOeM-
KOCTblO PTYTJI, B. HeM HaXO.ll.51IlI.eHC51, liTO MO)KHO npJlH51Tb
CIII
 C212 = cl = 0,45.


*


*


.


003TOMY C = cy. (VI + V2) = CIV, rIle V - BeCb 06'beM pe3epByapa.
LI.J151 BbIlIJlCJIeHJl51 06'beMa JI TenJ100T.lI.a1OIlI.eH nOBepXHOCTJI S pe3ep-
Byapa (UJlJIJlH.lI.P nJIIOC nOJIYlllap) .lI.OCTaTOliHO 3HaTb D JI Z. OKoHlIa-
TeJIbHO nOJIYlIJlM


1'.D2 1'.D3
C V 4' Z +T
<D = - = -,cl =
S S D Z rrD2
1'.' +2


JlJI JI


( I )
R T R
<D-- 1+- .r"V
- 2 Z + R -..


OpJlMeH5151 3T)' CPOPMYJIY K IlaHHoMY lIaCTHoMY CJIYlIalO, HaH)J.eM
<D = 2,5.10- 1 .0,5. [1 + 3(122
 2.5) ] cl =


= 1,32.10- 1 Cj KaJ/.CM- 2 'cpaa- 1 = 5,95.10- 2 KaJ/.cM- 2 'cpaa- 1 .


OYCTb nocTo51HHYIO TenJIOBOH JlHepUJIJI e He06xo)J.JlMO Bblpa3J1Tb
B MJlHYTax; TaK KaK IX, OT KOToporo 3aBJlCJlT e, HaMJI BCIOIlY )J.aHo
B TeXHJllIeCKJlX e)J.JlHliuaX, a <D Mbl Bblpa3J1JIJI B CJlCTeMe CM, ceK, KaJ/,
TO He06xo)J.JlMO HaHTJI cooTBeTcTByibIll.JlH nepeBoIlHblH MHO)KJlTeJIb
)J.JI51 7.. OH Hall)J.eTc51 nOCpe.ll.CTBOM CJIeIlYIOIlI.JlX onepau. JlH :
KIWI!' M- 2 . 'wc- 1 . cpaa- 1 = 10 3 KaJ/. 1O- 4 cM- 2 . (60)-1 MUH- 1 . cpaa- 1 =
1
600 KaJ/. CM I' MLIH I. C:jJW) I.


.


5 KOHllpSTbeO 2763




66


<!>U3UKO-MGTeMaTUlleCKue OCHOBbl U3MepeHUU Ten,WBbIX Be,WIIUH


3AeMeHTapHGR TeOpUR UHep
uu TeA U CUCTeM 6e3 UCTOIIHUKOB TenAG


67


B CI-IJIY C1I.eJlaHHbiX npe)J.noJlmKemliI HMeeM 1I.Jl5I norOlIHOH e1l.HHHI..{bi
)J.JIHHbl nl-lpOMeTpa:


DOCT05IHHaSl renJlOBOH I-IHepLll-I1-I )J.aHHoro TepMOMeTpa, B MI-lHyTax,
6Y)J.eT paBHa
5,95.10- 2 .600 357
a MI-IH. = --;- MI-IH., eCJlI-I [a.] = KKaJ! M- 2 'lac- l cpao-l.


€=


[ I ) 2 ( 1 . 2 ] .
V='It (2D1+O - 2Dl) .1 ='lto(D] +0),


S='ltD.l;


Dpl-lMeHI-lM HaH)J.eHHoe 3HaqeHi-le )J.JISI pa3J1l-1qHblX 1-13MepeHi-liL
DYCTb TepMoMeTpoM nOJlb3YlOTCSI 1I.JlSI 1-13MepeHi-lSI nocToSlHHOH TeM-
nepaTypbl B cnoKoHHoro B03)J.yxa, KOTopaSl 3apaHee H3BeCTHa; TepMOMeTp
neperpeT Ha 10° Bblllle :::noH TeMnepaTypbl (Hanpl-lMep, OT PYKI-I 1-1.(11-1 TeJla
Ha6JlIoJJ.aTeJISI) H B TaKOM COCTOSIHI-II-I OXlla)j()J.aeTCSI B B03)J.yxe nOMelll.eHI-lSI
Jla60paTOpl-ll-l.
DOCTaBI-IM Bonpoc, qepe3 CKOJIbKO BpeMeHI-I Z MI-IHYT cJ1e1l.yeT ero
OTCql-lTaTb, qT06b1 H3Mepl-lTb TeMnepaTYPY B03)J.yxa C TOqHOCTblO B 0,2°
()J.OBOJIbHO rpy6aSl TOqHOCTb!).
D.JlSI :)Toro HaM nOCJ1Y)j(I-IT cpopMYJIa (3. 25), B KOTOpOH CJ1e)J.yeT nOJlo-
)j(I-ITb U o - B = 10°, 11 = 0,2. 4T06bl onpe)J.eJlI-ITb €, He06xo)J.I-IMO ol..{e-
HHTb a.; B cnoKoHHoM I-IJlI-I nOtITI-I cnOKOHHOM B03)J.yxe cYMMapHblH
K03cpcpl-lI,\l-IeHT TenJlOOT)J.aql-l a. I..{I-IJlI-IH)J.pa MO)j(HO cql-lTaTb paBHblM
12 TeXH. e)J.., yql-lTblBaSl, qTO'CTeKJIO pe3epByapa TepMoMeTpa 1-13J1yqaeT
nOqTI-I KaK qepHOe TeJlO (Ta6J1. 1). Cne)J.yeT 3aMeTI-ITb, qTO a.« TeM 60JlbUJe,
qeM MeHbUJe )J.l-laMeTp D I..{I-IJII-IH)J.pa. OTclO)J.a B CHJlY npe)J.bl)J.Ylll.ero HaH)J.eM
357
8 = -&- :::::; 3 MI-IH. OTBeT Ha Bonpoc 0 BpeMeHI-I Bbl)J.ep)j(I-IBaHI-lSI Tep-
MOMeTpa no (3. 25) 6Y)J.eT:
10
Z=31n 0,2 =3.3,91 :::::;noqm 12 MHH.


OTCI01I.a npl-l yKa3aHHwx pa3Mepax
8
V 1+ D)
S= 0 1 8 = 1,62 CM.
1+-.-
2 DJ


HaXO)J.I-IM, 1I.aJlee, tJ>.' D.JlSI UJaMOTa I-IMeeM
C20o=0.2, c500o=0,27; Cj=O,42 KaA' CM- 3 .cpao- l ;
n03TOMY
<D = 0,42.1,62.K£lA'CM- 2 'cpao- l .


DYCTb TOT )j(e TepMOMeTp, TaK)j(e neperpeTblH Ha 10°, npl-lMeHeH )J.JlSI
H3MepeHi-lSI TeMnepaTypbl BO)J.bl B 06blqHOM TepMOCTaTe C YMepeHHblM nepe-
MeUJI-IBaHl-leM, TaK qTO a. MO)j(HO OlleHHTb llllcppOH 600 TeXH.. e)J.. 3)J.ecb
6Y)J.eT s =
o
 ::::::: 0,06 MI-IH. H Y)j(e qepe3 Z = 0,06. 3,9MI-IH. ::::::: 13,5 ceK.
nocJle norpY)j(eHI-lSI TepMoMeTpa B TepMocT8T ero TeMnepaTypa 6Y)J.eT
Ha 0,2° OTJll-lqaTbC5I OT TeMnep8Typbl TepMocTaTa.
npu.Mep 10. OxpaHHaSl Tpy6Ka repM03JIeKTpHqeCKOrO nHpoMeTpa
C XpOMeJIb-aJiIOMeJIeBOH TepMOnapoH I-IMeeT pa3Mepbl, YKa3aHHbie Ha
cpl-lr. 34: D - ee HapY)j(HbIH )J.l-laMeTp, DI - BHYTpeHHHH, 0 - TOJlIll.HHa
CTeHOK; Tpy6Ka H3rOTOBJleHa 1-13 nopHCToro IllaMOTa, nJIOTHOCTb KOToporo
paBHa "( = 1 ,5 e CM- s . PaCCql-lTaeM nOCTOSlHHYIO TenJlOBOH I-IHepl..{HH 8
npl-l YCJ10BI-ISlX, '1TO nHpOMeTp npHMeH5IeTCS! 1I.JlSI 1-13MepeHI-IS! TeMnepaTYP
B03)J.yxa B ne'lHOM npOCTpaHCTBe C TeMnepaTypOH t nop5l1l.Ka 500° C.
TaK KaK nHpOMeTpl-lqeCKaSl Tpy6Ka I-IMeeT .D.JlHHY He MeHee 1,5 MeTpa,
TO 6Y)J.eM paCCMaTpHBaTb ee KaK 6eCKOHeqHO .D.JII-IHHbIH nOJlblH llI-lJlI-IH)J.p.
KpOMe 1UIO, npeHeoperaCM IenJlUeMKUl:1 LIU I epMU
JleK I potlun 1-1 !IX apMa-
Typbl no cpaBHeHl-l1O C TenJlOeMKOCTblO MaCCHBHOH oxpaHHOH Tpy6KI-I.


OlleHKa: a. npe)J.CTaBJISleTCS! HaH60JIee 3a-
TPY1l.HHTeJlbHOH; OHa MO)j(eT 6bITb npOH3Be)J.eHa
C 1I.OCTaTOqHOH 1I.JlS! TeXHHKH TOqHOCTblO, eCJII-I
BOCnOJIb30BaTbCS! aJi bcpaKaJlOpHMeTpOM (CM.
rJl. 11); npH ero OTCYTCTBliI-I npHxo)J.HTCS! pac-
CqHTbIBaTb a., nOJlb3YSlCb q;opMYJIaMI-I (1. 10),
(1.19) 1-1 (1.20).
ECJ11-1 CqHTaTb, qTO neqHble ra3bl )J.BI-I)j(YTCSI
OqeHb Me)J.JleHHO, TO a. 6Y)J.eT nOp5l)J.Ka
12 TeXH. e)J.. H
<1> 600
s = - = ° 68. - MHH. = 34 MI-IH.
a ' 12


<1>lIr. 34. O.1\IIH H3 TepMo-
nplleMHHKoB TepM03JJeKT'
plllJeCKoro nHpOMeTpa;
1 -MaCCHBHali oxpaHHali Tpy6Ka
H3 waMOTa; 2 - TepMo3neKTpo'
Jlbl; 3 - TepMocn8H.


ECJ11-1 )j(e I-IMeeTCSI 3aMeTHaSl llHPKYJIS!lll-l51 ra30B 1-1 1I.OBOJIbHO 3aMeTHaSl
pa1l.HallHS! CTeHOK neqH, TO a. CJle)J.yeT B351Tb HeCKOJlbKO 60JIbIlle; npl-l-
MeM a. = 20; Tor)J.a HaH)J.eM
600
e = 0,67. 20 MHH. = 20,4 W.I-IH.


OnblTHOe onpe1l.eJleHi-le e 1I.aJlO 3HaqeHi-le 8 = 20,6 MI-IH.
npu.Mep 11. Dpe1l.nOJIo)j(I-IM Tenepb, qTO TepMonapa, 3aKJlJOtIeHHaSl
BHYTpl-l MaccHBHoH UJaMoToBoii Tpy6KH, 0 KOTOpOH rOBOpHJIOCb B npe1l.bl-
lI.Ylll.eM npHMepe, BbIBe1l.eHa HapY)j(Y H HenOCpe1l.CTBeHHo OMbIBaeTCS! ra-
3aMH neql-l (CJ1yqaH «rOJlOH» TepMonapbl). MeTaJlJIbl TepMonapbl: xpo-.
MeJlb, aJIIOMeJIb; TeMnepaTypa 1-13MepeHI-IS! t = 800° C; BHeUJHl-le YCJlO-
BI-IS! Te }Ke, KaK H BblUJe, TaK qTO a. ::::::: 20 TeXH. e)J..
OlleHIIM nOCToJlIIHYIO TenJlOBOII lII1epllIlII, npll'lC'1II yno]tooliM rnail
TepMonapbl npSlMoyroJlbHoMY napaJlJleJlenHne)J.y, KaK nOKa3aHO Ha
5*




3AeMeHTap'iaJl, TeOpUfl UHep4uu TeA U CUCTeM 6e3 UCTOIIHUlWB TenAG


69


68


tPU3UKO-MaTeJrlQTUlleCKue OCHOBbt U3MepeHuil TenAOBblX BeAUIIUH


cpHr. 35. a, 6 (1I.Ba TepM03JIeKTpo)J.a npHBapeHbl )J.Pyr K )J.pyry napaJI-
JIeJIbHO HX OCSlM). 0603HallaSl lIepe3 LI' L2' L3 ero pe6pa, HaXO)J.HM
V = L I L 2 L 3 ; S = 2 (LIL
 + L2L3 + L 3 L I ) - LIL2


LLJISI orreHKH q 3aMeTHM,
Bo-nepBbIX, liTO 1
8; BO-
BTOpbIX, liTO rJJaBHbIe KOM-
L3 nOHeHTbl MeTaJIJJOB TepMO-
napbl-HHKeJJb H )l{eJJe30-
HMelOT npH 800° y)J.eJJbHYIO
TenJJOeMKOCTb Ni 0,13 H
Fe 0,16, H n03ToMY MO)l{HO.
ClIHTaTb, liTO C
 0,14.
OTclO)J.a c1
 0,14.8 =
= 1,12. CJJeD.OBaTeJIbHO, $=
= c1 .
 = 1, 12 .9. 10- 3 =
= 1,01 . 10- 2 . OYCTb a=
a - ..ronaH Il TepMonapa: I - TepMo':;jneKTpo.nbI; 2 - TepMo-
cnaH; 6 - cnaH KaK npAMoyro.qbHblH napaJI.qeJIenHnell: L.I':::I = 20 TeXH. e)J.. 00 cpopMYJJe
. TonlllHHa TepM03"eKTpOllOB; L, .. 2L.. L. .. 3L.. (3. 23) nOJJYllHM
1,01.10- 2 .600 03 . 18
e= 20
 , MHH. = ceK.


H


a)


3M/If


3M/ol


v
s


.D.JJSI TOM me TepMonapbI, 3aKJJIOlIeHHOii B MaCCHBHYIO llIaMoToBYIO
Tpy6KY C TOJIIlI,HHOH CTeHOK B 23,5 MM, HaH1I.eM U - 6 =- 10.20 =--
= _200° C: OTCTaBaHHe He)J.onycTHMo 60JIbllIoe!
npu.Mep 13. OOKa)l{eM, KaK peampYIoT TepMonpHeMHHKH pa3JJHlIHbIX
npH60POB Ha nepHOD.HlIeCKHe KOJJe6aHHSI TeMnepaTypH.
OYCTb TeMnepaTypa nellH MeD.JIeHl-IO I<OJJe6JJeTCSI OKOJIO CpeD.HerO
3Hal/eHHSI 8m = 500° C C aMnJJIUYD.OH A = 50° C; nepHOD. KOJJe6aHHH
T = 30 MHH. .D.JJSI H3MepeHHSI 3TOH TeMnepaTypbI npI1MeHSlIOT OD.HH pa3
TepMonapy B MaCCHBHOM lIeXJJe, TaK liTO e MO)l{HO OueHHTb UHcppOH
15 MHH. aHaJJOrHlIHO npHMepy lQ.
HaHD.eM, HaCKOJJbKO TOllHO 6YD.eT TepMonapa BocnpOH3BOD.HTb nHKH
113MeHeHHSI TeMnepaTypbI nellH.
)J.n SI noro COrJJaCHO 06llI.eH TeopHH CJJeD.yeT HallTH B H
. 00 (3.16)
BblllHCJJSleM


6)


L3
1 + 2 (
 +
 )
L I L 2
pa3Mepb1 LI' L 2 . L3 YKa3a-
HbI Ha CPHL' 35 B MM; nepe-
BO)J.S1 HX Ei CM, nOJIYlIHM:
V 9.10- 2
S - 1 + 2 (3 + 1,5) -
= 9.10- 3 CM.


2'1t.I5
tg
 = 30 = 'it; ctg
 = 0,318;
 = 72°20'; cos
 = 0,3


11 no (3.21) 6YD.eT B = 50.0,3 = 15°.
::ho 3HatIHT, liTO TeMnepaTypa TepMonapbI Ha 35° He 6Y)J.eT 1I.0X01l.HTb
.'{O HaHBbICllIHX 3HatIeHliH TeMnepaTypbI CpeD.bI; npH 500° 3TO COCTaBHT
orpOMHYIO OllIH6KY. TaKoH nHpOMeTp COBepllIeHHO HenpHrOD.eH )J.JISI Tep-
MoperYJIHpOBaHHSI.
ECJJH BOCnOJJb30BaTbCSI rOJJOH TepMonapoii, TO B COOTBeTCTBHH
C npHMepOM 10 nOCTOSlHHYIO TenJJOBOH liHepUHH MO)l{IIO oueHHTb UHcp-
pOH e = 15 ceK. (B 60 pa3 MeHbllIe npe.'{bI11.YllI.eH), tg
 =
 , cos
 =
= 0,999; B:::::: A.
.D.pyn1MH CJJOBaMH TeXHHtIeCKaSl TepMonapa C D.HaMeTpoM TepMo-
3JJeKTpo)J.oB nOpSlD.Ka 3 MM B HaH60JIee 6JJarOnpHSlTHoM cJJYtIae, T. e.
KOrD.a OHa HaX01l.HTCSI B HenOCpeD.CTBeHHOM KOHTaKTe C ra3aMH netIu,
6Y)J.eT npaKTHtIeCKH CJIe1l.0BaTb 3a nepHO.,\HtIeCKHMU KOJJe6aHHSlMH HX
TeMnepaTypbI.
OpH 60JJee tIaCTbIX KOJIe6aHHSlX TeMnepaTypbI CpeD.bI 8 He,'\OXO)J. 6Y)J.eT
2'1t.15
60JJbllIe. TaK, HanpHMep, nycTb T = 5 MHH.; Tor)J.a tg
 = 5.60 =
'It
10 ; cos f; = 0,954; B = 47,7° H HeD.OXOD. COCTaBHT 2,3°; 3TO yme
npHeMJJeMO npH 8m nopSl)J.Ka 400-500° C.
lb 3THX npHMepOB XOpOllIO BIID.HO, HaCKOJJ bKO YCJJO)l{HSleTCSI np06JIeMa
TepMoperYJJHpOBaHHSI TenJJOBOH HHepUHeH TepMonpHeMIUlKOB H KaK ee
CJIe1l.yeT npH6JJH)I{eHHO paCCl/UTbIBaTb B npOCTeHllIHX CJIYl/aSlx.
OTcTaBaHHe no cpa3e, T. e. no BpeMeHH HaCTynJJeHHSI nHKOBbIX 3Ha-
l/eHHH TeMnepaTypbI, COrJJaCHO <jJopMYJJe (3.20), onpeD.eJJ S1eTCSI pa3-
HOCTblO 3HalleHHH BpeMeH 'r H 'r -
: T. e. OHO paBHO

T
'r
 = 2... .


11>l!r. 35. TepMonpnCMHHK - TepMonapa:


OnblT D.aJJ e = 0,23 MHH., T. e. l/HCJJO Toro me nOpSl1l. Ka .
npu.Mep 12. 0ycTbTeMnepaTypa netIH Hal/aJJa BHe3anHO nOBbIllIaTbCSI
co CKOpOCTblO 10 rpa)J.. B MHHYTY, T. e. b = 600 epaa 'Lac-I; nOCMOTpHM,
HaCKOJJbKO 6YD.eT OTCTaBaTb TeMnepaTypa nHpOMeTpa, 0 KOTOpOM rOBO-
pHTCH B npeD.bID.Ylll.HX npHMepax, eCJIH IX - O)J.HO H TO )l{e, a HMeHHO
20 TeXH. eD.. .
OTBeT Ha 3TO)' Bonpoc nOJIYllHM, npHMeHHB cpOPMYJJY (3. 13):
u - 8 = -be.
):LJJSI rOJJOH TeXHlltIeCKo!i Tep'\10napbI OTCTaBaHHe 6YD.eT paBHO U - e =
--= -10,0,3 - 3 r , I. C. H IIlJC,J.CJIa.'. ICXIlII1ICLI\uii IU'II1UCTII 1el\HIe-
paTypHbIX u3MepeHH{I.




.3 AeMeHTGpHaf/. TeOpllf/. uHep4uu TeA U CUCTeM 6e3 UCTOllHUKOB TenAa 71
OmcmafJaHue
fJ CeK E
a)
-i 72
6) e
 57
6) ,J
 ) 52


70 <!>U3UKO-MGTeMaTUIlecKlle OCHOBbl u3MepeHuil TenAOBblX BeAUIlUH


B KOHKpeTHblx c.nyqaSlx, paCCMoTpeHHblx B HaqaJle 3Toro npHMepa,
npH MeJ{J1eHHbIX KOJJe6aHHSlX TeMnepaTypbl cpeJ{bl T = 30 MHH. HaHJ{eM:
.nnH TepMonapbl B MaCCHBHOM lJeXJle 't x = 1.::3 30 = 6 MHH.;
2';.30
.D.nH rOJloH TepMonapbl 't x = 60.21t =0,25 MHH.
f1pHBeJ{eM npHMep 6blCTpb1X KOJJe6aHHH TeMnepaTypbl cpeJ{bl npH l:IX
MaJJOH aMnmnYJ{e.
f1YCTb cpeJ{a - B03J{YX HJlH ra3, TaK qTO K03cpcpHI.lHeHT renJlooTJ{aqH
K TepMOnpl1eMHHKY HeBeJJHK - nopSlJ{Ka 10-100 TeXH. eJ{. f1epHOJ{
KOJle6aHHH T = * MHH. = 6 ceK., HaH60JJbUJee OTKJlOHeHHe OT cpeJ{-
Hero 3HaqeHHSI 8 m , T. e. A = I rpaJ{.
f10cTaBHM ce6e 3aJ{aqy nOJ{06paTb HaCTOJJ bKO MaJJOHHeplUIOHHblH
TepMonpHeMHHK, qT06bI OH ycneBaJJ CJleJ],OBaTb 3a 3THMH KOJle6aHHSlMH
TeMnepaTypbl B03J],yxa C TOqHOCTblO J{O 0,1-0,2 rpaJ],. B03J],YX npeJ{-
nOJJaraeTCSI cnOKOHHbIM HJJH c.na60 UHPKYJJHPYIOIlI.HM.
CnepBa OCTaHOBHMCSI Ha MaJJOHHepUHOHHOM PTYTHOM CTeKJJSlHHOM
TepMOMeTpe. HaHMeHblllaSi B03MO'H<HaSi - npH YKa3aHHbiX BbIUJe ct -
nOCTOSlHHaSi TenJJOBOHHHepUHH J{JJSI PTYTHblX CTeKJJSlHHblX TepMOMeTpOB
MOMeT 6bITb, B cpeJ],HeM, oueHeHa UmppOH 8
 1 MHH. OTCIOJ],a tg
 =
. 1t
= 2'it.1O
 62,8; ctg
 = 0,016; nOJJaraeM:
 = 2" - Tj, rJ],e Tj > 0;
tg Tj
 Tj = 0,016; cos
 = sin Tj :::::::: Tj. OTclOJ],a B = 0,016°, T. e.
TepMOMeTp B 3THX yc.nOBHSlX H3MepeHHSI HpaHHe HHepTeH H MaJJblX
KOJJe6aHHH TeMnepaTypbI B03J],yxa C ero nOMOIll.blO YJJOBHTb nOqTH
He yJ],aeTCSI.
f103TOMY B03bMeM TOHKYIO MeJ],HO-KOHCTaHTaHOBYIO TepMonapy: J],l1a-
MeTp TepM03J1eKTpOJ],OB D = 0,4 MM. (Mbl npeJ],nOJIaraeM, qTO TeMnepa-
Typa B03J],yxa OTHOCHTeJJbHO HeBblCOKa - He BblUJe 300° C, TaK qTO
MeJ],HO-KOHCTaHTaHOBaSi TepMonapa 3J],eCb BnOJIHe npHroJ],Ha.) f1YCTb
l<opOJJeK TepMonapbl HMeeT pa3Mep Toro Me nopSlJ{Ka, qTO H TepMO-
3JJeKTpOJ],bI.
PaCCMaTpHBaSi TepMonapy KaK 6eCKOHeqHO )J.JIHHHbIH UHJJHHJ{P H CqH-
TaSi YD.eJlbHble TenJJOeMKOCTH MeJ],H H KOHCTaHTaHa B nepBOM npH6JJHMe-
HHH OJ],HHaKOBb!l\fH H paBHblMH C = 0,095 (npH 20-30° C), HaXOJ],I1M
<D = ....!.-DC 1 = 0,04 .0095.84 = ° 008'KaA'CM- 2 .z p aa- l .
4 4'"
.D.J1S1 TOHKOH npOBOJlOKH J{HaMeTpOM 0,4-0,5 MM B cnoKoHHoM B03-
J{yxe MOMHO npHHSlTb ct :::::::: ct" ;::::; 50 TeXH. e]\. f1YCTb HCKOMoe 8 MeJJa-
TeJJbHO Bblpa3HTb B MHHYTax; TorJ],a no (3. 23), nOJJb
YSlCb nepeBoJ],HbIM
MHOMIITeJJeM npHMepa 8, nOJJyqaeM:
o 008 600
8 = 50 MHH. = 0,096 MHH. ;::::; 0,1 MHH.
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PeZYARpU3G
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UMG CUCTeM 6e3 UCTO'lHUKOB TenAG


79


JlHIOTCH CJle)J.CTBHHMH OCHOBHbIX cpH3HLJeCKHX 3aKOHOB H OrOBOpeHHblX
HaMH )J.OnYllI.eHHH; 3aMeHa )l{e TOLJHbIX BbIpa)KeHHH npH6J1H)KeHHbIMU
He TOJlbKO 060CHOBbIBaeTCH LJHCTO MaTeMaTHLJeCKHMH C006pa)l{eHH HMI-! ,
HO nO)J.KpenJiHeTCH H onWTHWMH )J.aHHWMI-!.
4. PerYJlSlpHblH TenJlOBOH pe}l<HM nepBoro pO.ll.a
PaCCMOTpl-!M cHcTeMY TeJl, B KOTOpOH nepe)J.aLJa TenJia npoHcxo)J.I-!T
. COrJlaCHO 3aKoHY <Dypbe; eCJlI-! B COCTaB CHCTeMbl BXO)J.HT )KH)J.KOCTI-!,
TO npe)J.nOJIaraeTCH, LJTO nOJle TeMneparyp )KH)J.KOCTH paBHOMepHoe.
I1CTOLJHHKI-! TenJia B CI-!CTeMe OTCYTCTBYIOT; Tor)J.a, eCJlH TeMnepaTypa
cpe)J.bI e He 3aBI-!CI-!T OT BpeMeHI-!, CI-!CTeMa 6Y)J.eT OXJla)K)J.aTbCH I-!JlI-! Harpe-
BaTbCH.
113 TeOpHI-! ypaBHeHI-!H C LJaCTHblMI-! npOH3BO)J.HbIMH H3BeCTHO, LJTO
06W.HH I-!HTerpaJi ypaBHeHHH (1. 35) rJl. 1, KOTOPOMY )J.OJl)KHa y)J.oBJle-
TBOpHTb TeMnepaTypa U B moooH TOLJKe M CHCTeMbI, I-!MeeT BH)J.:


3Ta TeOpl-!H OTBeLJaeT Ha Bonpoc 0 TOM, KaK 1I3MeHHeTCH TeMnepaTYP-
Hoe nOJle CHCTeMbl C TeLJeHlIeM BpeMeHH npl-! OXJla)K)J.eHHH TeJla, npl-! HeH3-
MeHHOH BHeUIHeH 06CTaHOBKe, T. e. npH C06J1IO)J.eHI-!I-! YCJlOBH ii


e = const, ex. = const (He 3aBHCHT OT 't).


TenJloBaH 3BOJIlOLllIH CHCTeMbl BO BpeMeHI-! pacnallaeTCH Ha Tpl-! CTa)J.l-!l-!.
nepBaH 1-!3 HHX xapaKTepH3yeTcH pe3KHM BJlI-!SlHHeM Ha TeMnepaTYP-
Hoe nOJle CHCTeMbl ee HaLJaJlbHOrO COCTOHHI-!H, KOTopoe, Bo06w.e rOBopH,
HMeeT xapaKTep CJlYLJaiiHbIii - COBceM 0
u u 2
He CBSl3aHHbIH HI-! CO CBOI-!CTBaMH CH-
CTeMbl, HI-! C TeMH YCJlOBHHMI-!, B KOTO-
pblX nporeKaeT npOll.eCC OXJla)KlleHIIH
CI-!CTeMbl. 11J1J1IOCTpaLlHeH MO)KeT CJlY-
)KI-!Tb KapTi-IHa H3MeHeHI-!H co Bpe-
MeHeM reMnepaTypHoro nOJIH nJlocKoii
CTeHKI-!, OXJla)KllaeMOH O)J.HHaKOBO (npn.
O)J.HOM I-! TOM )Ke a:) c. 06eH x CTOpOH, KaK
no H306pa)l{eHO Ha cpHr. 38: )KHpHaH
JlHHHH AA' )J.aeT pacnpe)J.eJleHHe TeMne-
paTYP B creHKe B HaLJaJlbHbIH MOMeHT
BpeMeHH To; 3TO - 6ecnopH)J.OLJHaH,
CJlO)l{HaH KpHBaH. TaKoH )Ke xapaKTep
HMeeT KpHBaH BB', npe)J.CTaBJIHlOllI.aH
pacnpe)J.eJleHHe TeMnepaTyp B KaKOH-
JlH60 MOMeHT 'tl, 6J1H3KHH K HaLJaJlb-
HOMY 'to.
C TeLJeHHeM BpeMeHH BJlHHHHe Ha-
LJaJlbHbIX oc06eHHOCTeiiTeMnepaTypHoro
nOJIH Ha ero )J.aJlbHeHWee H3MeHeHHe
. CrJla)KHBaeTCH, LJTO BH)J.HO H3 xapaKTepa
JlHHHii CC ' , DD', . . . , COOTBeTCTBYIO-
W.HX 60Jlee n03)J.HHM MOMeHTaM (T2 <
< TS<' . .. npOll.eCC 1-!3 CTa)J.HH He-
ynopH)J.OLJeHHOH, «HpperYJlHpHOH», nepeXO)J.HT B CTa)J.HIO ynopSl)J.OLJeH-
HYIO, - OH CTaHOBHTCH perYJlHpHblM: BJlHHHHe HepaBHOMepHOCTeH
HaLJaJlbHOrO nOJIH CHCTeMbI Ha ee )J.aJlbHeHWee COCTOHHHe nepeCTaeT
CKa3bIBaTbCH H 3aKOH H3MeHeHHH ee TeMnepaTypHoro nOJIH npH06peTaeT
OLJeHb npoCTYIO cpOPMY, a HMeHHO TY )Ke 3KCnOHeHlI.HaJlbHYIO cpQPMY
(4.9)


::x-
U - e =
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;=0


(4.7)


(3)J.eCb HaLJaJlbHblii MOMeHT BpeMeHH 't )J.JlH npocToTbl npHH5IT paBHblM
HYJlIO).
B paBeHcTBe (4. 7) LJHCJla mj npe)J.cTaBJISIIOT c06010 pSl)J. n 0 JI O)K I-!-
T e JI b' H bl X B 0 3 pac T a 10 Ill. H X LJHCeJl:
mo < m J < m2 < . . . < m j < m/+l < . . , (*)
V j - cpYHKlI.l-!1-! TOJlbKO Koop)J.HHaT TOLJeK CI-!CTeMbl, TaK LJro OT T OHH
He 3aBHCSlT; B HX Bblpa)KeHHe BXO)J.HT cpH3HLJeCKHe KOHCTaHTW MaTepHaJlOB,
1-!3 KOTOpblX COCTOI-IT CI-ICTeMa, 1-1 K03cpcjmll.l-leHT TenJlOOT)J.aLJI-!' ex. Ha nOBepx-
HOCTI-I S; Aj - nOCTOSlHHble, He 3aBI-ICHllI.l-le HI-! OT Koop)J.HHaT, HH OT Bpe-
MeHI-!; OHH onpe)J.eJlHIOTCSI H3 HaLJaJlbHblX YCJlOBHH, T. e. 1-13 3a)J.aHI-!SI
TeMnepaTypHoro nOJIH B HaLJaJlbHblH MOMeHT 't = 0:


ex>
U o - e =
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;=0
B Bblpa)KeHI-!SI K03cpcpHlI.HeHTOB A j BXO)J.HT TaK)Ke K03cpcpHlI.HeHT TenJlO-
OT)J.aLJI-! ex. HJlI-! h (4. 3).
HaKOHell., K03cpcpHLlHeHTbi m o ' ml, . . . npe)J.CTaBJlHlC)T C060H nOCTOSlH-
Hble LJI-!CJla, He 3aBHCSlIlI.He HH OT Koop)J.HHaT npOH3BOJlbHO B3S1Toii
TOLJKI-I M CHCTeMbI (cpHr. 1), HH OT BpeMeHH; OHH 3aBI-!CHT:
1) OT cpH3HLJeCKHX CBOHCTB A" a" I' MaTepHaJlOB, 1-13 KOTOpblX CO-
CTOHT CHCTeMa;
2) OT K03cpcpHlI.HeHTa TenJlOOT)J.aLJH ex.;
3) OT cpOpMW, pa3MepoB H B3aHMHoro pacnOJlO)KeHHSI qacreii CHCTeMbl.
vb HepaBeHcTB (*) I-! BblWenepeLJHCJleHHWX CBOHCTB 061l1.ero HHTe-
rpaJia (4. 7) ypaBHeHHSI <DYPbe H 113 06061l1.eHHH pe3YJlbTaTOB onblTOB
C OXJl8>K1eIllH'M II lIarpenaIllICM TCJI nLITcKBIOT H OCllonllLlc 33KOHbi TeopHIl
perYJlSlpHOrO pe)KI-IMa (nepBoro pO)J.a).


(4.8)


U pez - 6 = AoV oe-m.
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B UJIOCKOH CTeHKC, oXJIa}K.naeMoH O.nH-
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"2 < ...; 'to-HalJaJIbHblii MOMeHT;
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KpHBble, COOTBeTCTBYlOll.lHe MOMeH-
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C KOTOpOi'! MbI BCTpeTHJlI-!Cb npH H3YLJeHHH O)J.HOrO H3 THnHLJHblX CJlYLJaeB
B 3J1eMeHTapHOH TeOp1-!1-! rJl. 3 - CM. cpOPMYJlY (3. 7). .
<DopMYJla (4.9) HBJlHeTCH CJle)J.CTBl-!eM CBOHCTB 061l1.ero I-IHTerpaJia
(4. 7) ypaBHeHHH <DYPbe (1. 35) H HepaBeHcTB (*).
tlw6bI 310 HblHCHHlb, npe)J.IIUJlUlhI1M, LJW paCCMaIpHBalOlOI MUMeHTbI
BpeMeHI-!, Bce 60Jlee Y)J.aJl5IIOIlI.HeCSI OT HaLJaJlbHOrO MOMeHTa or = O.




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82


C/JU3UKO-IttaTeMaTU'teCKue OCHOBbt U3MepeHUU Ten/tOBbIX BeAU'tUH


Pe2yARpusaquR TenAOB020 pe
UMa CUCTeM 6es UCTO'tHUKOB TenAa


IIJHI B 6YPHOnepeMellllIBaeMOH BO,Qe). KaJKJJ:oMY a 6Y,QeT COOTBeT-
CTBOBaTb CBoe m; npli B03paCTaHlili TenJ10BOrO B03JJ:eHCTBIiH cpeJJ:bl Ha
CHCTeMY, a MepOH B03,QeHCTBIiH II 6YJJ:eT a, B03paCTaeT 11 O!BeTHaH
peaKlJ. HH CIiCTeMbl - B03paCTaeT m ('leM m 60J1bWe, TeM 6blCTpeli OXJ1a-
}l{JJ:aeTCH - KaK eJJ:IIHoe lJ.eJ10e - clicTeMa). 31'0 B03paCTaHHe nO,QqlI-
H5IeTCH BTOPOMY OCHOBHOMY 3aKOHY Teoplill perYJ15IpHOrO pe}l{lIMa -
aCIIMnTOTlIl.JeCIWMY: npli YBeJ1lIl.JeHIIIi a B03pacTaHlie m 3aMe,QJ1HeTCH, a
npli YCTpeMJ1eHIIIi a K 6ecKoHeI.JHOCTII m
m CTpeMHTCH K KOHe'lHoH BeJ1l1I.JIIHe.
J],PymMII CJ10BaMII, eCJ1H paCCMaTplI-
BaTb m KaK IpYHI<lJ.lIlO a,
m = f (0.),


6Y,QeT o,gIIHaKOB - OHI1 CTaHYT napaJ1J1eJ1bHO ,QPyr ,Qpyry. J],J1H MOMeHTOB
BpeMeHII 60J1ee paHHI1X, HeJKeJ111 or*, rpalpliK OXJ1aJK,QeHIIH He IIMeeT npHMO-


iJ


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m",


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t
<I>lfr. 42. 113MeHeHHe TeMnepaTypHblX
pa3HOCTeii III If 11 2 - CM. qJlfL 41 -- B
n
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y.
orapl!qJMHlJeCKOii aHaMopqJ03e;
't - HalJaJlO HacTynJIeHIfH pery.
Hp-
HOro pe}KIfMa.


II 11306pa311Tb :JTY IpYHKlJ.l1lO rpalplIl.Je-
CKII, OTKJ1a,QblBa5I no OCIi a6clJ.licc a,
a no OCIi Op,QlIIIaT m, TO nOJlYI.JIITCH Bbl-
nYKJ1aH KpliBaH (lpHr. 44) C aCIIMnTO-
Toti, napaJ1J1eJ1bHOH OCH a6ClJ.HCC II
Haxo,Q5Illl.eikH 01' Hee Ha paccToHHHII


<I>IfL 41. KplfBbIe H3MeHeHlfH TeM'
nepaTypHblX pa3HocTeH {tl = u 1 - B
If 11 2 = u 2 - 6 co BpeMeHeM 't; Ul-
TeMnepaTypa B TOlJKe M 1 clfcTeMbl,
u2--TeMnepaTypa B .npyroH ee TOlJKe
M 2 (cp. C qJHL 44); 6 = const- TeM-
nepaTypa CpeJ1bI. 't*-HalJaJIO HacTY-
nJIeHIfH perYJlHpHoro pe}KHMa.


aD a, CX2 cxJ a"


rY


<I>lfr. 44. ACHMnTOTlf4ecKHii 3aKOH
B03pacTaHlfH TeMna tTl perYJlHpHoro
ox.
a}K.neHHH CHCTeMbl C 6ecnpeJ1eJl.b-
HblM B03pacTaHHeM K03qxpHlJ,lfeHTa
TenJIOOT ;(alJlf a.


(4. 13)


moo = Iim f (a).
a
oo


JI!fHeHHOH 1p0pMbl: npli or < or* Ha 1p0PMY rpalpHl<a elll.e OKa3bIBalOT 'BJ1IIH-
Hlie HaqaJ1bHbIe YCJ10BIIH (4.8), MeCTOn0J10}l{eHHC TOI.JKII 11 np.
ECJ111 CIiCTeMa B HaqaJ1bHbIH MOMeHT
HarpeTa ,QOCTaTOqHO paBHOMepHO, TO
qaCTb rpalpliKa 01' or = 0 ,go or = -.*
HMeeT ,QJ1H TOqeK B ee u.eHTpaJ1bHOH
qaCTH npaBIIJ1bHYlO BbmYKJ1YlO 1p0PMY,
ImK 1I306pa}l{eHO - Ha Ipl1r. 43.
Bce CKa3aHHoe OTHOCIiTCH He TOJ1bKO
K «TeMnepaType B TOqKe» U: TO }l{e
caMoe OTHOCIiTCH II K KaIWH-J11I60 1I3
cpe,QHIIX TeMnepaTYP - qaCTII 06'beMa
H qaCTII nOBepXHocTII CIiCTeMbI 1IJ111
Bcefl CIiCTeMbI.


IhaK, eCJ1H ,QaHHa5I CI1CTeMa oX.TW}I{,QaeTcH B YCJ10BII51X Bce B03pacTa-
10IllH x a:


trrp = m


l(j
9
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7
6
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a o < al < a2 < . . . - 00,
TO ee Tel'\m oXJ1aJK,geHIIH B03pacTaeT, HO He 6ecnpe,geJ1bHO:
mo < m l < m2 < . . . - moo = KOHeqHOe I.JIICJ10.


q



 6. PerYJlSlpHblH pe>KHM OJJ:HopoJJ:Horo TeJla
PaCCMOTpl1M npOCTeHWI1H CJ1YI.JaH, Kor,ga CIiCTeMa CBO,QIlTCH K O,gHOMY
TeJ1Y, COCTOHlll.eMY 1I3 O,QHopo,gHoro II 1I30TponHoro Belll.eCTBa, T. e. TaKora
Belll.ecTBa, ,QJ1H KOToporo A 11 a He 3aBHCHT 01' HanpaBJ1eHH5I y,geJ1bHOrO
TenJ10BOrO nOTOK3 (HeKOTopLle CJ1yqal1 aHI130TpOnHbiX TeJ1 6Y,QYT pac-
CMOTpeHbI ,gaJ1ee B
 4 rJ1. 15). B 3TOM cJ1yqae npe,QcTaBJ15IeTC5I B03MO}l{HbiM
c,geJ1aTb 60J1ee onpe,QeJ1eHHOe 3aKJ11OI.JeHlIe OTHOCIITeJ1bHO BH,Qa IpYHKL(IIO-
HaJ1bHOH 3aBHCHMOCTH (4.12).
npe>K,ge l.JeM K 'HeMY nepexo,TI,HTb, OCTaHOBHMC5I Ha O,gHOM nOH5ITIiH,
IIrpalOlll.eM 60J1bWYlO pOJ1b B cOBpeMeHHoM yqeHlI1i 0 TenJ1006MeHe, -
Ha TaK Ha3bIBaeMbIX KpHTepl15IX nO,Q06H5I [2], [8 L C aH3J10mqHbIMH
BeJ1lIqlIHaMII Mbl BCTpeqaeMCH H B TeOp111I perYJ15IpHOrO pe>KHMa. no,g 3THM
TCpMHHOM nOHIiMalOT aJ1re6paHQeCKHe BbIpa}l{eHHH IIYJ1eBOli pa3MepHocTH,
(OCTaBJ1eHllbIe 113 IpII3lIQeCKI1X II reOMeTpUI.JeCKI1X BeJ1lIqIIH, IWTOpblMIi
!lUJ1L3YIOTCH npll MaTCMaTIIQCCKoi'1 xap3l<TepIICTIiKP K3K0r0-Tj1lf)() flr()-
lJ.ecca. CaMblH }l{e npOlJ.eCC MaTeMaTlIqeCKI1 ODIICbIBaeTCH TaK, '11'0 ADa UJ1H
6*


LniJ;,//
2



 5. ACHMnTOTHQeCKHH 3aKOH
B03pacTaHHSI TeMna OXJla>K,ll,eHHSI
CHCTeMbl m C B03pacTaHHeM
K03<l>4mLl.HeHTa TenJlOOTJJ:aQH a
npe,Qn0J10}l{I1M, 'ITO 1I3GpaHa BnOJ1He
onpe,Qe,,1eHHaH CHCTeMa TeJ1 H Ha6J11O-
,QaeTCH TeMn ee OXJ1aJK,geHHH 11J11I
HarpeBaHIiH B pa3J1lIqHbIX YCJ10BHHX -
npli pa3JIHQHbIX 3HaQeHHHX K03lplpHlJ.lIeHTa TenJ100T,gaql1 a, HaqlIHaH
01' CrlMLIX MrlJ1LIX (IIanpIlMep, OXJ1[1)K,QCHIIe B cnOI\oiillUM BU3,Qyxe) ,QO
caMbIX 60JIbIllHX (HanpHMep, HarpeBaHlie B paCnJ1aBJ1eHHOM MeTaJ1J1e


,
o


t1 t n
<I>HL 43. nOJlYJIOraplfqJMH4ecKlfH rpa-
qJlfK 1f3MeHeHlfH TeMnepaTypbI B ueH-
TpaJIbHOii lJaCTIf TeJIa, KorJ\a HalJa-Jlb-
Hoe nooe TeMnepaTYP TeJIa - paBHO-
MepHoe.




84


CPU3U1W-MUTeMaTU'IeClcue OCHOBbl U3MepeHuit TenllOBblx BeAU'IUH


PeZYllRpU3DU,UR TenllOBOZO pe
UMa CUCTeM 6e3 UCTO'lILUKOB TenAU


85


6o
ee KaKIIX-JIII60 KpliTepliH CBH3bIBatOTC5I Me)K,QY C060H IpYHKUIiOHaJIb-
HOli 3aBliCIiMOCTbIO. COCTaB KpliTeplieB YCTaHaBJIIiBaeTCH TeOpliell no,Qo-
61IH; OHa )Ke YCTaHaBJJllBaeT, lJTO Me)K,QY TaKIiMII IIMeHHO KpliTeplIHMII
CYllI.eCTByeT 3aBIiCIiMOCTb. Ee BII,Q HaXO,QIITCH, rJIaBHbIM 06pa30M, Ha OCHO-
BaHli1i 3KcneplIMeHTaJJbHbIX II OTlJaCTII TeOpeTHlJeCKIiX IICCJJe,QOBaHlill.
B BbIpa)KeHlIe Toro IIJJII IIHoro KpliTepliH MorYT BXO.QIITb II nepeMeHHbIe
BeJIlIlJlIHbI, HanpliMep BpeMH II Koop,QIIHaTbI TOlJeK TeJIa,.1I nOCTOHHHbIe,
HanpliMep, TenJJonpOBO.L\HOCTb BellI.eCTBa. KpliTeplfli OlJeHb lJaCTO 0603Ha-
lJaIOTC5I HalJaJIbHbIMII 6YKBaMlf lpaMIiJIlIi-'r YlJeHbIX, KOTOpbIM npIIHa,QJIe)KaT
oco6eHHO Ba)KHbIe HCCJIe,QOBaHIiH B ,QaHHOH 06JIaCTIi. flpliMepOM KpliTeplI5I
MO)KeT CJIY)KIITb BbIpa)KeHlIe :
 , r,Qe 6YKBOll Lo 0603HalJeH on p e,QeJI H 10-
o
llI.IIH IIJIIi rJIaBHbIH pa3Mep TeJIa [21. [91. 110 I. [13]; 3TOT KpliTeplill
Ha3bIBalOT «KpliTeplieM <Pypbe» II 0603HalJ31OT Fo, T. e. nepBblMIi ,QBYM5I
6YKBaMII lpaMIiJIlili 3Toro 3HaMeHIITora 1p1I31IKa.
B HaCTOHlueM YlJe6HlIKe He 1I3JIaraeTCH TeopliH nO,Qo6IIH; 3TOMY OT,QeJJY
HaYKH nplIMeHIITeJIbI-IO K TenJIOBbIM npoueccaM nOCBHlueI-I pH,Q CneUlIaJIb-
HbIX TPY.L\OB [2], [10] II .L\p. X3paKTep KpliTeplIaJIbHbIX 3aBlicliMocTeii
II npliMep HX IIcnOJIb30BaHliH .L\JJH TenJIOBbIX paClJeTOB nplIBe,QeHbI B
 3
rJI. 1.
Kp"Tep"aJlbllbIe BeJl"IJ"Hbl P " Hi. AHaJIIITHlJeCKaH TeopHH TenJJO-
npOBO,QHOCTlI n03BOJIHeT BbIpa3lITb 06llI.1IU: 3aKOH [4.12] nocpe,QcTBoM
ypaBI-IeHII
, CBH3bIBalOllI.erO Me)K,QY C060H ,QBa KpliTeplIH, KOTopbIe
B ,QaJIbHelIWeM 0603HalJeHbI 6YKBaMII Bi 1-1 p.
CTPYKTypa nepBoro onpe,QeJIHeTC5I paBeHcTBoM
Bi = a"A Lo = Loh. (4. 14)


YpaBHeHlIe (4.16\ n03BOJJ1!eT YCTaHoBIITb Ii COOTHOIlleHlIe Mem.l\Y
p II Bi.
BeJIlIlJHHbl m II IX, CBH3b Me)K,QY KOTOpbIMII ,QaHa paBeHcTBoM (4.16),
CneUlilplIlJHbI .L\JIH .QaHHora TeJJa II ,QJIH ,QaHHbIX BHeWHIIX YCJIOBIIH, 1160
Bce BXO,QHllI.lIe B 3TO paBeHcTBo BeJIIi 'III HbI CYTb IpIl3H'-H'CKIIe BeJI II 'III HbI,
HMelOlUlie Ka)K.L\aH CBOIO pa3MepHocTb II CBOll 1p1I3I1lJeCI<HH CMbICJI.
L L

YMHO)KIIM BeJJIIlJlIH Y IX B (4.16) Ha
 , a m Ha -. CBH3b (4.16)
A a
Me)K,QY m 1-1 IX TOf,Qa o6paTHTCH B CBH3b Me)K.L\Y p II Bi BII,Qa


p= t (Bi), Bi = q;(p),


(4. 18)


r,Qe Lo -TaK Ha3bIBaeMblll «onpe,QeJIHIOllI.Hll» pa3Mep TeJJa; 3TO KaKoH-
HH6Y,Qb xapaKTepHbIll reoMeTpwIecKIiH napaMeTp .L\aHHOrO TeJIa, Hanpll-
Mep TOJIlUliHa nJJaCTlIHKH; pa,QIIYc IIJJII .L\lIaMeTp UIIJJIIH.L\pa II T. ,Q.
BeJIlIlJlIHY Bi nplIHHTO Ha3bIBaTb «KpliTeplleM EIIO». CTPYKTypa BTO-
pora KpliTepllH ,Q3Ha qJOPMY JIOH
L 1 1m
p= ° Q'


(4. 15)


KOTopaH 6Y.L\eT ,QeHCTBlITeJJbHa He TOJJbKO ,QJIH ,QaHHoro TeJIa 113 .L\aHHOrO
MaTeplIaJIa, He TOJIbKO .L\JJ5I ,QaHHoro K034.JlpIiUlleHTa Ten JJOOT,QalJH, HO
6Y,QeT MaTeMaTlIlJeCKlI onlICbIBaTb BceB03MO)KHbIe perYJJHpHbIe pe)KIIMbI
Bcex TeJI ,QaHHOll <j:>OpMbI; B aHaJJHTlIlJeCKOe Bblpa)KeHlle CBH3H (4.18)
Me)K,QY p l:I Bi Y)Ke He BXO.L\HT napaMeTpbI, 3aBliCHlUlie OT CBoikTB MaTe-
pllaJIa TeJJa H OT era pa3MepOB. TaKIiM 06pa30M, ypaBHeHIIH (4.18) HB-
JI5IIOTCH o606llI.eHlIeM (4.16).
AI-IaJIliTlIlJeCKlill BII,Q ypaBHeHHH (4.18) YJ{aJIOCb YCTaHoBHTb ,QJIH
HeMHOflIX IWHKpeTHbIx CJIYlJaeB, Kor;J.a lpopMa Te.lJa HeCJJO)KHa [3 J.
HO H B 3TH X CJJYlJafIX MaTeMaTlllJeCKaH CTopOHa Bonpoca ,QO Toro rpOM03J{Ka,
lJTO ,QJIH npaKTIIKH He06xo,QIIMO ,QaTb KaKOe-JIII60 ynpOllI.eHHOe peIlleHlIe
3a,QalJlI, n03BOJIHIOllI.ee OXBaTIITb YHIIBepCaJIbHOH 3aBliCliMOCTblO TeJI

pa3JIlIlJHOll <j:>OpMbi. flp1I6JJII)KeHHOe peweHlIe C TOlJHOCTblO, J{OCTaTOlJHOIi
,QJIH npaKTlIlJeCKIiX ueJJeH, Y,QaJJOCb nOJIYlJlITb, BBe,QH HOBbIe KpliTepHII M
II H, 0 IWTOPbIX pelJb 6Y,QeT HlI)Ke.
Kp"TepliH W; Koalf!4mLl."eHT If!OPMbl K. DpeJ{BapHTeJIbHO OCTaHO-
BIiMCH Ha cBollCTBax KpliTepliH \If.
113 (4.16) BII,QHO, lJTO TeMn m perYJIHpHOra OXJIa)K,QeHHH H30Tpon-
HOro II O,QHopo,QHoro TeJIa JII060H If!OPMbI npll KOHelJHOM 3HalJeHllii K03cp-
If!IIUlIeHTa Ten_'JOOT.L\alJlI a nponOpUIIOI-I3JJeH nOBepxHocTH TeJ1a II o6paTHo
nponopUIiOHaJIeH era TenJJOeMKOCTIi. K03lpdJllUHeI-IT nponopUHOHaJIbHOCTII
eCTb npolI3Be,QeHlIe 1I3 IX Ha KpllTeplill W. KpliTepHll W MOHOTOHHO
y6bIBaeT npH B03paCTaHlili IX II HBJIHeTCH If!YHKulIeH KpliTepliH Bi =
= Loh, ,Qpo6eli LlILo, L2ILo, . . . H IpOpMbI TeJJa. HalI60JIbWee 3HalJeHlIe W
IIMeeT, Kor,Qa IX MaJJO IIJJI-I, TOlIHee, Kor,Qa Bi MaJIO, T. e. B YCJJOBIIHX MaJJoii
HHTeHCIIBHOCTli B03.D.eHCTBIiH cpe,QbI; B 3TOM cJIYlJae W = 1; 3TO 5ICHO
II H3 1p1I31-1lJeCKOrO CMbICJIa KpHTepHH W - CM. (4.17): npli MaJIbIX a.
Kor,Qa OTHlIM3eM3H OT TeJIa MOllI.HOCTb MaJIa. TeMnepaTYPbl BHYTPH TeJIa
ycneBalOT BblpaBHHTbcH; TeMnepaTypHoe nOJIe 6Y.L\eT paBHoMepHbIM
(% = lj,), T. e. W = 1. Do Mepe B03pacTaHliH a pa3HocTb TeMnepaTYP
nOBepXHOCTlI TeJIa H cpeJ{bI 6Y,QeT CTpeMHTbCH K HYJIIO - B CllJIY (4.5)
H (4.6), (tis
 B), T. e. Wa-)-oo
 0 IIJIIi WBI+OO
O.
D03TOMY a W npli IX -+ 00 nplIHlIMaeT BII,Q HeOnpe.L\eJJeHHOCTH 00.0;
U.L\Hdh.U lim (IX \If), B Cl-IJI
 u6llI.eI U aCliMlIlU111lJeCl\0I U J<.II,ull<.l l\Uj
dC I dlllUI
m C IX, 6Y,QeT IJIICJIO KOHelJHOe (f1loo - BeJIUlJHHa KOHelJHaH). B ,QaHHO
l


J],JIH TBep,Qoro TeJIa m II IX, KaK nOKa3bIBaeT TeopliH [31. CBH3aHbi
Me)K,QY C060H paBeHCTBOM


S
m=aW-
C '


(4.16)


B KOTOP.OM W eCTb HOBbIH KpliTeplIH, paBHbIH OTHoweHlIlO cpe,QHell nOBepx-
HOCTHOli TeMnepaTypbI TeJIa -3-s K era cpe,QHeli 06'beMHOll TeMnepaType -3-v
(OTClJllTbIBaH llX OT TeMnepaTypbI B oKPY)KalOllI.ell cpe,QbI):
q' lis Us -11
--,;; - uv':'- If '


(4. 17)




86


ctJU3UI\O-MaTC .11aTU'ICC/CUC OCHOBbt U3MepCHUU TCnllOBblX BCllU'IUH


PCZYllJlpU3al{UJI TCnllOB020 pC3/CUMa CUCTCM 6C3 UCTO'lHUlCOB TCnlla


87


nVTeM Mbl 3aMeH5IeM I<pHTepl1H Bi HOBblM I<pHTepHeM H, a I<pHTepHH p -
I<pHTepl1eM M. I1x CTpYKTypa )J.aHa cpopMYJIaMH:
H a. KS -hL' M= mK =
. (4.20)
=Tv-' a moo
J],JI5I Ka}l{)J.oH reOMeTpl1lJeCKOil £pOpMbl TeJIa, nO,Q,QalOrueHC5I aHaJIHTH-
lJeCKOM aClJeT MO}l{HO YCTaHOBI1Tb CBH3b Me}l{,QY M I1 H. ECJIH 3aTeM
Y 6 p y, a rt--U lJeC KI1 TO )J.JIH Bcex TeJI OHH j\O.l}1{Hbl HalJHHaTbCH
HX 1130 pa3HTb rp 't'U ,
c O,QHOH TOlJKH (OHI1 I1CXO,QHT H3
HalJaJIa KoopJJ:HHaT) II npH YCTpeM- (0
JIeHIiH H K 6eCKOHelJHOCTH ,QOJI}I{-
Hbl CTpeMHTbCH K 1. OKa3aJIOCb,
lJTO KpHBble Q8
M=M(H) (4.21)


lJaCTHOM cJIYlJae, Kor,Qa CIiCTeMa CBO,QHTCH K O,QHOMY TeJIY, OKa3bIBaeTCH,
lJTO moo OlJeHb npOCTO CBH3aHO co CBOUCTBaMH TeJIa: moo H TeMnepaTYpo-
npOBO,QHOCTb BerueCTBa TeJIa npHMO nponopUHOHaJIbHbl, TaK lJTO MO}l{HO
HanHcaTb


, K - K03cpcpHUl1eHT nponopUIIOHaJIbHOCTH; OH HMeeT pa3MepHOCTb
nJIorua,QH, BbIpa}l{aeTC5I B .«2 H 3aBHCHT 01' £pOpMbl H pa3MepOB TeJIa.
J],JIH HeKOTopblX cpOpM K MO}l{HO HaUTH paClJeTHblM nYTeM, 3HaH
OTpe3KH L o , Ll. . ., CJIY}I{aruHe ,QJIH onHcaHHH £pOpMbl TeJIa CM. npH-
Mepbl 14-16); ,QJIH JIl060H £pOpMbl
era MO}l{HO HaUTH nOJIY3KcnepH-
MeHTaJIbHblM nYTeM.


EMY npHCBoeHO, nO,Q06HO BeJIH-
lJHHe L*, C KOTOpOH Mbl BCTpeTHJIHCb
B
 5 r JI.
, H3-3BaHHe «K03qxlmUHeH-
Ta cpOpMbl TeJIa»; B TO BpeMH KaK L *
CB5I3aH C 06H3aTeJIbHblM 3HaHIieM pacnOJIO}l{eHHH H £pOpMbl ,QBYX H30-
TepMHlJeCKHX nOBepXHOCTeu (L';: OTHOCHTCH K CTaUHOHapHOMY TenJIOBOMY
pe}l{HMY Ii IIMee,. pa3MepHOCTb ,QJIHHbl), 1W3<PCPHUHeHT K HMeeT pa3Mep-
HOCTb nJIorua.n.lJ, HBbllJHCJIHlOl ero, He 3HaH H30TepMHlJeCKHX nOBepXHOCTei1.
YHJlBepCaJIbHble Kpl1Tepl111 M 11 H. <PopMYJIa (4. 18) rpa£pHlJecKH
H306pa3HTC5I Ha cpur. 45 I<pHBOU, 'HMelOruei1 COBepweHHO TOT}I{e xapaKTep,
lJTO H KpHBaH cpHr. 44.
OAHaKo KpHBaH p = t(Bi) ,Qa)j{e ,QJI5I ,QaHHou cpOpMbl 6Y,QeT pacnoJIa-
raTbCH no-pa3HoMY B 3aBHCHMOCTU 01' Bbl60pa pa3Mepa Lo. KOTOpblti
cOBepweHHo npOH3BOJIeH; eCJIH }l{e Mbl B03bMeM KaKYlO-JIu60 ,QPyrylO £pop-
MY. TO nOJIYlJHM ,QPyrylO KPHBYlO, KOTOpaH onHTb-TaKU pacnOJIO}l{UTCH
I1HalJe. Ha cpHr. 46 nOKa3aHbl ,QBe TaKHe KpuBble I II II; Ka}l{,QaH U3 HUX
SIBJIHeTCH rpa£pHlJeCKHM npe,QcTaBJIeHUeM Bcex perYJIHpHblX p e}l{H MOB ,
B KOTOpblX MO}l{eT npe6bIBaTb ,QaHHoe Te.1JO.
flOCTaBHM cBoeii UeJIblO COBMeCTUTb Bce KpuBble 3Toro pO,Qa; ,QJISI
"JTnrn HY>KHn npp>K!lp Rf' p r0 f'ORl\.feCTUTb UX :JCUl\.fnTflThT, 3 )J.3JIPP nO,QrllfHIITh
onpe.qe.neHHOMY YCJIOBHIO UeJIHlJUHY L o ' KOTOpml npOU3BQJTI;>Ha. aTHM


fJ


{J



81


<I>Hr. 45. 3aKoH B03pacTaHHH TeMna
perYJlHpHOrO OXJIa}KJ1eHHH (HJIlI ua-
rpeBaHHH) TeJIa r
 KpHTepHaJlbUOH
qJopMe P= Lo V : B 3aBHCHMOCTH
OT B03pacTaHHH KO
Hu.HeHTa TenJIO-
OTJ1alJH, TO}Ke BbIpa}KeHHOm B KPH-
TepHaJIbHOii qJopMe Bi = Loh


a = K . moo.


(4. 19)


[J,.fiJ,


H


I


,QJIH reoMeTpUlJeCKH lOBepweHHo
pa3JIHlJHbIX TeJI - wapa, napa.l-
JIeJI{
nHne,Qa, UHJIUH,Qpa H ,Qp. -
HaCTOJIblW 6JIH3KO pacnOJIaralOT-
CH ,QPyr K ,QPyry, lJTO npaKTHlJeCKU
Bce ceMeHCTBO HX MO}l{HO 3aMe-
HUTb O,QHOH ocpe,QHeHHOH KPHBOti,
npOBe.n.eHHOH Me}l{,Qy KpUBblMH 1
H 2 cpur. 47. 3,Qecb KpUBa51 1
OTHOCHTCH K nJIaCTHHKe, 2 - K
wapy, 3
 K UUJII1H,QPY.
flpH 3TOM IIMeeM:


Bi/,Bi/ J
<I>Hr. 46. rpaqJHKH 3aBHCHMOCTH P = f (Bi)
J1JJH TeJl I 11 II pa3J1l1lJHOH qJOpMbl: PI =
= h (Bi l ) Pu = fII (Bi II ).


M= HW.


(4.22)


M .....-
3" .......,.




f'z
I
f


0,6


0,4


4


B


12



 16


<I>Hr. 47. YHHBepCaJIbHaH npH6JIH}KeHHaH
3aBHCHMOCTb M = M (H) TeMna peryJIHp-
Horo OXJla}KJ1eHHH HJlH HarpeBaHHH TeJIa
JII060H 4>opMbi OT 0606rn.eHHoro KpHTepHH
f>Ho.


3aBl1CHMOCTb (4.21) 3HalJHTeJIbHO TOlJHee 6bIJIa u npe,QcTaBJIeHa
H. A. 5IpbIweBblM npocTOH aHaJIHTHlJeCKOH £pOPMYJIOU:
M I (4. 23)
111' = H = J/H2+ I,437H + I
Ta6JI. 2. CB5I3bIBalOWaH BeJIHlJUH
1 M, H 11 111', npHBO,QI1TCH HH}I{e.
flpU.Mef 14. Onpe,QeJIHM cpe,QHHH K03qxpHUHeHT TenJIOOT,QalJH ,QJIHH-
1I0ro CTep}l{H5I H3 KepaMHKH, nOnepelJHOe CelJeHHe KOToporo, I1MelOruee
li)OPMY paBHocTopoHHero TpeyrOJIbHHKa, MO}l{eT 6blTb 3aMeHeHO C


Ta-
TOlJHOU TOlJHOCTblO KpyroBblM ceKTopoM C yrJIOM npl1 BepwHHe -
cpHr b.:
' 3TOU cpOpMbl H3BeCTHO aHaJII1THlJeCKOe Bblpa}l{eHUe BeJIHlJl1Hbl K:
R2 . V 1CR2 -!i.
K = 40.1 ; Lo =
 = 6.21CR - 12 .


n03TOMY


., p
H=T'T


m p2
M-a 40'




88


CPU3UKO-MaTeMaTU'IeCKue OCHOBbl U3MepeHUil TenllOBblX BellU'lUH


PeZYAJlpU3al{UJI TenAOBOZO pe3/CUMa CUCTeM 6e3 UCTO'lHUKOB TenAG


89


Ta6AUI{a 2


np0J10Jl}KeHHe Ta6J1. 2


H I \IT I M II H I \IT I M
0,00 1.000 0.00000 0.66 0,648 0,428
0,01 0,993 0,00993 0.68 0.640 0,435
0,02 0.986 0,01972 0,70 0.633 0,443
0,04 0,972 0,0389 0,72 0,626 0.451
0,06 0,958 0,0575 0,74 0,619 0.458
0,08 0,944 0,0755 0,76 0,612 0,465
0,10 0,931 0,0931 0,78 0,605 0,472
0.12 0,918 0.1l0 0,80 0,599 0,479
0.14 0,905 0,123 0,82 0,592 0,485
0,16 0,892 0,143 0.84 0,586 0,.492
0,18 0,880 0,158 0.86 0.580 0,499
0.20 0,868 0,174 0,88 0,574 0,505
0,22 0,856 0,188 0,90 0,568 0,511
0,24 0,84.4 0,203 0,92 0,562 0,517
0,26 0,833 0,216 0,94 0,556 0,523
0,28 0,822 0,230 0,96 0.550 0,528
0,30 0,811 0,243 0,98 0,545 0,534
0,32 0.800 0,256 1.00 0,539 0,539
0,34 0,789 0,268 1,05 0,526 0.552
0,36 0.779 0,280 1,10 0,514 0,565
0.38 0,769 0,292 1,15 0,502 0,577
0,40 0.759 0,304 1.20 0,490 0,588
0,42 0.749 0,314 1.25 0,479 0,599
0,44 0,740 0,326 1,30 0,468 0,608
0,46 0,731 0,336 1,35 0,458 0,618
0,48 0,722 0.346 1,40 0,448 0,627
0,50 0,713 0,356 1.45 0,439 0,636
0,52 0,704 0,366 1,50 0,430 0,645
0,54 0.695 0,375 155 0,421 0,653
0,56 0,687 0,385 1,60 0,413 0,661
0,58 0,679 0,394 1,65 0,405 (j,668
0,60 0,671 0,403 1,70 0,397 0,675
0,62 0.663 0.411 1,75 0,390 0,682
0,64 0.655 0.419 , 1.80 0.383 0,689


H I \IT I M II H I II' I M
1,85 0,376 0,696 I 5,5 0.160 0,880
1.90 0,369 0,701 I 6,0 0,148 0,889
1.95 0,363 0,708 6,5 0,138 0.897
2.00 0,356 0,712 7,0 0,129 0,903
2.1 0,344 0,722 7,5 0,121 0,908
2.2 0,333 0,733 8.0 0.1l4 0,913
2,3 0,323 0,742 8,5 0,108 0.918
2.4 0,313 0,751 9,0 0.1026 0,929
2.5 0.304 0,760 9,5 0.0976 0.927
2,6 0,295 0,768 10,0 0,0931 0,931
2,7 0,287 0,775 10,5 0,0890 0,934
2,8 0,279 0.781 11.0 0,0852 0.937
2,9 0.271 0,786 ll,5 0,0817 0,940
3,0 0,264 0,792 12,0 0,0785 0,942
3,1 0,257 0.797 12,5 0.0755 0,944
3.2 0,251 0,803 13,0 0,0728 0,946
3,3 0,245 0.809 13,5 0.0703 0,948
3,4 0,239 0.814 14,0 0,0678 0,950
3,5 0,234 0,819 14,5 0,0655 0,952
3,6 0,229 0,824 15.0 0,0636 0,954
3,7 0,224 0,828 16,0 0,0598 0,957
3,8 0,219 0.832 17,0 0,0564 0,959
3,9 0,214 0,836 18,0 0,0534 0.961
4,0 0,210 0,839 19,0 0,0507 0,963
4,1 0,205 0,841 20 0,0482 0,965
4.2 0,201 0,844 21 0.0460 0,967
4,3 0,197 0,847 22 0,0440 0,968
4,4 0,193 0.851 23 0,0421 0.969
4.5 0,190 0.854 24 0,0404 0,970
4,6 0,186 0,857 25 0,0389 0,972
4,7 0,183 0,860 30 0,0325 0,975
4,8 0,180 0,863 40 0,0245 0,980
4,9 0,177 0,866 50 0,0197 0,986
5.0 0.174 o Rfiq 100 o ooqqq 0993
II co 0,00000 1,000




c1JU3UKo-MUTeMaTll'ieCKUe OCHOBbl U3MepeHuit TenllOBblX BellU'iUH


PeZYAflpU3UI{Ufl TenAOBOZO pe:JICUltla CUCTeM 6e3 UCTO'iHUKOB Tenlla


91


90


COrJIaCHO 06llI.HM 1p0PMYJJaM (4. 20). CTopoHa TI:JeyrOJIbHHKa (pa,QHYc
CeqeHHH) nycTb paBHa R = 6 CM.
CTep:>KeHb nOMellI.eH B neqb H HarpeBaeTCH B HeH, npHqeM TeMnepaTypa
neqH t = 200° C; OnblTHblM nYTeM, KaK :no onHcaHO ,QaJIee, B
 4 rJIa-
BbI 7, H3 Ha6mo.D.eHHH Ha,Q perYJIHpHblM HarpeBaHHeM CTep:>KHH HaH-
.D.eHO m = 10. KOHcTaHTbI MaTepHaJIa cTeplliHH npH 200° C H3BeCTlIbI
H paBHbI (B TeXH. e,Q.):
A=I,O; 1=2170; c=0,25; a=18.10- 4 .


J],JIH OTbICKaHHH m CJIe,QyeT' HaHTH M, a ,QJIH 3Toro npe:>K,Qe Bcero OTbl-
CKliBaeM H, qTO, B CBOlO Oqepe,Qb, Tpe6yeT 3HaHHH L. J],JIH L HMeeM:
V 2 I
S = '3 R. 2+ctg 100 = O,0869R


II


KS R2
L = V = 121.0,0869R = 0,0951 R.


a}


6)


-


85
H no nepBoH H3 1p0PMYJI (4.20) 6Y,QeT paBHO: H = "[5.0,0951.0,1=
= 0,54. no Ta6JI. 6 onpe,QeJIHeM M = 0,375 H no BTOpOH H3 Ip0P-
MYJI (4. 20)
a.M 25.5.10- 4
m = K = 100.10_4 .121.0,375 =


w ,.,
.
-


TlJ


30


=-


= 11,6 qaC 1 .







HL 48 CTep}KeHb a H 3KBHIJaJleHTHb1H eMY
CTep)l(eHb 6.



UL 49 KOHYC, oXJla}KJ\3IOIu,uHCH
B cTpye ra3a; HanpaBJIeHHe CTPYH
nOKa3aHO CTpeJlKaMH.


CTeneHb HepaBHoMepHocTH TeMne-
P aT yp Horo nOJIH W (no Ta6JI. 2) rn 50 D
'FHL . OJIywap.
0,695.
flpu.Mep 16. nOJIYlllap (R = 10 CM), H3rOTOBJIeHHbIH H3 XpO-
MHTa (lpHr. 50), OXJIa:>K,QaeTCH npH Tex :>Ke YCJIOBHHX (a = 85). J],JIH
GOJIYlllapa K03lpcjmuHeHT tPoPMbl BbIqHCJIHeTCH no cjJopMYJIe K = 2:':5 .
Haii,QeM \If H m.
)1JIH nOJIYlllapa


Ll 10.36.10-4
JIH HaXO:>K,QeHHH a npe:>K,Qe Bcero BbJqHCJIHM M: M = 18,4.10- 4 .40 =
= 0,49; no rpalpHKY HJIH Ta6JI. 6 nOJIYlJaeM H = 0,82; nOCJIe lJero Hi.1XO-
,QHM


3"A 3.0,82
ct = R' H = 6.10- 2 = 41 .


V 2 K.S'
S = 8" R; L = -----v- = 0,22R;


J],JIH cY:>K,QeuHH 0 CTeneHH HepaBHO!VIepHOCTu TeI\mepaTypHoro nOJIH
paCCMaTpl1BaeMOro 06beKTa nOJIb3yeMcH KpJ1TepJ1eM W, KOTOpbllf, 3HaH H,
uaxo,QHM no (4.23) HJIH H3 Ta6JIHUbI: B ,QaHHOM cJIYlJae MbI BU.D.UM, lJTO \P =
= 0,59: HepaBHoMepHocTb TeMnepaTypHoro nOJIH 3HaqHTeJIbHa, 11 elO
Hl1KOHM 06pa30M HeJJb3H npeHe6pelJb.
flpu.Mep 15. no,Q CTPyeli ra3a, HMelOllI.erO TeMnepaTYPY 500°C,OXJJ3:>K-
,QaeTCH neperpeTbIii BbIllle 3TOH TeMnepaTypbI XpOMJ1TOBbIii KOHYC C lllapo-
BbIM OCHOBaHHeM; yroJI npH BeplllHHe KOHyca 40°; cpe,QHHfi K03lpcjm-
LI.HeHT TenJIOOT,QalJH a OT ra3a K KOHYCY H3BeCTeH H paBeH 85. Onpe,Ql'JJIIM
TeMn OXJIaiK,QeHHH 3Toro 06'bCKTa, 3Hi.1H, qTO IpH3H'IeCKHe KOHCTaHTbl
xpoMHTa, H3 KOToporo H3rOTOBJJeH KOHYC, CJIC,QYlOIIJ.He:
A = 1,5; a = 25,5. 10- 4 ; "( = 2730 (npJ1 t = 500 0 C).
J],mJ KOHyca C wapoBbIM OCHOBaHHeM Ii yrJIOM npu BeplllliHe 400
R2
K03lplpliUHeHT IpOpMbI HaH,QeH BbIlJHCJIeHHeM H paBeH K = ill r,Qe R -
06pd3
 IOllI.dH h.OUYLd, PdBlW}1 pdJ1.U>L) Wdpd (ilJUI. 13). n) LlL D IWWlIII
CJI
lJae R = 10 CM = 0,1 M.


85
H = 1:5.0,22.0,1 = 1,25: M = 0,60; W = 0,48,


T. e, CTeneHb HepaBHoMepHocTH leMnepaTypHoro nOJJH 3HalJl-lTeJIbHa


m=


25,5.10- 4 .0,60.20.45 - 3 13 --1
100.10- 4 -, lJac


Eho 3HaqliT. qTO, XOTH nOJJywap OXJJ3>K,QaeTCH ropa3,Q0 Me,QJJeHHee
KOHyca, paccMoTpeHHoro paHee, CTeneHb HepaBHoMepHocTH ero TeMne-
paTypHoro nOJJH 60JIbWe, qeM KOHyca.
npOli3Be.D.H aijaJIorJ1lJHblii paClJeT ,QJIH nOJIywapa, 06'beM IWTOporo
. paBeH 06'beMY KOHyca npe,Qbl,QYllI.erO npliMcpa (a pa,QHYc TaJ\oro nOJIY-
wapa paBeH 3,91 CM), npli.D.eM K CJIe,QYlOllI.HM UHlppaM:
H=0,49; M = 0,35; qr = 0,72; m = 12 Qac 1 .




92


t!>U3U1CO-MareMarUflec/we OCHOBbl U3MepeHUU renAOBblX BellUflUH


3TO 3HalJ1IT, lJTO, HeCMOTpH Ha B03paCTaHlie 'feMna OXJla:>K,QeHII1J,
KaK II CJle,QOBaJlO O)KII,QaTb. HepaBHOMepHOCTb TeMnepaTYPHOrO nOJlH
HeCKOJlbKO YMeHbllIlIJlaCb, 1I60 BTOpOH nOJlYlliap nOlJTII B,QBOe MeHbllIe
(no JlIIHeHHbIM pa3MepaM) nepBoro.



 7. PerYJlSlpHblH pe>KHM SlJl.pa C paBHoMepHoH TeMnepaTYPoH,
oKpY>KeHHoro TOHKOH TenJlOH30JlSl
HOHHOH 060Jl04KOH


Km< MbI YBIIJJ:HM HII)Ke B
 8, ::nOT lJaCTHbIH BII,Q CIiCTeMbI HMeeT npm<TH-
lJeChOe nplIMeHeHlIe. 3,QeCb 6YJJ:eT C006lll.eHO ee npII6J11I)KeHHOe, CTIIJlII30-
BaHHoe, pellIeHlIe.
PaCCMa TpHBaeMa SI
3JJ:eCb CIiCTeMa COCTOHT
1I3 ,QBYX lJaCTeH: SI,Qpa A
II H3 oKPY)KalOlll.eM ero'co
Bcex CTOpOH 060JlOlJKII B,
_ KOTOpa5I OT,QeJlHeT ero
COB
pllIeHHO OT HapY)K-
- HOM cpeJJ:bI E (qmr. 51).
C.D.eJlaeM CJleJJ:YIOlll.lIe
JJ:onYlll.eHIIH:
I) 060JlOlJKa - «TOH-
KaH», T. e. MaKCIIMaJlb-
HaH TOJllll.HHa MaJla no
CpaBHeHl-IIO C HaHMeHb-
llIHM H3 JlIIHeHHbIx pa3-
MepoBH,Qpa.npaKTHlJeCKH
rOBopH IIX OTHOllIeHlIe
He npeBbIlliaeT -1/8;
2) nOJle Tel\mepaTYP
JI,Qpa - nOlJTII paBHo-
MepHoe; TOlJHee roBOpH, rpa,QlIeHTbI TeMnepaTYP BHYTPIi 5I,Qpa B ,QeC5ITIUI
pa3 MeHbllIe rpa,QlIeHToB TeMnepaTYP BHYTPIi 060JlOlJKII;
3) HapY)KHa5I nOBepxHocTb H,Qpa, BeJlHlJIIHY KOTOpOH 0603HalJlIM S',
HMeeT nJlaBHbIe OlJepTaHH5I; .D.OnYCTHMO TOJlbKO He60JlbLUOe lJlICJlO JlHHHH:
cOnp5I)KeHHH Me)K,QY lJaCT5IMH nOBepxHocTII no,Q npHMbIM HJlII TynbIMH
yrJlaMH (npIiMep: OrpaHHlJeHHbIH LI.IIJlHH.l\p); BHYTPIi H.D.pa MorYT 6bITb
H nOJlOCTII, HO He conpHKacalOLUlieCH C 060JlOlJKOH, a OT,QeJleHHbIe OT Hee
MeTaJlJlOM SlJJ:pa;
4) 060JlOlJKa MO)K-eT 6bITb O,QHOCJlOH:HOH: IIJlII COCTOHTb 1I3 HeCKOJlbI<HX
CJlOeB; TOJlLUliHa ee 0 TaKLKe MO)KeT 6bITb He BnOJlHe O.D.IIHaKOBOH BO Bcex
TOlJKaX;
5) K03qxplILI.lIeHT TenJlOOT.l\alJlI 6Y,QeM C1IHTaTb tPYHKUlIeH: KoopJJ:IIHaT
TOlJeK nOBepxHocTII S;
G) lCIlJIOCMhuclLlU U(jUJIULJhH C nu LJ,)dliHl:lllllU I,; It:IlJlueMKUl,;lblO
HJ{pa C'
O)KHO npeHe6pclJb.






<I>Hr. 51. 51.npo A paBHoMepHoii TeMnepaTypbl, 3aKJlIO'
lJeHHOe B TenJIOH30JJHl.lHOHHYIO 060JIOlJKY B.


Pe2YARpu3aquR renllOB020 pe
uMa cucreM 6e3 ucrOflHUKOB renAa


93


npH 3TlIX ,QonYlll.eHIIHX perYJlHpHbIH: TenJlOBOH pe)KIIM CHCTeMbI MO)KeT
6bITb MaTeMaTHlJeCKH H306 p a)KeH ypaBHeHHeM


C
m.S' (P,,+ Pn) = I,
p P
3' II 7f IIMelOT CMbICJI.


(4.24)


B KOTOpOM 0603HalJeHlI5I
1 JI. 2.
ECJlH no aHaJlOflIli C ynoTpe6J1eHHblM B
 7
BBe,QeM 0603HalJeHlIe
k' = 1
I ·
-;- + Pa


YKa3aHHbIH: B
 6,


r JI. 2 K03tPtPH LI.lIeHTOM k


(4.25)


.


1
r,Qe
 = P n 0603HalJaeT conpOTIIBJleIme TenJlOnepex0JJ:Y OT S K OKPY-
)KalOrn;eH: clicTeMY cpe,Qe E, TO tP0PMYJlY (4. 24) MO)KHO npe,QcTaBIITb
B BH.D.e:


C' ,
m.S'k = 1.


(4. 26)


TaKYIO npoCTYIO tP0PMY MO)KHO nplI,QaTb ypaBHeHlI10 (4.12) B pac-
CMaTpliBaeMOM 3,QeCb, XOT5I H lJaCTHOM, HO JJ:aJleKO He npOCTOM cJlYlJae
CHCTeMbI; tPopMYJla (4.26) HJlII (4.24) oTpaLKaeT rJlaBHbIe lJepTbI perYJlHp-
Horo ee oXJla)K.D.eHl1H, II npHro,QHocTb JJ:aHHbIX tP0PMYJI ,QJlH onHcaHIiH 3Toro
HBJleHIIH 060cHoB'aHa OTlJaCTII TeOpeTlIlJeCKH, OTlJaCTII onbITHbIM nYTeM;
cYLUeCTBeHHO, lJT06bI B npouecce onbITa 6bIJlH C06J1IO,QeHbI ,QonYlll.eHIIH 1-
6 [3 L
no,Q a, 0, k' B npe.l\bl,QYlll.IIX tP0pMYJlaX CJle,QyeT nOHHMaTb ocpeJJ:HeH-
HbIe no nOBepxHocTII S 3HalJeHHH 3THX BeJllIlJlIH.


"



 8. PerYJlSlpHblH pe>KHM npoCTeHuIHx J1.BYXCOCTaBHbIX Ten - rnapOBoro
H nnocKoro 6HKaJlOpHMeTpOB (npH a
 (0)
Ba)KHOe npHMeHeHlIe B TenJlOBblX 1I3MepeHlIHX nOJlYlJlIJla TeOplI5I
perYJI5lpHOrO OXJla)K,QeHHH TeJl, Ha3BaHHblX YCJlODHO «6HKa.TIOpllMeTpaMII
perYJl5Ipnoro pe)KIIMa». 3TO - TBep.D.bIe TeJla, COCT05Illl.He 1I3 H,Qpa I,
IIMelOLUero paBHoMepHYIO TeMnepaTYPY, 06bllJHO MenlJlJlHlJeCl<oro, II 06J1e-
ralOlllero ero co Bcex CTOpOH CJlOH I I TenJlOII30JlHLI.IIOHHOro MaTeplIaJla
.(tPHP. 52).
B llIapoBoM 6lIKa,,10pliMeTpe H.l\PO I II llIapOBaH 060JlOIIl<a I I pacno-
JlO)KeHbl KOHueHTplIlJeCKH (tPlir. 53). B nJlOCKOM 6HKaJlOpliMeTpe nJlOcK'o-
napaJlJleJlbHaH nJlaCTIIHKa co Bcex CTOpOH oKPY)KeHa TenJlOII30JlHUIIOH-
-HbIM MaTepW;lJlOM (tPllr. 54), IIMelOLUIiM TOJlLUHHY o.
TOlJHaH TeopllH perYJlHpHoro pe)KIIMa 3TlIX TeJl npocTeHllIei-i tPOpMbI
B npe,QnOJlO)KeHIIIi KOHelJHOrO a nplIBo,QIIT K CJlO)KHbIM tPopMYJlaM, KOTO-
pI.I:'.' nC1IW !I(, )'1\<1.10('1. npn';{<1TL BIIA, npnrO)l.nbIii .D.JlH npm\lll'll:LKIIX
npIIJlO)KeHIIII; OJJ:HaKO MaTeMaTHlJeCKOe onlicaHlIe perYJlHpHOrO pe)KIIMa




PezYARpu3UIlUR TenAOBOZO pe3/CUMa CUCTeM 6e3 UCTO'lHUKOB TenAU


95


9!


4JU3U1w-MUTeMaTU'IeCKUe OCHDBbl U3MepeHUU TenAOBbix BeAU'IUH


"ITI-IX TeJI 3HaQlITeJIbHO ynpOIll.aeTC5I, ecJm: OXJIa}!{
eHlIe npOIICXO
IH
B YCJI OB II 51 X IX
 00,
PYrHMH CJIOBaMIi -KOr
a TeMnepaTypa t
a IIX Ha-
PY}!{HOH nOBepXHOCTIi 5 nOMep}!{IIBaeTC5I nOCT05lHHOH, paBHoli 8 (eM.

 2, rJI. 4). 11TaK, nycTb:
(]. -.. 00 HJIH Us = 8 = const (*)
(He 3aBHCliT 01' or).
B 31'OM npe
nOJIO}!{eHIIIi perYJI5IpHblH
pe}!{IIM 060lIX 6HKaJIOplIMe1'pOB MO>KHO
onlIca1'b npn nOMOllI.1I KplI1'eplieB 5 II )l\,
KOTopble onpe
eJI5IIOTC5I CJIe
YIOllI.IIMIi pa-
BeHC1'BaMlf :

JI5I wapa


,


<DHr. 52. DHKa.nopHMeTp (061l.l HiI
CJIYlJall):


npHqeM D' II 1) 0003HaqalOT BHYTpeHHIIH II HapY>KHblll
lIaMeTpbl TenJIO-
1I30JI5I UIIOHHoro CJI05l;
<P - «KOHC1'aH1'a 5I
pa», paBHa51


C'
<P=Y'


(4. 31)


r
e 5' - IIOBepXHOCTb 51
pa, C' - era TenJIOeMKOCTb. 5YKBOH C 0603-
Ha qen3 TenJIOeMKOCTb Ten JIOIl 30JI51 UIIOHHoro CJI05l.
KplITepHH 5 II )I( C13513aHbl Me}!{
y coc5oii 3aBliCHMOCTblO


5 = f OK, I).


(4. 32)


5 = I<pP m;
1 ( D D' ) C'
)1(=3 1+15'+7) c;


5 ' ,U
t 0,9
0.8
0,7
0.6
0.5
0,4
0.3
0.2
0,1
o


ACUMnmoma


(4. 27)


I
I .......v -- f--_ \ \ \ \1
-:7 /' v /" \ \ L
O
/' ,/ \ L=03
j/ L
; L
0.7
'j


1 - H!tpO paBHOMepHoii reMneparypbl;
/I - CJloii renJlOH30JlHL\HH.
JI5I nJI3CTHHKH


(4, 28)


5 = <pP m'


BXO
5IllI.He B npaBble qaC1'H 31'lIX
CMblCJI :


D'
I=If'


.C'
)I\=y.
CPOPMYJI 6YKBbi
t
P=-=-,
I.


M


1

W
2

U
3



9

)/{
<Dur. 55. rpa4JHK 3aBUCUMOCTII B = f OK, [j 1\JHI mapo.
BOro 6HKaJIOpHMeTpa npH 3. -+ 00.


IA


D


<Dllr. 53 lllapoBoH 6HKaJIO-
pHMeTp.


IIMelOT cJIe
YIOIll.lIii
(4. 29)


rpacpllqeCKH OHa npe
CTaBJI5IeTC5I B Bn
e ceMeik1'Ba KpIIBbIX, KaK 31'0
1I306pa}!{cno Ha cplff. 55. DJIacTHHKe cOOTBeTCTByeT Ta 113 3THX KpHBblX,
D'

JI5I IWTOpOll If
 I.
OTMenlM xapaKTepHYIO oc06eHHOCTb JII060H 1I3 3THX KpIIBbIX: npH
3a
amlOM 3HaqeHlIli KpHTeplI5I D'ID = I 31'0 - 13bInVKJIa51 l<pIlBa51
C C6llI.eH aCHMnTOTOH, napaJIJIeJIbHOll OCIi a6CUlfCC (OCII')I() II HaXO
5I-
Ill.ellC5I 01' 3TOH OCII Ha paCCTOHHIIII, paBHoM 1, TaK KaK


lim 5 = 1 npn JIIOUOM
' = t.
)!{+JO


( 4. 33)


rpacpHK c!mf. 55 nOCTpoell Ha OCHOBaHIiH
aHHbIX Ta6JI. 3, KOTOpa51
3
eCb II npIIBo;.\IITCfl.



 9. Pe310Me npe.ll,blJl.YLIJ.ero
Pe31OMlIPY5I CO
ep}!{aHlie 31'011 rJIaBbl H conOCTaBJI5I5I ec C aHa.'In30M
TaKoro }!{e cJIyqa5l. paccMoTpeHHoro B rJI. 3 (0 TepMnqeCKOii IIHepUIIII),
npnxo
IIM K 3aKJIIOqeHHIO, qTO nCXO
Hoe ypaBHeHlIe (4.9) npe
CTaBJI5IeT
LuGurl lie '!fu II IIUC , I,dl
 uGuGIll.clillC .:IJICl\IClllapllul u )
cIlJlIClIIIH (3.7),
01' KOTopora OHO OTJIlflWeTC5IlIaJIWlHeM K03cpcpnuneHTa U (x, y, z), npHHII-


<DHr 54. n.
OCKHH 6HKaJlopu-
MeTp cHMMeTpHlJHOrO THna.


r
e 0 - TOJIllI.IIHa TenJIOlI30JI5IUlIOHHOro CJI05l, T. e. B cJIyqae wapa
o = LJ - LJ (4 30)
2




96


CPU,3UKO-MaTeMaTU'IeCKUe OCHOBbt U.3MepeHUli TenAoBbtx BeAU'IUH


PeZYARpU3UtiUR TenAOBOZO pe:J/CUMa CUCTeM 6e3 UCTO'lHUlWB TenAa


97


T a6Au/{a 3
«1>YHKQHSI B = f ()K, I) .nJlH mapoBoro H nJlOCKOrO 6HKaJlOpHMeTpoB
B = f (I, )K)


npO.i\OJl}KeHHe Ta611. 3



\ 0,3 I 0,4 I 0,5 I 0.6 I 0,7 I 0,8 I 0,9 I I,D
0,1 0,412 0,362 0,320 0,292 0,268 0,242 0,220 0,208
0,2 0,602 0,540 0,490 0,452 0,425 0,392 0,370 O,35D
0,3 0.712 0,658 0,602 0,565 0,528 0,500 0,472 0,450
0,4 0,778 0,725 0,680 0,640 0,600 0,578 0,545 0.522
0,5 0.818 0,770 0.730 0,692 0,660 0,632 0,605 0,580
0,6 0,842 0,800 0,765 0,732 0,702 0,672 0,648 0,625
0,7 0,865 0,825 0.792 0,762 0,735 0,708 0,682 0,660
0,8 0,880 0.845 0,815 0,788 0,762 0,735 0,712 0,692
0,9 0,895 0,862 0,835 0,810 0,785 0,760 0,738 0,720
1,0 0,905 0,875 .0,850 0,828 0,805 0,780 0,760 0,742
1,1 0,915 0,885 0.862 0,842 0,820 0,798 0,778 0,762
1,2 0,920 0,895 0,875 0,855 0,835 0.815 0,792 0,778
1,3 0,928 0,902 0,882 0,862 0,845 0,828 0,805 0,790
1,4 0,932 0,908 0,888 0,870 0,854 0,835 0,818 0,800
1,5 0,935 0,915 0,895 0,878 0,862 0,845 0,828 0,810
1,6 0,940 0,920 0,900 0,885 0,870 0,852 0,838 0.820
1,7 0,942 0,925 0,908 0,890 0,875 0,860 0,845 0,830
1,8 0,946 0,928 0,910 0,895 0,880 0,870 0,852 0,838
1,9 0,950 0,932 0,912 0,900 0,888 0,872 0,860 0,£45
2,0 0,952 0,935 0,918 0,905 0.892 0,878 0,866 0,855
2,1 0,955 0,938 0,920 0,908 0,898 0.885 0,872 0,860
2,2 0,958 0,940 0,922 0,912 0,902 0,888 0,878 0,866
2,3 0,962 0,942 0,928 0,915 0,906 0,892 0,882 0,870
2,4 0,962 0,945 0,930 0,920 0,910 0.898 0,888 0,875
2,5 0,962 0,948 0,934 0.922 0,912 0.£00 0,8,,0 0.880
2,6 0,965 0,950 0,936 0,925 0,915 0,902 0,894 0,885
2,7 0,965 0.950 0,938 0.928 0.918 0,906 0,898 0,888
2,8 0,965 0,952 0,940 0,930 0,918 0,910 0,900 0,890
2,9 0,968 0,954 0,941 0,931 0,920 0,912 0,902 0,8J5
3,0 0,968 0,955 0,942 0.932 0,922 0,914 0.905 0,898
3,1 0,968 0,956 0,944 0,935 0,925 0,916 0,908 0,901
3,2 0,970 0,958 0,945 0,938 0,928 0,920 0910 () C)I'\<;



I 0,3 .1 0.4 I 0.5 I 0,6 I 0,7 I 0.8 I 0,9 I I,D
3,3 0.970 0,960 0.948 0.939 0.930 0.920' 0,912 0,908
3,4 0,970 0.960 0.949 0.940 0,932 0.925 0,915 0,910
3.5 0,970 0,960 0,950 0,942 0,935 0.928 0,918 0,912
n p H M e 4 a H H e. 311eCb npellnOJlO>l<eHo. 'ITO a
 00.


MaIOwero qHCJIeHHOe 3HaqeHHe, paBHoe 1, Kor,Qa pacope,QeJIeHHe TeMoepa-
TYP B CHCTeMe CTaHOBHTC5I paBHOMepHbIM. KaJ( MbI BH,QeJIH B HaCT05lI.I
eH
rJIaBe, HepaBHOMepHOCTb TeMoepaTypHoro nOJI5I KpaHHe YCJIO:>KHHJIa
MaTeMaTHqeCKYIO TpaKTOBKY 3a,QaqH.
ECTb H ,QPyra51 HOBa51 qepTa ,noH TpaKToBKH: MbI oT6poCHJ1H Bce qJ1eHbI
p5l,Qa (4.7), npe,QCTaBJ151IOruero o6ruee peIlleHHe 3a,QaQH, KpoMe nepBoro,
a OHH KaK pa3 cooTBeTcTBYIOT COCT05lHH5IM CHCTeMbI, npe,QIllecTBYIOWHM
HacTynJIeHHIO perYJ151pHoro pe:>KHMa; HX-TO HaJIHqHeM H 06'b5lCH5IeTC5I BH,Q
rpaqmKoB 42 H 43, H306pa:>KaIOWHX TeMnepaTYPHoe nOJIe B nOJ1YJIorapmp.
MHQeCKHX Koop,QHHaTax: perYJ151pHbIH pe:>KHM HacTynaeT He MrHOBeHHO,
a cnYCT5I HeKOTopoe BpeM5I (or*), Tor,Qa KaK, COrJ1aCHO 3JIeMeHTapHOH Teo-
pHH rJI. 3, 3TOT pe:>KHM HaQHHaeTC5I cpa3Y :>Ke - C HaQaJIbHOrO MOMeHTa.
1-13 npe,QbI,Qyruero BH,QHO, QTO cxeMaTH3aUH5I npouecca opoCToro OXJIa-
:>K,QeHH5I HJIH HarpeBaHH5I 51BJI5IeTCfI BMeCTe C TeM H llmpoKHM o606rueHI-IeM
3JIeMeHTapHoH TeopHH; aHaJIHTHQeCKOe :>Ke onHcaHHe ero C cpH3HQeCKOH
TOQKH 3peHH5I eCTb, Bo-nepBbIx, oepeBo,Q Ha fl3bIK MaTeMaTlIKH cpH3HQeCKHX
3aKOHOB o6ruero xapaKTepa (CM.
 I, rJI. 4) H, BO-BTOPbIX, HeKoTopblX
,QonyrueHHH (CM. paBeHcTBo (**) 3TOH :>Ke rJIaBbI), OCHOBaHHblX Ha on bITe.
fl03TOMY BbIBO,QbI TeopHH perYJI5IpHOrO TenJIOBOrO pe:>KHMa CJIe,QyeT pac-
CMaTpHBaTb KaK o606weHHe BeCbMa 60JIbillOrO QHCJIa onbITHbIX ,QaHHbIX.
aHa OXBaTbIBaeT 60JIbillOH KJIaCC 51BJIeHHH, npOTeKaIOruHX B npHpO,Qe 6e3
BMeIllaTeJIbCTBa 3KcnepHMeHTaTopa, caMonpOH3BOJIbHO, HJIH ocyrn.eCTBJIfle-
MbIX B JIa60paTopHH npOCTbIMII cpe,QCTBaMH.


7 YOHllpa.be
 2763




PeZYARpHble TenllORble pe3fCUMbl BTOPOZO U TpeTbeZO poaa


99


fJIABA 5


CKOpO ero MO)KHO 6YJl.eT oT6poCHTb, Tor)!.a H H3CTynHT «perYJHlpHbIH
pe)KHM». Bblpa)KeHHH Jl.JIH p HaMH Jl.aHbl 6bIJIH B rJI. 3 B npe)!.nOJIO)KeHHH
paBHoMepHoro TeMnepaTypHoro nOJIH; Tenepb Mbl H3YlIHM H Te CJIYlIaH,
KorJl.a :noro HeT: BHYTPH CHCTeMbl HMelOTCH 3HallHTeJIbHble TeMnepaTypHble
rpaJl.Ht:HTbl, H TenJIo06MeH BHYTPH Hee Bblp3)KaeTCH 3aKOHOM <PYPbe.
B 3TI-IX CJIYlIaHx TaK)Ke YJl.aeTCH CPOPMYJIHpOBaTb npocTbIe 3aKOHbI pery-
JIHpH3aLI.HH, K lIeMY MbI H nepexo)!.HM.


OTJIHlIHTeJIbHOe CBOHCTBO paccMoTpeHHoro B npeJl.bIJl.yrn.eH rJIaBe
perYJIHpHOrO pe)KHMa, KaK Y)Ke 6bIJIO CKa3aHO, COCTOHT B TOM, liTO no ero
HaCTynJIeHHH Ha TeMnepaTypHOM nOJIe CHCTeMbl He OTpa)KaIOTCH oc06eH-
HOCTI! HallaJIbHOrO COCTOHHHH - 6y)!.eT JIH B HallaJIe CHCTeMa HarpeTa
paBHoMepHo HJIH HeT, 6YJl.eT ;HI HallaJIbHOe TeMnepaTypHoe nOJIe HOCHTb
CJIO)KHbIii xapaKTep, HanpHMep, KaK 3TO H306pmKeHO KpHBOH AA'
Ha cpHr. 38, - HH B KoeH Mepe 3TH 06CTOHTeJIbCTBa He OTpa3HTCH Ha U
HJIH Ha nz. flp, aBJl.a OT HallaJIbHoro COCTOflHHH 3aBHCHT K03<PcpHLI.HeHT A
B BbIpa)KeHHH (4.7) TeMnepaTypHoro nOJIH, HO 3Ta 3aBHCHMOCTb paBHo-
CI-IJIbHa TOJIbKO BapbHpoBaHHIO MaClllTa6a TeMnepaTypHblX pa3HocTeH
u - t H )!.JIH renJIOBbIX H3MepeHHH HHKaIWrO 3HalleHHH He HMeeT.
T2Koe )Ke flBJIeHHe perYJIflpH3aLI.HH TenJIOBOrO pe)KHMa HMeeT MeCTO
H B J{BYX )!.PYrHX CJIYlIaflX, 3JIeMeHTapHaH TeopHH KOTOpbIX Jl.aHa B
 2,
4, 6 rJI. 3. flpe)KJl.e lIeM nepeXO)!.HTb K HX paccMoTpeHHIO. 3aMenIM, liTO
H 3JIeMeHTapHaH HX TeopHH npHBOJl.HT K paccMoTpeHlIIO perYJIHpHoro
lenJIOBOrO pe)KHMa, nOHHMaH no)!. 3THM TOT TenJIOBOH pe)KHM CHCTeMbI,
KOTOpbIH HacTynaeT nOCJIe HaCTOJIbIW npOJl.OmKHTeJIbHOrO BpeMeHH, liTO
Ha HeM Y)Ke nepeCTaJIO CKa3bIBaTbC5I HallaJIbHOe COCTOHlllie CHeTeMbI.
B 3JICMelITapHOH TeopHH OH MO)KeT 6bITb onHcaH npOCTbIMH 3aKOHOMep-
HOCTHMII. 1-13 06llJ,eH CPOPMYJIbI (3.5), KaK Mbl BHJl.eJIH B
 1 rJI. 3, BbITeKaeT,
liTO



 1. OCHOBHOH 3aKOH peryJlSlpHoro TenJlOBoro pe>KHMa BTOpOro pOJl.a
OCHOBHOH 3aKOH perYJIHpHoro pe)KHMa BTOpOro po)!.a 51BJIHeTCH
lIaCTHlIHO pe3YJIbTaTOM MaTeMaTHlIeCKoro aHaJI1I3a, lIaCTHlIHO 3TO-
0606rn.eHHe onbITHbIX )!.aHHbIx. Cyrn.eCTByeT cJIeJl.YIOw,ee, cOBepweHHo
06rn.ee nOJIO)KeHHe, pacnpocTpaHHIOrn.eecH Ha Bce cHcTeMbI. CKOJIb 6bI
CJIO)KeH HH 6bIJI HX COCTaB (3J1.ecb, KaK II paHee, no)!. CJIOBOM «ClICTeMa»
nOHHMaeTCH cOBoKynHoCTb nJIOTHO npIIJIeralOllJ,HX Jl.pyr K J{pyry pa3JIHlI-
HbIX TeJI /, /I, . . . , COCTaBJISlIOllJ,HX MexaHHlIeCKH 06"beJl.HHeHHoe LI.eJIoe).
ECJIH TeMnepaTypa BHewHeH cpeJ{bI 8 H3MeH5IeTCH C nOCT05lHHoi:'!
CKOpOCTblO b (>0 HJIH < 0), TO no HCTeLJeHIIH J{OCTaTOllHoro npOMe)KYTI<a
BpeMeHH TeMnepaTypbI Bcex TOtIeK CIICTeMbI cTaHYT 113MeHHTbC5I C nOCT05lH-
HOi:'! CKOpOCTblO, paBHoi:'! b.
CJIe)!.OBaTeJIbHO, eCJIH

 = b rJ{e b = const ,
d't '


PEfYJISIPHblE TEnJIOBblE PE)I(l1Mbl BTOPOfO 11 TPETbEfO
POJ],A


TO no I-ICTelleHI-IH J{OCTaTOllHO Jl.c5JIroro BpeMeHH Jl.JIH TeMnepaTYPbI U
JII060H TOLJKH M 6YJ{eT HMeTb MecTO YCJIOBHe
du
(h = b = const.
.D:JI5I MaTeMaTHlIecKoro onHCaHH5I TeMnepaTypHoro nOJI5I CHCTeMbI
06llJ,eMY HHTerpaJIY 3aJl.allH LI.eJIeC006pa3Ho npHJl.aTb CPOPMY


00


U - 8 = [U o - 8 0 + -,k-P' (
)] e-ml
-
.) - --k- P'" (
),


U = 8 + {} +
AjUje-ml,
;-0


(5. 1)


D _ ( ) -m (
-
.) + ( )
U - v - PI 't,1:o e p 1:, 1:0 '


rJl.e {} - CPYHKLI.HH TOJIbKO KOOpJl.I-IHaT.
flpH 3TOM aHaJII-I3 npHBo)!.HT K 3aKJIlOlIeHHIO, liTO CPYHKLI.H5I {} y)!.OBJIeT-
BopHeT ypaBHeHHIO B LJaCTHbIX npOlI3BOJl.I1bIX:
2' b
\ I} = a . (5. 2)
KorJl.a 1: CTaHOBHTCSI J{OCTaTOllHO 60JIbWI!M, nOC,TJeJ{Hee CJIaraeMOe
B npaBoH LJaCTH (5.1) 6YJl.eT npeHe6pe)KIIMO MaJIbIM, H Mbl nOJIYLJHM:
U - 8 = u Pel - 8 = {}, (5. 3)
T. e. pa3HoCTb TeMnepaTYP JII060li TOllKH CHCTeMbI H CpeJl.bI CTaHeT nOCTO-
HHHOH.
1"


rJl.e
- MOMeHT BpeMeHH, JIe)Karn.I-I H Me)KJl.Y 1:0 H 1:. 003TOMY pa3HocTb TeM-
nepaTYP CIICTeMbI II CpeJl.bI, no KaKoMY 6bI 3aKoHY TeMnepaTypa cpe)!.bI
HH MeHHJIaCb, BcerJl.a MO)KeT 6bITb npeJl.CTaBJIeHa B BHJl.e aJIre6paHlIeCKoH
CYMMbI Jl.BYX CJIaraeMbIx, a I-IMeHHO:


"pIllleM PI II P - Bcer.na KOHellHbIe 4>YHKLI.HH.
flepBoe H3 HHX cTpeMHTcH K 0 no Mepe B03pacTaHIIH 1: H Jl.JIH MOMeHTOB
I3pCMCIIlI, )!.uLldJu'IIlU )!.dJICI
lIX VI IldlldJlbllVI U 'to' 6Y,'J.cI llU dQCUJIIVIHUH
l3eJIHLJHHe npeHe6pe)KHMO M3JIbIM no cpaBHeHHIO CO BTOpWM H D03TdMY




PeZYJ1RpHbte TenAOBbte pe:JfCUIr!bl BTOpoZO U TpeT.bei!O poilu


101


100


c1JU3uKO-MaTeJtWTUflec/we OCHOBbt U3MepeHuiJ. TeIlAOBblX BeAuflUH.


I1TaK, aHaJIl-ITH"IeCKH 3a)l.a"la 0 perYJHlpHOM pe}l{HMe BTOpOro pO)l.a
CBO)l.HTCH K 3a)l.a"le CTaUHOHapHOrO TenJ10BOrO n0J151; OTCIO)l.a H TepMHH
«KBa3HCTaUHOHapHbIH», KOTOpblM n0J1b3YIOTC5I HeKOTOpble aBTopbl [8 L
rpaqm"lecKoe npe)J.CTaBJ1eHHe H3Me-
HeHH5I Tel\mepaTypHoro n0J151 co BpeMe-
HeM npH YCJ10BHH, "ITO TeMnepaTypa
BHelllHen Cpe)l.bl B03paCTaeT J1HHefIHO,
)l.aHO Ha qmr. 56, r)l.e 6 - TeMnepa-
Typa cpe)l.bl. vb qmr. 56 BH)l.HO, "ITO
TeMnepaTypHoe nOJ1e no HaCTynJ1eHHH
perYJ1HpHOrO pe}l{HMa BToporo pO)l.a
npe)l.CTaBJ151eTC5I CHCTeMOH napaJ1J1eJ1b-
HblX np5lMbiX (ll1) , (U2), (U3), . . . .
" ECJ1H TeMnepaTypHoe nOJ1e CHCTe-
Mbl - paBHOMepHoe, Bce 3TH np5lMbie
CJ1HBaIOTC5I B O)l.HY np5lMYIO: qmr. 56
('TaHOBHTC5I aHaJ10rIlqHOH O)l.HOH 113
qmr. 27.



u


T,


<])I-Ir. 56. rpaqJHlJeCKOe H306pa}Ke-
HHe perYJlHpHOrO pe}KHMa BToporo
pOJ1a CHCTCMbl.


eCJ1H H36paTb CHCTeMY UHJ1HH)l.pHqeCKHX KOOp)l.HHaT (qmr. 12). YpaB-
HeHHe (5. 2) )l.J151 UHJ1HH)l.pa npHMeT BlIlI.:
d 2 \\ Idb h
dr
 Tr'l.[;-=a


HJ11I


d (r
: ) _ h .
--.r
dr a'


OTCIO)l.a nOJ1yqaeTC5I npoCTblM HHTerpHpOBaHHeM
dlt b 2 C
r.l.[;- = 2iJ.r + .'


r)l.e Ci - nOCT05l1l1la51 HHTerpHpOBaHlI5l. l1.aJ1ee
dli =..!!....r +
.
dr 2a r .


{} =

 . r 2 + C. In r + C 2 ,



 2. PerYJ1HpHbIH pe>KHM BToporo pOJI.a OJI.HOpOJI.HOro H30TponHoro TeJla.
npoCTeHmHe CJlYlJaH nJlaCTHHbl, L1.HJlHH)l.pa, mapa
Ope)l.n0J10}l{HM, qTO CHCTeMa CBO)l.IlTC5I K O)l.HOMY TOJ1bKO TeJ1Y, O)l.HO-
pO)l.HOMY H H30TponHoMY; nycTb ero HarpeBaHHe (HJ1H oXJ1a)l()l.eHHe)
C nOCT05lHHOH CKOpOCTblO npOHCXO)l.llT B cpe)l.e, HHTeHCHBHOCTb TenJ10BOrO
B03)1.eHCTBIl51 KOTOpOH Ha TeJ10 onpe)l.eJ151eTC5I K03qxpHUIleHToM TenJ100T)l.a-
"Ill ex. Tor)l.a ypaBHeHHe (5.2) BMeCTe C YCJ10BH5IMH Ha HapY}l{HoH nOBepx-
HOCTH n03B0J151eT (npHHUllnHaJ1bHO rOBOp5l) )l.aTb nOJ1HOe pemeHHe 3a)l.a"lH.
YCJ10BH5I (4.2) Ha nOBepxHocm:
du
- A dn = ex (u - 6) (5. 4)


r)l.e C 2 - nOCT05lHHasL ROJIaraH B nOCJ1e)l.HeM ypaBHeHIlH r = 0, npH-
XO)l.HM K 6eCKOHeqHbiM 3HaqeHH5IM TeMnepaTypbl, eCJ1H TOJ1bKO C.-He 0;
n03TOMY C] )l.OJ1}1{HO OblTb paBHO HYJ110 H
h 2 . d& b
(}=4Q.r +C 2 , {jf= 2a .r.
l1.JHJ onpe)l.eJ1eHIl51 C 2 BOCn0J1b3yeMc5I rpaHH"IHbIMH YCJ10BH5IMH (5. 5),
npH"IeM 3aMeTHM, qTO HanpaBJ1eHHe BHemHeH HOpMaJ1H K HapY}l{HoH
nOBepxHocTIl n COBnall.aeT C HanpaBJ1eHlleM pa)l.Hyca; nOJ1y"laeM
[ 2 h r + Id - 4 b r2 + C 2 ) J = O.
a \ a r=R


HJ1H B CHJ1Y (5. 3), nOCKOJ1bKY 6 - (PYHKUH5I TOJ1bKO T, a OT KOOp)l.HHaT
He 3aBHCHT:


( dlt + h& ) = O.
dn s
061ll.HH HHTerpaJ1 ypaBHeHH5I (5.2) npHHHMaeT npoCToH BIl)l. B Tex CJ1Y-
qa5lX, KOr)l.a TeJIO HMeeT O)l.HY 113 Tpex npoCTeHllIllx cpOpM - nJ1aCTHHKH,
UHJ1H H)l.pa , mapa; B 3T1iX CJ1Y"laHx nOJ1e TeMnepaTYP - O)l.HOpO)l.HOe,
H ypaBHeHHe (5. 2) 06palll.aeTC5I B 06b1KHOBeHHoe )l.HqxpepeHUHaJ1bHOe
ypaBHeHHe C nOCT05lHHblMH K03
(pHUHeHTaMH.
PaccMoTpHM CJ1Y"laH 6eCKOHeqHO lI.J1HHHOrO UHJ1HHJI.pa pall.Hyca R.
l1.J151 3Toro cJ1Y"la51 onepaTop JlanJ1aca, cpHrYPHPYlOlll.HH B ypaBHeHHM
(5. 2). 6VlI.eT HMeTb BHlI.:


003TOMY ypaBHeHHe TeMnepaTypHoro nOJl51 H306pa3HTC5I npocToH
op-
MYJIOH


(5. 5)


fI = _..!!.... (R2_r 2 ) -
.R.
4a 2ah


(5.6)


l1.J151 mapa pa)l.Hyca R, eCJIl:l BblopaTb C(pepMqeCKHe KOOp)l.HHaTbl r,
cp, (j (cpHr. 17),


" d 2 \\ 2 dlt I efl

--& = ---;- + - - = -.- ({tr)
dr 2 r dr r dr 2


B CJ1yqae O)l.HOMepHoro TeMnepaTvpHoro nOJl5l; n03ToMY ypaBHeHHe (5. 2)
npMMeT BH)I.:


Z!:I _ d'ltt I I dtt

U-:- dr2 T,([;"


tflll!/) b
---cJr2 = a r.




102


c[J1l3UKO-MureMarU'leCKUe OCHOBIJt U3MepeHui1 renJ10Bbtx BeAU'lUH


CJ1e,AOBaTeJ1bHO
-&r = :0 r 3 + C]r + C 2 H -& = :a r" + C] + :2 .
Y CTpeMJ15151 r K O. BH}]JIM H3 co06pa}!{eHlJii (pH3H4eCKoro xapaKTepa,
41'0 C 2 ,AOJ1)1\HO 6bITb paBHO O. Ycn0J1b30BaB (5. 5), onpe,AeJ151eM C]
H HaXO,AHM


-&= -
(R2-r2)-
'R.
6a 3ah


(5. 7)


l1.J151 HeorpaHH4eHHoH nJ1aCTfIHKH, TOJ1Il1.HHa KOTQPOH paBHa 2L,
n0J1Y4HM


-& = -
 (P_A 2 ) -
. L
2a ah '


(5. 8)


eCJ1H 3a nJ10CKOCTb ,AeKapTOBbIX KOOp,AHHaT yOz BbI6paTb nJ10l KOCTh
CHMMeTpHH nJiaCHIIIKH.
kiTaK, BO Bce'( 3TH X CJ1Y4a5lX TeMnepaTYPHoe nOJ1e TeJ1a npe,ACTaB-
J151eTCH napa60J1H4eCKHM 3a
OHOM.
PaCCMaTpI1Ba51 perYJ1HpHbIH pe}!{HM BToporo pO,Aa TeJ1 npOCTeHLUeH
(POPMbl, npHXO,AHM K 3aKJ1104eHHIO, 41'0 BCJ1e,ACTBHe HepaBHOMepHOCTH
TeMllepaTypHoro n0J151 TeJ1a OTCTaBaHHe ero OT,AeJ1bHbIX T04eK pa3J1H4HOe;
OHO HaH60J1bLUee B UeHTpaJ1bHOH 4aCTH TeJ1a H, B nepBOM npH6J1H}!{eHHH,
ero pa3J1H4H5I Bblpa}!{alOTC5I napa60J1H4eCKHM 3aKOHOM.
TellJ10Ba51 HHepUlI5I TeM MeHbUle, 4eM 60J1bLUe ex, T. e. h; HO H npH
ex -+ 00 OHa He HC4e3aeT, 1I0TOMY 41'0


B CJ1Y4ae nJ1aCTHHKH 3=-
(P_X2)
2a
B CJ1Y4ae UHJ1HH.L\pa {} b (R" 2'
=-- -r) (5. 9)
4a
B CJ1Y4ae LUa pa -&=_
 (R2_r 2 )
6a



 3. PerYJ1S1pHbJH pe)KHM TpeTbero P0)l.8. npOCTeHIUH" CJ1Y"IaH
TeMnepaTYPUbJX BOJ1H B CTep)KUe 1-IJ11-1 II0JlynpocTpaHCTBe
np.e,AII0J10}!{HM Tenepb, 41'0 TeMnepaT)"pa Cpe,Abl B H3MeHHeTCH co Bpe-
Met:eM lIepHO,AH4eCKH no 3aROHY, npOCTeHLUeMY H3 B03MO}!{HbIX, T. e. CO-
rJ1aCHO ypaBHeml10 (3.14). H B 3TOM CJ1Y4ae, KaKOB 6bl HH 6bJJ1 COCTaB
CHCTeMbl, HMeeT MeCTO 3aKOH, aHaJ10rH4Hb1H npe,Abl,AYUl.HM, (POPMYJ1H-
pOBaHHbIM B
 1 3T01i rJ1aBbJ H B
 4 rJ1. 4: no HCTe4eHHH ,AOCTaT04Hora
BpeMeHH HaCTynaeT perYJ151pHbl1i pe}!{HM CHCTeMbJ, 1'. e. 1'eMnepa1'ypa
B J1IooOH ee 1'04Ke K0J1e6J1e1'C5I OK0J10 HeJW1'OpOro cpe,AHero nOC1'05lHHOrO
llH!4eIIIJfT t C 1'(,M me nCpllO,AOM 1\O.ne6allJlii, KaJ( I! TeMnep
nypa 60KPY'
maK>IlI.eH Cpe,Abl, 1'. e. 1'O)!(e no CHHycoH.qe, C nepHO,AOM, o.qHHaKOBbIM ,&JI5I


, .


PeZYAJlpHbte renAORble peafCllJ,lbl BropOlO II rperbezo poiJa


103


Bcex T04eK CHCTeMbl H co C,ABHrOM no cpa3e OTHOCHTeJ1bHO Ko.ne6aHHij TeM-
nepaTypbl BHeLUHe1i Cpe,AbI. 3TOT C,ABHf H 31'0 cpe,AHee 3Ha4eHHe TeMnepa-
TYPbl, a c.ne,AOBaTeJ1bHO, H 3MnJIlITY,Aa K0J1e6aHHH pa3J1H4Hbl )lJI5I paSHblX
T04eK CHCTeMbJ, 41'0 06YCJ10BJ1eHO HaJ1H4HeM TeMllepaTypHbJX rpa,AHeHTOB
B CHCTeMe. B 3TOM H COCTOlIT CYIll.eCTBeHHoe OTJ1l14He 01' 3.neMeHTapHoro
CJ1Y4a5l, paCCMOTpeHllOro HaMli B
 6 fJ1. 3: TaM MbJ HMe.nH t= 6m-
paBHOH Cpe,AHeH Tel'vmepaType oKpy)!(alOUl.eH Cpe,AbJ; 311.ecb t-CPYHKUH5I
KOOp,AHHaT. .
HepaBHOMepHOCTb TeMnepaTypHOfO nomI B Te.ne BbJ3bTBaeT KpaHHee
YCJ10)!(HeHHe aHaJ1HTH4eCKoro ero npe,ACTaBJ1eHH5I B CJ1Y4ae perYJ151pHOrO
pe)!(HMa TpeTbero pO,Aa, 41'0, B CBOIO
04epe,Ab, KpaHHe 3aTpY,AH5Ie1' B03MO)l(-
HOCTb npHJ10}!{eHII5I 31'oro 51BJ1eHHH
K npaK1'HKe TenJ10Bb1X Jl3MepeHHH.


0'




w


:
 "


?/.
0"
«lJHr. 57. DOJlynpoCTpau-
CTBO.


«lJHr 5
. HeorpaHH'IeHHO npoCTlIpalOlI.lHiicH
B cTOpoay OCM OX npRMoH CTep)KeHb.


D:a}\{e ,A.nH npoCTeHLUHx cpopM Te.n8 n0J1Y4aIOTc,", CJ10)KHbJe, HeY,A06Hble
Bblpa}\{eHH5I [81. [9]; 1I03TOMY 3,AeCb 6Y,AeT paCCM01'peH TOJ1bKO O,AHH
CJIY4aH - CHHYCOIf,AaJ1bHbIX BOJ1H B HeorpaHH4eHHoM CTep}\{He HJH1 nOJ1Y-
npOCTpaHCTBe. OO,A noc.neJl.HHM TepMHHOM nOHHMalOT TeJlO, orpaHH4eHHoe
C O,AHOH CTOpOJ-JbJ nJ10CKOCTblO H HeorpaHH4eHHo npOCTHpalOIll.eeCH B .APY-
rYIO CTOPOHY (cpHr. 57).0'00" - CJIe.q 3TOH II.nOCKOCTH Ha nJ10CKOCTH
qepTe}\{a; cnpaBa 01' Hee HaXO,AHTC5I H3Y4aeMoe HaMH no.nynpoCTpaHCTBo;
c.neBa-HJ1H cpe,Aa HJ1H K2Koe-.nH60 npHcnoc06.neHHe. n03B0J1HIOIlI.ee no
npOH3B0J1Y H3MeHHTb TeMnepaTYPY U o nJ10CKOCTH 0'00". .D.Jl5I ynpoIll.eHH5I
3a,Aa4H C,AeJ1aeM npe,An0J10}!{eHHe A: TeMnepaTypHoe nOJ1e no.nynpOCTp<JH-
nBa - O,AHOMepHoe, T. e. TeMllepaTypa U B .'11060H T04Ke M nOJ1ynpo-
npaHCTBa - (PYHKUH5I TOJ1bKO ee paCCTOHHHH or nJlOCKOCTH x (H, KO-
He4HO, BpeMeHH -r).
04eBI1,AHO. 41'0 eCJlI1 3aMeHHTb nOJ1ynpoCTpaHCTBO 6eCKOHe4I1bIM IIpH-
MblM CTep}!{HeM (J11060ro ce4eHHH) H npe.AnOJ1O)l(flTb, 41'0 YCTpaHeH
Ten.n006MeH Me}!{,Ay era 60KOBOH nOBepXHOCTblO H oKpy}\{alOUl.eH Cpe,AOH E,
TO TeMnepaTypHoe era 1I0.ne 6Y,AeT TO}!{,AeCTBeHHO C TeMnepaTypHblM nOJ1eM
nOJ1ynpoCTpaHCTBa (cpur. 58).
PeaJ1bHO K TaKoMY c.nY4alO Mbl nO,AOHJl.eM, eCJIH 3aMeHUM 1I0J1ynpo-
cTpaHcTBo 04eHb TOJ1CTOH CTeHKOiL TorJl.a Ha ee TenJ10BOM pe}!{HMe npaKTu-
'JerKI! III" nY,AYT 0Tp;nY1ThCH yc '10RJHI TpfT '1nn(,\,p,,
 I-!
 f'P lryrn
 f'TnpnHf'.
BeCbMa Y,Aa.neHHoii 01' 0'00".




104


r!>U3UKO-MaTefttaTU'leCIWe OCHOBIJI U3MepeHui1 TenJ10BblX BeJ1U'lUH


OpeJl.n0J10:>KHM, "ITO TeMnepaTypa U o Ha llJ10CKOCTH 0'00" (r,Ae X = 0)
K0J1e6J1eTC5I OK0J10 Cpe,AHerO 3Ha"leHH5I, KOTopoe 0603Ha"lHM Un, no 3aKOHY
rapMOHH"IeCKOrO K0J1e6aHH5I
U o -= urn + A cas ( 2;1: ) (5. 10)
C nepHO,AOM T. 3TH TeMnepaTypHbIe BOJ1Hbl nepe,AaIOTC5I 13 nOJ1ynpoCTpaH-
CTBO, KaK 3TO nOKa3bIBaeT onblT, npHqeM OHH CTaHOB5ITC5I TeM MeHee
3aMeTHbI, "IeM 60J1bWe MbI Y,AaJ151eMC5I OT nJ10CKOCTH 0'00"; npH 3TOM
H3MeH5IeTC5I HX aMnJ1HTYJl.a H cpa3a. 003TOMY TeMnepaTypa U - cpYHKUH5I X
H T - Ha paCCT05lHHH x OT 0'00" Jl.OJ1:>KHa HMeTb BHJI.:


U = urn +- Aj (x) cas (2" ; - cp (x) ) ,


(5. 11)


BBeJl.eM ,AJ151 npocToT
 nHCbMa
-&=u - urn'


(5. 12)


<l>YHKLI.H5I -& Jl.OJ1:>KHa Y,AOBJ1eTBOpHTb, Bo-nepBblx, ypaBHeHHIO <l>ypbe
a3 a 2 \}
Ch = a. ax 2 ; (5. 13)
BO-BTOPbIX, Ha nOBepXHOCTH 0'00", T. e. npH x = 0, ,AOJ1:>KHa 130 BC5IKHH
MOMeHT BpeMeHH Y,AOBJ1eTBOpHTb ypaBHeHHIO (5.10), T. e.
-& Ix=u = -&0 -= A cas C;'t ) . (5. 14)


JJ:J1H HaXO:>K,AeHHH HeH3BeCTHblX cpYHKLI.HH f(x) H cp(x) nO,ACTaBHM Sblpa-
:>KeHHe (5.11) 13 ypaBHeHHe <l>yp be; no cOKpaw.eHHH Ha A nOJ1Y"laeM
f 21t . (2 -;; ) t " ( + f ' ,
- uT Sin "-T--9 = cas...) 9 sin(...) +-


+- ({,'f' + fef') sin (. . .) - fcr'2 cas (. . .);


OTClOJl.a


( :; f +- 21'9' + fcp") sin (. , .) = (/9'2 - n cas (. . .).


OOCKOJ1bKY no,A 3HaKOM Sill H COS CTOHT cpYHKUI-iH X H €, a K03qxpH-
LI.HeHTbl npl-l HHX-cpYHKLI.HH TOJ1bKO x, He06xo,AI-IMblM YCJ10BHeM, qT06bl
3TO ypaBHeHl-le YJl.OBJ1eTBOpHJ10Cb npl-l Beex 3HaqeHHHX x 1-1 T, HBJ1HeTCH
paBeHcTBo HYJ110 K03cpcpHl.lHeHTOB npH sin (. . . ) H COS (. . .); CJ1e,AOBa-
TeJ1bHO, Ht;,1-I3BeCTHbIe cpYHKUI-iH f 1-1 cp OT X ,AOJ1:>KHbI y,AOBJ1eTBOpHTb CI-ICTeMe
ypaBHeHlIH:


f " f '2 2f ' ' + f " 21t f
.= 'D
 ':II =--
I' I '. aT


(5, 15)


cr, cp' 1'1 T. ,A. 0603Ha'laloT npOT-I3BO,AHbIe no x).


. j


iI'


PeZYARpHbte TenAoBbte pe:JfCUMbt BTOpOZO U TpeTbezo poaa


105


VIHTerpHpOBaHHe 3THX ypaBHeHHH Kpaih-fe TPYJl.HO, a n03ToMY ,AJ151
ynpow.eHH5I 3a,Aa"ll-l 3aJl.a,AHMCH BH,AOM OJl.HOH 1-13 cpYHKUHH f 1-1 cpo OCTaHO-
BHMCH Ha cp 1-1 C,AeJ1aeM OTHOCHTeJ1bHO Hee npe,An0J10)j(eHHe, npOCTeHwee
1-13 B03MO:>KHbIX, a HMeHHO, qTO cp np5lMO npOnOpLI.HOHaJ1bHO x: cp = kx,
r,Ae k - HeH3BeCTHoe "I I-ICJ1 0 , nOJl..rIe:>Kalllee onpe,Ae.rIeHl-lIO.
OO,ACTaHOBKa 13 cHcTeMY (5.15) ,AaeT ,ABa ypaBHeHHH ,AJ151 f, KOTopble
,AOJ1:>KHbI 6bITb y,AOBJ1eTBOpeHbI O,AHOBpeMeHHO:


r = k 2 f, f'k = :T .f.


06111HH HHTerpa.rI nepBoro H3 HHX f = C1e kx + C 2 e- kx . OOCTOHH-
Hble C 1 H C 2 ,AO.rI:>KHbl 6blTb Bbl6paHbI TaK, 'n06bl 3TO Bblpa:>KeHHe no
nO,ACTaHoBKe 130 BTopoe ypaBHeHHe 06paTH.rIO ero 13 TO:>KJl.eCTBo; nO,ACTa-
HOBKa npHBoJl.HT K paBeHCTBY:
k 2 (C/'x - C 2 e- kX ) = - a
 (c1i X +- C 2 e- kX ).


OHO He npHBeJl.eT K a6cyp,Ay, TOJ1bKO KOr,Aa 6YJl.eT C 1 = 0; TOr,Aa
1-13 Hero nOJ1y"laeM 3HaqeHl-le ,AJ1H k:


k = 1 / TO .
aT


t.lT06bI HaHTH nOCTOHHHYIO C 2 , BOCn0J1b3yeMcH rpaHl-lqHblM YC.rIO-
BHeM (5. 14), nOJl.CTaBHB TY,Aa Ha MeCTO -& ero Bblpa:>KeHHe (5. 11), r,Ae
9 (x) = I
x, f (x) = C 2 e- kx;


nO.rIY'-II-iM


r AC 2 e- kx cas(2;:.
 -kX)] = Acas(27t ; ).


I
\


OTKYJl.a CJ1e,AyeT, '-ITO C 2 = 1.
. 1
003TOMY OKOH"IaTe.rIbHO HaXOJl.HM
-&=U_Um=Ae-tV a
 cas(x-V a
 -21'( ; ). (5.16)
MbI 3J1.eCb H3 Jl.BYX B03MO:>KHbIX 3l1aKOB Jl.J1H k npl-lHHmI 3HaK +,
nOTOMY qTO 3HaK - npHBeJ1 6bl K BbIpa:>KeHHlO JI..rIH f (x), 6ecnpe,AeJ1bHO
B03paCTalOllleMY C x, a 3TO npoTHBOpeqHT onblTY.
rpacpH"IeCKOe 1-1306pa:>KeHHe TeMnepaTypHoro nOJ1H nO.rIynpoCTpaHCTBa
(HJ1H oqeHb TOJ1CTOii CTeHKI-I) Jl.aHO Ha cpI1T. 59, r,Ae npe,ACTaB-
JIeHbI TeMnepaTYPHble nOJIH ,AJIH ,ABYX MOMeHTOB BpeMeHH. TaK KaK aMnJ1H-


J BbIBOJ1 (5. 16) 3aH\ICTBOBaH H3 (15).




106


r!>U3UKO-"WTeMaTUfleCKue OCHOBIJI U3MepeHulJ. TenAOBIJIX 8eAUflUH


PezyARpHlJle TenAOBlJle pe:J/CUMIJI BTOpOlO U TpeTlJeZO pOaa


107


1)'
a K0J1e6amIii TeMnepaTypbl KaKOH-J1H60 TOlJKH OK0J10 cpe
Hero 3Ha-
lJeHHfI U m paBHa - B CHJ1Y (5.16) - Ae -x Y ;
 , TO TeMnepaTypHble
KpHBbie Bcex TOqeK nOJ1ynpoCTpaHCTBa 3aKJ1lOqeHbl Me)j(
Y
BYMfI 3Kcno-
HeHlJ.HaJ1bHbIMH KpHBbIMH:


npUMep 17. 3aKpbITafl K3Mepa C qYBcTBI-ITeJ1bHbIMH npH60paMH,
TeMnepaTypa KOTOpOH
OJ1)j\Ha OCTaBaTbCfI nocToflHHOH, HaXO!(HTCfI B B03-
.u.yxe C TeMnepaTypoH, nepHO!(HqeCKH K0J1e6J1IOw.eHcfI B TeqeHHe CYTOK;
aMnJ1HTy
a K0J1e6aHI1H 20 0 . .D.J1f1 3allJ.I1Tbl KaMepbl, nOMep}KaHHe TeMne-
paTypbl KOTOpOH paCCql1TaHO Ha Cpe.u.HIolO TeMnepaTYPY B03.u.yxa, a He
Ha K0J1e6aHI1H ee, npl1MeHeH TenJ10H30J1f1UI10HHbIH 6YM3}KHbIH BOHJ10K,
TeMnepaTyponpOBO!(HOCTb KOTOpOro paBHa 5.10-'" M 2 'iQC-l, Onpe!(eJ1HM,
KaKYIO TOJ1llJ.HHY H30J1f1UHI1 x CJ1e!(yeT B3HTb, qT06bl K0J1e6aHHfI TeMnepa-
TYPbl Ha nOBepxHocTH 1130J1HpyeMoH KaMepbl He npeB30111J1H 0,1°.


-xvr
 _x -/7
U - U = Ae aT H U _ U = _ Ae V aT
m m ,


KaK 31'0 nOKa3aHO Ha cpl1r. 60. c:.ne
oBaTeJ1bHO, no Mepe Y.AaJ1eHllfI 01' n.lJo-
CKOCTlI 0'00" TeMnepaTYPHble BOJ1Hbl 3aTyxalOT 11 TeM CI1J1bHee. qeM

oo


60J1bllle . napaMeTp
T ' T. e, qeM MeHbllle TeMnepaTyponpOBO.AHOCTb
BellJ.eCTBa CTeHKH a 11 qeM 60J1bWe q3CTOTa K0J1e6aHHH TeMnepaTypbl
Ha ee HapY}KHoli nOBepxHocTH.
Pewelme 3a
aqH 0 TeMnepaTypHblX BOJ1Hax B CTeHKe KOHelJHOH TOJ1-
llJ.HHbl, eCJ1i'1 YCJ10BI1f1 0.AHH3KOBbI Ha 06eHX ee cTopoHax, H306pa}KeHO
rpacpHqeCKH Ha (tmr. 61. JJ:JlfI OqeHb TOJ1CTOH CTeHKH nOJ1yqaeTCfI KapTI1Ha,
npe.AcTaBJ1e
Hafl Ha (tmr. 62.
ConOCTaBJleHHe BbIBO.AOB TeopHH, OTHOCflllJ.HXCfI K nJ1aCTHHKe, LI.HJ1HH-
.u.py, lllapy, nOJ1ynpoCTpaHcTBY, Me}K
Y C060H 11 C pe3YJ1bTaTaMH OnblTOB
npHBO.AHT K 3aKJ1IOqeHH10, qTO npoCTeHlllafl (pOpMYJ1a (5.16) MO}KeT 6bITb
npHMeHeHa B KaqeCTBe nepBoro npI16J11I}KeHHfI K TeJ1aM 113 nJ10XHX npo-
BO
HHKOB TenJ1a, HMeIOllJ.HX MaJ1YIO TeMnepaTyponpOBO.AHOCTb, eCJ1H no-
BepXHOCTH 3TIIX u TeJ1 nOl1RPprmonU-iXf'fT T\pr,CTRJ.1JO TPl\1 n pp;nypHbIX BOJ1H,
06J1a.AaIOT MaJ10H KpHBH3HOiL


Q50


Q25


qoo


.02
'0 ? 3 If 5 6 7 8
cI>Hr. 59. Pacnpe.neJleHHe TeMnepaTYP B 6ec-
KOHe4HO )1J1HHHOM CTep}KHe, TeMnepaTypa OJ1HO-
ro KOHua KOToporo H3MeHHeTCH nepHo.nlilJecKH
no 3aKoHY rapMouH4ecKoro KOJle6aUHH; cTep'
}KeHb 3all.lHIl.leH OT 60KOBbIX nOTepb TenJIa KPH'
BaH A - TeMnepaTypHoe nOJle CTep}KHH
(x, 't - 3a.naHHble), KOrJ13 H3MeueUHe TeMne.
paTypbI ero Kouua J10CTHraeT M3KCI1MYMa;
B - TeMnepaTypHoe nOJle, H3cTynalOIl.lee n03-
}Ke Ha 1/8 nOJlHOrO nepHOlla.


,/
/ I ,
I ,
I x
x \


"
/
/


,+ '


cI>Hr 60. npeJ1eJlbUbIe KpHsbIe
(+ Ae - xY a; ) H ( Ae -x Y a
 ) ,
KOTOpblMH OrpaHHlJeHbI HaH60JIblllHe
B03MO}KHbIe KOJle6aHHH TeMnepaTYP
nOJIynpoCTpauCTBa npH rapMOHillJe-
CKHX KOJle6aliHHX TeMnepaTypbI ua
OrpaHHlJHBalOIl.leH ero C 0J1UOH CTO,
pOUbl nJIOCKOCTH.


cI>Hr. 61. TeMnepaTypubIe
CTeHKe cpe.nHeH TOJlU.lHHbl
TenJlOOTJ1:.JlJH no 06eHM ee
cHMMeTpH4HbI.


BOJIHbl B
YCJlOBHH
cTopoHaM


<DHL 62. TeMnepaTypHbJe BOJlHbI

 04eHb TOJICTOH CTeHKe-, YCJlOBHH no
06eHM cTopoHaM CHMMeTplollJUbI.


TaK KaK K03cpcpHLI.l1eHT TenJ100T
aqH 01' B03
yxa K BHelllHeH nOBepX-
HOCTH H30J1f1UI1I1 S (cpl1r. 63) He 6eCKOHeqHO BeJ1HK, TO TeMnepaTypa ee
6Y.AeT MeHflTbCfI C aMnJ1HTY.AOH A MeH, bllleH qeM aMnJ1HTy.u.a K0J1e6aHI1H
TeMnepaTypbl B03.Ayxa, n03ToMY npHMeM A = 100.
AMnJ1HTy.u. a K0J1e6aHHH TeMnepaTYPbl H30J1f1LI.IlH B paccToflHHH x
01' HapY}KHOH nOBepxHocTH 6Y.AeT:
Ax = Ae-k
,


r.Ae


k=ll (
 .


Cor J1aCHO Tpe60BaHlll0.


Ax 0,1
A-W'


OTKy
a


e kX = 100 H kx = 4.6.
TaK KaK a = 5.10- 4 ,M 2 'Lac- l , T = 24 'Lac, TO


k = V 5.;4 . 104 = V 262 = 16,2,




108


r!>U3UKO-MaTeMaTU'leCKUe OCHOBbt U31r!epeHuii. TenAoBbtx BeAljflUH


a OTCIo
a


4,6 28
x = 16.2 M = CM.
dTO 3HaqHT, qro Jl.J15J YCTpaHeHH5J BJ1IHIHH5J Ha TeMnepaTYPY KaMepbl
K0J1e6am1H TeMnepaTypbl BHellIHeH CpeJl.bI npHlllJ10Cb 6b1 npHMC!IHTb
He06blqaHHO roJ1CTYIO H30J15JUHIO. TaKoe pellleHHe Bonpoca, XOT5J H OqeHb
npocroe, BJ1eqeT 3a C060H 60J1blllOe YBeJ1HqeHHe ra6apHTOB, n03ToMY
He06xo,AHMO TepMoperYJ15JUHOHHOe YCTPOHCTBO.


z
8 3
5
5


cI>Hf 63. OJ1HOCJlOHHaH TenJlO-
BaH H30JIHUHH KaMepbI c npl!'
60pOM.


<DilL 64. MuorocJIoiiuaH TenJIOBaH
H30JlHUHH KaMepbl:


/ - nepoblH TenJlOH30JlRLlHOHHblH enOM;
2 - 8.'JlOMHHHeB8J1 4Jonbr8.; 3 - TOHKHH
B03JlYWHblH CJloA:; 4 - BTOpOH TennOH30nR-
I1HOHHhli< enoi<; 5
 K8Mep8 .Ilna npHoopa;
6 - npHoop.


CTOJlb 60.TJblllOe 3HaqeHHe x nO.TJyqaeTC5J nOTOMY, qTO K0J1e6aHH5J
TeMnepaTypbl CpeJl.bl HMelOT 60J1blllOH nepHOJl. - CYTKH; 3TO Bbl3bIBaeT
3HaqHTeJ1bHOe YMeHbllleHHe napaMeTpa k = -V a
 ' a c.'leD.OBaTeJ1bHO,
YBeJ1HqeHHe x. ITpeJl.n0J10}KHM Tenepb, 4TO IWJ1e6aHH5J TeMnepaTypbl
B03J1.yxa HMelOT MaJ1bIH nepHOJl., KaK 3TO 06blqHO H 6bIBaeT B YCJlOBH5JX J1a-
60paropHH, H60 TeMnepaTypa B03J1.yxa ,Aa}Ke npH HaJ1HqHH repMoperYJ15J-
Topa He MO}KeT OCTaBaTbC5J CTporo nocTo5JIIHOH. ITYCTb nepHO,A KO.TJe6a-
HHH T=3 MHH.= 0,05 'lac. (B COOTBeTCTBHH C pa60roH TepMOperYJ15J-
Topa, nOMelll.eHHoro B J1a60paTOpHH).
ITocTaBHM aHaJ10rHqHblH Bonpoc OTHOCHTeJ1bHO 3alll.HTbI KaMepbl C npH-
oopaMH, Tenepb Y}Ke nOMelll.eHHOH B J1a60paropHIO, npHqeM npHMeM,
liTO aMnJ1HTY,Aa KO.le6aHHH TeMnepaTypbl B03,Ayxa B J1a60paTopHH
paBHa 1°; Ha HapY}KHOH nOBepxlIocTH H30J15JUHH OHa CHH3HTCH; npHMeM
A = 0,5°.
ITocTaBHM }KeCTKHe YCJ10BHH, a HMeHHO, qT06bl H30J15JUH5J (H3 Toro
>Kf:' VlaTepHa'la, KaK II pallee) CIIIIJIIJ1a aMnJlIITy,AY KUJleGaliliu ua !lU
BCpXHOCTH KaMepbI ,AO Ax = 0,01°.


PeZYAJtpHb!e TenAOBble pe3ICUIr!bt BTOpo20 U TpeTbezo poaa


109


HTaK, Tenepb A/Ax = 5 H
kx = In AAr = 3,91;


k Y}Ke 3HaqHTeJ1bHO Bblllle, qeM npe}K,Ae :
k = -V 5.
'.


2 = 354;
3,91 M = 1 , 1 CM. 3a n aqa KOHCT PY KTHBHO pelllaeTcH OqeHb
OTCIO,Aa x = 354 ,....
npoCTo.
B CJlyqae K0J1e6aHHH 60J1blllOrO nepHo,Aa ueJ1eC006pa3HO TenJ10H30-
J15JUHIO KaMepbl BbJnOJ1H5JTb B ,ABa CJlO5J, OTJl.eJ1H
 HX ,Ap
r OT ,APyra
B03J1.YlllHOH npOCJIOHKOH, OKJ1eHB HX aJ1l0MHHHeBOH cpOJ1broH 11.J15J YMeHb-
llleHHH nepeJl.a4H TenJ1a pa,AHaUHeiJ (q,m. 64).








LJACTb BTOPA5I
J13MEPEHHSI H OPH60Pbf


H3MepeHue K03t/J4JUI{UeHTOB TenAOnpoBoiJHOCTU TeXHU<l.ecKUX MaTepuaA08 III


C06J1eHlHIMH H npH6opaMH. B B TeMI1epaTypa KOMHaTHafl - 6 B , B A -
BbICOKafl: 6 A> 6 B «(tmr. 65). fl peJ].nOJlO)l\HM, 'ITO TeI1J10BOU pe)l<HM-CTaUHo-
HapHbIu: fJ A H (JB-nocTOflHHble. PaccMoTpHM J].Ba cJly'Iafl, npeJ].cTaBJleH-
HbIe Ha cpHr. 65. B I1epBOM CJlY'Iae «(PIlr. 65, a) cpeJl.bl A H B OT-
J].eJleHbI TOHKOU cTeHKou C, TeI1J10BOe conpOTHBJleHHe KOTOpOU Po HeBe-
JlHKO; BO BTOpOM (qmr. 65,6) - Me>KJl.Y A H B YCTpoeHa eru.e H H30JlflUHfI
1 - MHoroCJlOUHafl HJlH OJl.HOCJIOUHafl.
0603Ha'IHM yJ].eJlbHblt'I TenJlOBOU nOTOK, HanpaBJleHHblU 'Iepe3 cTeHKY
OT A K B - B nepBoM CJlY'Iae Qo, BO BTOpOM - q. Ha'IepTIIM TeMnepa-


rnABA 6
M3MEPEHME K03

M
MEHTOB TEnnOnpOBO
HOCTM
TEXHM4ECKMX MATEPMAnOB


oj


.


0-) q


u



 1. POJlb TenJlOH30JmpOBaHHSI npOMblWJleHHblx 06"beKTOB, 3J].aHHH H T. n.
K03cpcpHUHeHT TenJlOc6epeiKeHHSI
3a,11,aQa onpeJ].eJleHHfI TeI1J10BbIX CBOUCTB MaTepHa.TJOB - B nepBYlo
O'IepeJl.b H
 TeI1J10npOBoJl.HOCTH
, a 3aTeM TeMnepaTyponpoBoJ].HOCTH a
H y,AeJlbHoH TenJlOeMKOCTH C - B03HHKJla H I1pH06peJla Ba>KHOe, Bce06ru.ee
3Ha'IeHHe B CBfl3H C Tpe60BaHHflMH OJ].HOH H3 BeCbMa llmpoKHx OTpaCJleH
TeXHHKH - TeI1J10H30JlfllJ,HOHHOU npOMbIWJleHHOCTH, a TaK>Ke H CTPOH-
TeJlbHOrO J].eJla.
B cOBpeMeHHoH TeXHHKe I10CTOflHHO npHMeHfllOTcfI cpeJ].bl - ra30BbIe,
>KH,AKHe,- HMelOru.He HJlH BblCOKYlO TeMI1epaTYPY, KaK, HanpIlMep,
ne'IHble ra3bl, neperpeTblH BO,AflHOH I1ap, I:IJlH HH3KYlO TeMI1epaTYPY,
Hanpl1Mep >KHJ].KHH KHCJlOpO,11, H a30T, a nOCJIeJ].Hee BpeMH >KHJ].KHH BOJ].OpO,A.
TBep,AbIe cTeHKH, B KOTopble 3aKJllO'IeHbi 3TH cpeJ].bl, HMelOT TeMnepaTypbI,
ropa3J].0 6?Jlee BbICOKHe I:IJlH HH3KHe, He>KeJlH TeMnepaTypbI B03,Ayxa
I10Meru.eHHH, r,Ae HaXO,AHTCfI onepaTOp - pa60'IHH, HH>KeHep, 3KClIepl:l-
MeHTaTOp - co CBOHMH cpeJ].CTBaMH KOHTpOJl51 H YI1paBJleHHfI npOH3BO,A-
CTBeHHbIMH npoueccaMH HJll:l pa60TOH YCTaHOBKH - ne'Il:l, XOJlO,AI:IJlbI-lHKa,
n
poBoro KOTJla H T. JI.. fl03TOMY BCI0J].Y B03HI:IKaeT He06xoJl.HMOCTb
I10KpbITHfI ropH'IHX HJlH XOJlO,AHbIX I10BepXHOCTeH MaTepHaJlaMH, nJlOXO
npOBOJl.flru.HMH TeI1J10, - TaK Ha3bIBaeMblMH TenJlOH30.TJflUHOHI-IbIMH HJlH
«TenJlOH30JlHTOpaMH» (HHorJ].a rOBopflT «TepMOH30JlflTOpaMH»). KOHCTPYK-
UHH, npHMeHfleMble Jl.JlfI 3TOH ueJll:l, pa3J1H'IHble B 3aBHCIIMOCTH OT (POPMbI,
pa3MepOB H TeMnepaTypbl H30.TJHpyeMoro 06"beKTa, Ha3bIBaIOT TeI1J10H30-
JlflUHOHHbIMH, BClO cOBoKynHocTb HX - TeI1J10H30JlflUHeH HJlH H30JlflUHeu.
POJIb TenJlOH30!flUHH MO)l\HO HJlJllOCTpHpOBaTb cxeMOU, KOTopafl
flBJlfleTCfI THnH'IHOH; BbIBO,11,bl, BbITeKalOru.He H3 ee aHaJlH3a, MorYT 6bITb
060fru.eHbI H pacnpOCTpaHel!bI Ha 06"beKTbl HHOro pO,Aa.
flYCTb A - npoCTpaHcTBo, 3anOJIlleHHOe ra30BOH HJlH >KHJIKOi'i
Cpe.n.OH, B KOTOpOU npOTeKaeT KaKOH-JlH60 I1pOH3BO,AcTBeHlIbIu npouecc
I1PH ,AOBOJlbHO BbICOKOt'I TeMnepaType, HanpIlMep 06)1\Hr KHpnH'Ia HJlH Tep-
MII'I
Clwn u6pa6ulha M
ldJI.TJuH3A
JIH>I H 1. II.; H - nOM
ru.eHHe, rJ].e
HaXO,AHTCfI OI1epaTOp, ynpaBJIfllOru.HH 3TI:IM npolJ,eccoM co CBOHMH npHcno-


r



B


8,1


A


B


!


0 0


d


=
-:::::=----:::
-===- - ::;:::::
,/ _ === --::::: c
-L // -= -=:s S


d.


f a


8 JJ
-L


<t>nr. 65. CxeMa pa3J1eJlCHnSi pa60lJero npoCTpaHcTBa A npOMbIIlIJleHHOH YCTaHoBKH
OT cpe.l\bl B:
a - CTeHKoi! C 6e3 H30nHlIHH H 6 - cTeHKoH C C H30nHIIHei! I; g a o ho b o Co d H g a h b k c d -
TeMnepaTypHble I<pHBhle.


TypHbIe KpHBbie ,AJIfI HHX 060HX; 3TO 6Y,AeT JlHHHfI gaohObQcgd-JIJlfI HeH30-
JlHpOBaHHOH CTeHKH, gahbkcd-,AJIfI H30JlHpOBaHIIOU CTeHKH (0603HaQeHHfI
nOHflTHbl H3 (PHr. 65). 0603Ha'IHM nepeXO,AHble TeI1JIOBble COI1pOTHBJIeHHfI
Ha rpaHHue Me>K,Ay cpe,AOH A H CTeHKot'I C B nepBOM CJlY'Iae CHMBOJlOM P
t
Me>K,Ay CTeHKOH C H Cpe,AOH B - CHMBOJlOM PCB' Bo BTOpOM cJlY'Iae,
KOr,Aa CTeHKa H30JlHpOBaHa, Mbl 6Y,11,CM HMeTb Me)l(J].y A H C TenJlOBOe
conpOTHBJleHHe PAC' 3aTeM BOHJ].eT eru.e TeI1J1C>BOe COnpOTHBJleHHe 1:130-
JlflUHH PI H TenJlOBOe COnpOTHBJleHHe Me>K,Ay HapY)l\HOH ee nOBepX-
HOCTblO 55 H cpe,AOU B, KOTopve 0603Ha'IHM PIB'
Cor JlaCHO 06ru.eH TeopHH, H3J10>KeHHOH B
 7 r JI. 2, I10JlY'Il:lM


{JA - {JR
q6 = p
b + PO+PCB


{JA-{JB
q = PAC T Po + PI + P/B .


KOJlHQeCTBO KaJlOpHH TenJla, c6epe>KeHHblX 6J1aroJIapfl H30JlflUHH I,
paBHo qo - q; OTHOCHTeJlbHOe >Ke CHl:l)l(elme TenJlOBblX nOTepb, BbI3BaH-
1I0e eIO, Bblpa3HTCfI (B npoueHTax) ,Ap06blO


11 - qn - q . 100 _ ( 1- ..!L ) . 100.
q. q{j




J13.:repeHlte 1;0aq)(I}/
1I11eHTOB Tel1AOnpOBOOI-lOCTU TeXHU<ieCKU-': Mauplta 10B 113


112


H3MepeHUf/ U npu60pbt


npeHe6peraH Po no cpaBHelUilO C JJ:PyrHMH conpOTHBJIeHHHMl:I
(3TO - CJIyqaH MeTaJIJIHqeCKOH CTeHKl:I), nOJIyqHM oTclOJJ:a
P AC - P
t + PIB+P
B
PI PI
PAC + P IB
1+ P
I


1+
11=


(6. 1)


lIeB03MomHOCTH j1JIH qeJIOBeKa pa60TaTb B nOMern.eHHHx, rJJ:e HMeIOT
H
60JIbillHe nOBepxHocTH C BbICOKOii (l:IJIl:I Hl:I3KOll) TeMnepaTYPoli; KpoMe
Toro, HeJJ:ocTaTOqHaH H30JI5IllHH Bb13.bIBaeT JJ:onOJIHl:ITeJIbHYIO pa60TY
BeHTHJIHUHOHHbIX YCTaHoBoK.
HaJIHque TenJIOI130JIHUHH cnoc06cTByeT BblpaBHHBaHHIO TeMnep<. Typ
B H30JIHpyeMoM npoCTpaHcTBe. 3TO HJIJIIOCTpHpoBaHo (tmr. 65 a, 6.
npH OTCYTCTBHH H30JI5IUHH (H.TJH eCJIH OHa He3HaqHT
JIbHa) TeMnep -
Typa CTeHKH, oTJJ:eJImorn.eli A OT B, H306pamaeMa51 TOqKOH b o Ha TeMnepa-
TYPHOii JIHHHH gaohobocod, 6Y}J.eT 3HaqI-iTe.TJ bHO HHme f:J A' a 3TO Bb130B€T
nOHHmelme Tel\mepaTypbI npOCTpaHCTBa neqH B ero qaCTHX, npHJIeraK-
W.HX K CTeHKaM. npH xopoIlleii H30-
JI5IUHH 6Y}J.eT )J:OCTHrHYTO 3aMeTllOe
nOBbIIlleHHe TeMnepaTypbI CTeHKH,
OMblBaeMOH neqHblMH ra3aMH: Ha TeM-
nepaTypHOH JIHIUIH gahbkcd OHa
H306pa3HTC5I TOqKOt'I b, .TJemaw.eIi
BbIIlle TOqKH boo n03TOMY 30Ha nOHH-
meHHOll TeMnepaTypbI ra30B 6Y}J.eT
CHJI bHO YMeHbilleHa: 06JIaCTb HepaB-
HOMepHocTH TeMnepaTypHoro nOJIH
neqH, 06YCJIOB.TJeHHa51 XOJIOJJ:HOH CTeH-
KOH, YMeH bIllHTCH.
HacKoJI bKO 31'0 06CT05lTeJI bCTBO
Ba)l(HO }J.JIH TepMoperYJIHpOBaHHH,
BH)J:HO H3 qmr. 66: eCJIH nOJIe Tel\mepa-
TYP neqH HepaBHOMepHO, TO TepMope-
rYJIHTOp, }J.aTqHK KOTOpOro T nona}J.aeT B XOJIO)J:HYIO 30HY, He 6Y}J.eT
BbmOJIH5ITb CBoero Ha3HaqeHH5I; paBHOMepHOCTb TeMnepaTypHoro nOJIH -
He06xo}J.HMaH npe;J.nOCblJIKa ero npaBlIJIbHOii pa60TbI.
llpuMep 18. Pacc4HTaeM K03clqnulHeHT TenJIoc6epemeHH5I }J.JI5I H30-
JIHpOBaHHoII CTa.TJbHOH Tpy6bl .l\HaMeTpOM npHMepHo 70-100 CM; Ten.TJO-
HOCHTe.TJb HMeeT TeMnepaTYPY 550 0 C (3TO MomeT 6blTb neperpeTblH BO}J.5I-
HOH nap BblCOKOro .l\aBJIeHH5I); K03(pqm1lHeHT Ten.TJOOT.l\aqH OT Hero
; 1
K BHYTpeHHell nOBepxHocTH CTeHKH TPYObI ex AC = PAC ' COrJIaCHO pac-
4eTY H .l\aHHbIM, nOJIyqeHHbI
 H3 3KcnepHMeHTOB C

aJIO

qHbIM
106'beK-
TaMH oueHHBaeTC5I umppou ex AC = 20 KKaA M 'lac cpao (}J.JI5I
BbIHY}K.l\eHHOrO Typ6YJIeHTHoro nOTOKa cpe.l\Heii CKOpOCTH).
npe}J.nOJIOmHM, '11'0 Tpy6a C C TenJIOHOCHTe.TJeM A HaX
.l\H:cH B nOMe-
lI1.eHHH, TeMnepaTypa 8 B B03.l\yxa B KOToporo paBHa 20 C, B03)J.y
-
cnoKollHblll; TeMnepaTypa OKPY)l,alOrn.Hx Tpy6y Q6'beKTOB TaKme 20 C.
TaK KaK Tpy6a HMeeT 60JIbIllOt'I ;J.HaMeTp, a TOJIrn.HHa H30JIH1l.HH no KOH-
CTPYKTHBHblM co06pameHHHM He MO)l(eT 6bITb C}J.e.TJaHa qpe3MepHO 60JIb.:
IllOll, TO COrJIaCHO
 8 rJI. 2 paCqeT MO)!(HO BeCTH no cpopMYJIaM .l\.TJ5I nJIOCKOH
CTeHKH; B03HHKalOw.aH OT 3Toro norpeillHOCTb He 6Y.l\eT BbIXO}J.HTb 3a npe-
'{P.TlnT TpPOORaHnn. npPT['bHB.TIHeMhIX K TeXHHqeCKHM paCqeTaM. npHMel\

Tomll.HHY l:I30JI5IllHH 0 = 15 CM = U,15 .Ill.
8 KOilApaTbeO 2763


nOJIb3YHCb npe,lJ.bI}J.yulHMH CPOPMYJI3MH, 11 MO)l(HO npe)J.CTaBHTb B CJIe-
.l\ylOweM BH.l\e:
p
b + Po t PCB
1j = 1- PAC + Po + PI + P /B


P / + (PAc-p
b)+(PlB-PCB)
PAC + Po + P / + P/B


ECJIH eA>f:J B H eCJIH BcnOMHHTb, qTO K03(p(pHIl.HeHT
I TenJIOOT.l\aqH a
B03paCTaIOT C B03paCTaHHeM TeMnepaTypHbIX pa3HOCTeH ra3a H creHKH,
TO 3aKJIlOqHM, '11'0 PAC > p
b H P IB > PCB; n03TOMY H3 npe.l\bl}J.yrn.ero
paBeHCTBa CJIe.l\yeT HepaBeHCTBO


1+


1
PAC + P IB
PI


11>


OTBJIeqeHHOe qHCJIO 11 Ha3bIBalOT K03cpcpH1l.HeHTOM TenJIoc6epemeHH5I;
OH 06bIqHO COCTaBJI HeT 85-95 % .
TaKHM 06pa30M. H30JI5IIl.H5I 51BJIHeTCH CHJIbHbIM 0pY.l\HeM B 60pb6e
c renJIOBbIMH nOTep5lMH, a 3TO paBHOCHJIbHO c6epemeHHlo TOnJIHBa;
B cOBpeMeHHI:iIX MOrn.HbIX YCTaHOBKax CHHmeHHe nOTepb TenJIa (IiJIH KO-
JIo.l\a) JJ:ame Ha 1% HMeeT 60.TJbIllOe 3KOHOMHqeCKOe 3HaqeHHe. CTpeMJIeHHe
K 3KOHOMHH TOnJIHBa paBHOCHJIbHO, B CBOIO Oqepe.l\b, CTpeMJIeHHIO CHH-
3HTb K03(P(pH1lHeHT renJIOnpoBo}J.HOCTH J...: H3 (6.1) MbI BH}J.HM. qTO 1j
(,
B03paCTaeT C YMeHbIlleHHeM J...; CJIe.l\yeT TOJIbKO 3aMeTHTb, qTO PI = T'
KOHeqHO, MO)l(HO H}J.TH ewe no nYTH YBeJIHqeHHH TO.TJrn.HHbI H30MI1l.HH 0;
HO 3TO Be.l\eT K qpe3MepHoMY YBeJIHqeHHlO ra6apHToB, K YT5Ime.TJeHHIO Ii30-
JI5IIl.HOHHbiX KOHCTPYKIl.Ht'I H HX rpoM03.l\KOCTH. n03TOMY OCHOBHaH TeH.l\eH-
UHH BceH cOBpeMeHHoH TenJIOH30JIH1l.HOHHOH npOMbIIllJIeHHocTH: H3bICKa-
HHe MaTepHaJIOB C B03MomHO HH3KHM K03(pcpHIl.HeHTOM TenJIOnpOBO.l\-
HOCTH J.... 3TOT K03(pcpHuHeHT HMeeT peIllaIorn.ee 3HaqeHHe B 01l.eHKe Kaqe-
CTB3 TenJIOH30JJH1l.HOHHoro MaTepHaJJa H TenJIOH30JI5IIl.HOHHOH KOHCTPYK-
Il.IiH, a n03ToMY MeTO.l\bI H npH60pbI )J.JI5I H3MepeHH5I J... 51BJI5IIOTCH MeTOJJ:aMH
KOHTpOJI5I KaqeCTBa npo}J.YKIl.HH H IfMelOT TaKoe me BamHoe 3HaqeHIie
JJ:JI5I npOMbIIllJIeHHOCTH H TeXHHKH, KaK - K npHMepy CKa3aTb - cneKTpo-
cKonHH, peHTreHOBCKHH aHaJIH3 H TOMY nO,lJ.06HbIe 06rneH3BecTHble H
npH3HaHHbie MeTOJJ:bI KOHTpOJIH CBOHCTB MeTaJJJIOB H .l\pyrHx MaTepHaJIOB.
PUJIL H30JJHUUlI He UrpdHlIqllllilCICH lUJlbhU UJlHHM .:11 11M: H3UJJHpU-
BaHHe rop5lqHX HJJH XOJIO.l\HblX nOBepxHocreiI - HeH36emHO yme B CHJIY


cI>Hr. 66. HepaBHoMepHoe TeMnepa-
TypHoe nOJIe nelJHOrO npocTpaHcTBa
A (JIHHHSI pmgh).




H3MepeHUJ/ U npu60pbt


J13MepeHue K03ljJt/JulIueHToB' TenAOnpOBOOHOCTU TeXHU<teCKUX MaTepua,wB 115


114


npH TaKOM COOTHOIIIeHHH BHYTpelmero H BHelliHero Jl.HaMeTpoB H30-
Jl5Iu,HoHHoro CJl051 Mbl BnpaBe BOCnOJlb30B3TbC5I Jl.Jl5I pacLIeTa (POPMYJlOll
(6.1), oCHoBaHHoll H3 ypaBHeHHH cTauHoHapHoro TenJlOBoro nOTOKa tIepe3
nJlOcKYIO cTeHKY.
P3ccMaTpHBa51 Ten
OOT,AatIY HapY)j\HOH nOBepxHocTH Tpy6bl, CJle,AyeT
YtIeCTb, LITO HCKOMblH K03cpcpHu,MeHT TenJlOOT,A3tIH aCB = a(') CYTb
CYMMa Jl.BYX CJlaraeMblX a = al( + a A , KaK 31'0 6bIJlO pa3'b5lCHeHO
B
 4 rJl. I.
JJ:Jl5I onpe,AeJleHH5I K03cpcpHUHeHTa TenJloc6epe}/{eHH5I 'Ij CJle,AyeT,
HCXO,A5I H3 (POPMYJlHpOBaHHbIx BblIIIe YCJlOBHH HapY}/{HOll TenJlOOTJl.atIH
H 3 u 3J1.aBa5lCb TOll HJlH HHOH TenJlOBOll H30Jl5lUHell, T. e. TeM HJlH HHbIM A,
HailTH Bce Ten.TJOBble conpOTHBJleHH5I, CT05lIII.He B (pOpMYJle (6.1).
uPaccMoTpHM a npe}/{,Ae Bcero ,AJl5I CJlY'Ia51 HeH30JlHpOBaHHoll - «ro-
JlOil» - Tpy6bI.

03cpcpHUileHT KOHBeKTHBHO-KOHlI.\'KTHBHOll TenJlOOTJl.atIH a I( Jl.Jl5I
ropH30HTaJlbHbIX nOBepxHocTell H Tpy6 60JlblllOrO ,AHal\leTpa, OXJla}/{Jl.alO-
III.HXC5I CB060,AHO, MO}/{eT 6bITb paccLIIiTaH no cpopMYJle (l.II), KOTOpYIO
npeJl.CT3BHM B BHJl.e:
al(=A31t1/., (6.2)
rJl.e 6. t - «TeM
epaTYPHbIll Hanop» - pa3HOCTb TeMnepaTYP nOBepxHocTH
H OKpY}/{a!OIII.eH cpe,AbI, B Jl.aHHOM CJlYLIae B03,Ayxa. BeJlHLIHHY A COrJlaCHO
Ta6J1Hlle
 3 rJl. I MO}/{HO npHH5ITb A3 = 1,13 (TexH. eJl..) H n03ToMY
at( = 1,13.(550- 20)1/°=8,3.
4T06bI HaHTH a A' BOCnOJI b3yeMC51 CPOpM YJI Oi'l (1.16), npHLIeM npH-
,AaJl.HM ell TOT }/{e BHJI. (1.18), KaK H TaM; BMecTO 0 BBe,AeM C =
= 100 4 '0 (1.14). nOJlYLIaeM:
q =C ( t _ t ) . (k)' - (ioor
A 0 t - to
a n03TOMY MO)j\HO HanHcaTb


CTeneHb LIepHOTbl OKHCJleHllOi'1 CT3J1bHOH Tpy6bl e: MO}/{HO npHH5ITb
0,80. n03TOMY C = 0,80.4.88 = 3,9. no (6.3) HallJl.eM
aAy<t = 3,9.8,5 = 33,2.
n03TOMY cYMMapHblll K03cpcpHu,HeHT TenJlOnepe,AatIH roJlOi'I Tpy6bI
B OKPY}/{a!OIII.YIO cpe,AY 6Y,AeT:
....!..- - a(O) -- 8 3 + 332 - 41 5
PCB - -, ,-, .


TenJlOBblM conpOTHBJleHHeM Po MeTaJlJlHtIeCKOll CTeHKH, TOJlIII.HHa
KOTOpOll HeBeJlHKa, MO}/{HO npeHe6peLIb no cpaBHeHHIO C ,APyrHMH TenJlO-
BbIMH conpoTHB.TJeHH5IMH.
K03cpcpH 1 lHeHT TenJlOOTJ],3LIH (cYMMapHbIH) OT rop5ltIero TenJlOHOCH-
TeJlH A K BHYTpeHHei'I nOBepxHocTH CHaMH npHH5IT paBHbIM 20. n03TOMY
MbI HMeeM:


(0) _ 1 _ 5 .
P AC - 20- 0,0 ,
]
PCB = 41.5 = 0,0241.


aAy<t = Cf,
r,Ae f-MHO}/{HTe.JIb, 3aBHC5IIII.Hi'I OT 06eHX
TeMnepaTypbl nOBepxHocTH, To - CpeJl.bI
1'13 npe,Abl.u.YIII.ero OLIeBHJl.HO, LITO
( T \' ( To ) 4
f= TOO ) - TOO .
t - to '


(6.3)
TeMnepaTYp: T -a6COJIIOTHOll
II oKpy}/{alOIII.HX npe,AMeTOB.


P3CCMOTpMM Tenepb TenJlOH30JlHpOBaHHYIO Tpy6y, oTenJleHHYIOMaTe-
pHaJlOM HeBbICOKoro KaLIeCTBa, TenJlOnpoBo,AHOCTb KOToporo .u.Jl5I TeM-
nepaTypbl Cpe,AHeH Me}/{,AY 550° H 50° (3TO - npH6J1H3HTeJlbHble TeMne-
paTypbl BHYTpeHHeH H BHeIIIHeH nOBepXHOCTeH H30Jl5lU,HOHHOro CJl05l)
nycTb paBHa 0,20.
BeJlHtIHH3 PAC 6YJ],eT He3Ha4lfTeJlbHO OTJlH4aTbC5I OT p
b H 3THM OT.TJH-
LIHeM Mbl np
He6pe}/{eM.
1
JJ:Jl5I nOJlY4eHHH P IB = - CJle,AyeT Ou,eHHTb aCB. He OCT3HaB.TJH-
'11'1
Ba5lCb Ha BblKJlaJl.l<ax, KOTopble cOBepIIIeHHo 3HaJlOrHLIHbl BbmOJlHeHHblM
HaMH p3Hee npH pac4eTe a

, MO}/{eM C4HTaTb alB = 12.
no (6.1) nOJlY4aeM:


PAc
p
b


1
P IB = 12 = 0,083; P CD = 0,024;


(6. 4)


015
PI = 0.20 = 0,75;
1 + 0,059
11 o
i

 .100 - 91,5%.
1 + 0,75


MHO}/{HTeJlb f T36YJlHpOBaH [2 J. no Ta6.TJlfu,aM H.TJIi pac 1 1eTHbIM nYTeM
HaXO,AHM: npH t = 550 0 C H '0 .:...... 20° C, T. e. npH
T = (550 + 273) OK


H


To = (20 + 273) OK,
f= 1"R77 73,7 _ 1fiI1 _
5
550 - 20 - 530 - , .



T()T KOHKpPTHHIH npHMPp XOPOllTO H.nJlIOCTpHpveT. KaKVIO orpol\llIV IO
3KOHOMHIO ,AaeT H30JlllpOBaHHe Tpy60npOBO,Aa.
8*




116


H3MepeHUR U npU60pb!


H 3MepeHUe K03tPt/JUI(UeI-lTOB TenAOnpOBOaHOCTU TeXHUfJeCKUX MaTepUaAOB 117



 3. 061l\aSl cxeMa MeTo.nOB " np"60pOB
.n
SI onpe.ne
eH"SI Ten
OBWX CBOHCTB MaTep"a
OB


OxapaKTepH30BaHHafl B npe)J.bIlI.Ylll.eM YHHBepCaJlbHafl pO.TJb TenJlO-
H30JlflllHOHHblX MaTepHa.TJOB (K KOTOpbIM HHOrll.a Y Hac npHGHC.TJflIOT H
CTpOHTeJlbHbIe MaTepHaJlbI) flBH.TJaCb npHGHHOH Toro, GTO H B CCCP H
3a rpaHHuet'I pa3pa6aTbIBaIOTCfI (oc06eHHO YCHJleHHO 3a nOCJIell.HHe 15-
20 JleT) MeTO.IlbI H npH60pbI lI.JlfI onpe.IleJleHHfI K03<pqmuHeHToB J..., a, C
3THX MaTepHaJlOB. KO.TJHGecTBo npe.IlJlO)KeHHbIX H 60Jlee H.TJH MeHee cOBep-
IlleHHO pa3pa60TaHHbIx MeTO.IlOB H pa3J1HGHbIX npH60poB HaCTOJlbKO Be-
JlHKO, GTO 6bIJlO 6bI cOBepIlleHHo HeueJleco06pa3Ho onHCblBaTb Bcex HX;
MbI OrpaHHGHMC5I TOJlbKO TeMH, KOTopble flBJlflIOTC5I HaH60Jlee npocTbIMH
(CMbICJI 3Toro TepMHHa BbI-
51CHHTCfI BnOCJle1l.CTBHH),
HaH60.TJee pa3pa60TaHHblMH
H HaH60Jlee npHro.IlHbIMH
.Il.TJfI TenJlOBbIX HcnbITaHHH
TeXHHGeCKHX MaiepHaJlOB.
3TH MeTO.IlbI B COOTBeTCT-
BHH C TenJlOBblM pe)!\HMOM,
OCYIll.eCTBJl5!eMbiM B pa3pa-
60TaHHbiX no HHM npH60-
pax, MO)!\HO pa311.eJlHTb Ha
.IlBe OCHOBHbIe rpynnbI.
K nepBOH rpynne OTHOC5ITCfI
Te, B KOTOpbIX TenJlOBOH
pe)KHM - CTaUHOHapHblH,
KO BTOpOH - r.Ile OH He-
CTaUHOHapHbIH B CHJlY caMOlf H.IleH MeTOlI.a. YCJlOBHO 6Y:leM nx
Ha3bIBaTb «MeTO.Ilbl CTaUHOHapHoro TenJlOBOrO nOTOKa» H «MeTO.IlbI
HeCTaUHOHapHoro TenJlOBOrO nOTOKa».
MeTO.IlbI nepBOM rpynnbl n03BOJl5lIOT onupe.IleJlSlTb TOJlbKO K03<p(lm-
UHeHT TenJlOnpOBO.IlHOCTH J..., MeTO.Ilbl BTOpOH rpynnbI - JlH60 K03(l)(PH-
UHeHT TeMnepaTyponpOBO.IlHOCTH a Henocpe.IlCTBeHHO, JlH60 KOMnJleKCHO a
H J... H TOJlbKO B OGNlb pe.IlKHX CJlyqa5lX J... Henocpe.IlCTBeHHO.
JlIOOOli Ii3 npH60pOB, KOTopble 6Y.IlYT paCCMOTpeHbI .IlaJlee. COCTOHT
H3 .IlBYX OCHOBHbIX qaCTei1: KOH.IlYKTHMeTpa H KOMnJleKCa KOInpo.TJbHO-
H3MepIiTeJlbHbIX npH60pOB: noli. TepMHHOM «KOH.IlYKTHMeTp» Mbl nOHHMaeM
YCTPOIICTBO, n03BOJIflIOIll.ee C03.IlaTb B «06pa3IJ.e», T. e. B np06e. HCCJle.Ilye-
Moro TenJlOH30JlflUHOHHoro MaTepHaJla, TeMnepaTypHoe nOJle, xapaKTep
KOTOpOro onpe.IleJlSIeTC5I H.IleeH H TeopHeH MeTOlI.a, npHGeM B COCTaB
KOH.IlYKTHMeTpa BX0ll.HT H 3TOT 06pa3eIJ. B KaGeCTBe He06xo.IlHMoro 3J1e-
MeHTa. 06pa3eu co Bcex CTOpOH oKpY)KeH qaCTflMH KOH.IlYKTH
eTpa, KOTO-
pblH coe.IlHHeH JlHHH5IMH CB5I3H C KOInpOJlbHO-H3MepHTeJlbHOH annapaTY-
pOH (<pHL 67).
Ha TJIPme 'nnw nnlT1PII (,XP1'v1'hI nn.TJPrqHT HaM B naJi bHellIlleM aHaJlH3
qaCTHblX cxeM npH60pOB.



 2. PO
b BbICOKOKalJeCTBeHHbIX TenJIO"30
SlTOpOB
3.Ilecb 6bIJI npHMeHeH He oc06eHHO XOpOIllHM TenJlOH30Jl5lTOp; eCJlH
B3f1Tb BblCOKOKatJeCTBeHHbI1I MaTepHaJl, lI.JlfI KOToporo J... = 0,12, TO 'Ij eIll.e
60JlbIlle nOBbICHTC5I H CTaHeT paBHbIM 94,5%. CJle.IloBaTeJlbHO, 3HatJH-
TeJlbHOe H3MeHeHHe K03(p(pHUHeHTa TenJlOnpoBo]J.HOCTH - notJTH B .IlBa
pa3a - BbI3bIBaeT He3HaGHTeJlbHOe - nop5l1l.Ka 4% - H3MeHeHHe K03cjJ-
<pHIJ.HeHTa TenJloc6epe)KeHH5I 'Ij; n03ToMY Ha nepBbIH B3rJl5l1l., Ka3aJlOCb 6bI,
HeT oc06eHHoro CMblCJla CTpeMHTbC5I K 3HaGHTeJlbHoMY CHH)KeHHIO J....
TaKoe MHeHHe HeBepHo: Bo-nepBbIx, HMeIOT tJpe3BbIGaHHYIO Ba)KHOCTb
TenJlOBble nOTepH C HapY)!\HOH nOBepxHocTH SS H30JlflIJ.HH B HX a6COJlIOT-
HOM Bblpa)KeHHH, T. e. q KKa/l .M- 2 'laC- I ; BO-BTOpbIX, He1l.0nycTHMa
Gpe3MepHo BbICOKa51 TeMnepaTypa is 3TOH nOBepXHOCTlJ: 3Ta TeMnepaTypa
He .IloJl)!\Ha npeBOCXOll.HTb 40-50° C npH HopMa.TJbHOH TeMnepaType nOMe-
llI.eHHfI 20° C H npH YMepeHHoH IJ.HPKYJlHIJ.HH B03.Ilyxa, HHTeHCHBHOCTb
KOTOpOH 06YCJIoBJlHBaeTcfI caIlHTapHo-rHrHeHHqeCKHMH co06pa)KeHH5IMH.
vhaK, MaTepHaJibI C HH3KOII TenJlOnpOB01l.HOCTbIO BCer1l.a BbIrO.IlHbI B OTHO-
IlleHHH c6epe)KeHHfI TenJia.
11.JI5I BbItJHCJleHH5I TeMnepaTypbl is 06paTHMcfI K cjJHr. 65, 6 H npHMe-
HHM K nepe1l.aGe TenJIa OT cpe]J.bI A K cpe.Ile B Gepe3 CJlO)!\HYIO CTeHKY CI
ypaBHeHHfI (2.30) H (2.31); TenJIOBblM conpOTHBJleHHeM CTeHKH C .IlJl5I
npocToTbl paCqeTa npeHe6peraeM; nOJIYtJHTC5I
6 A - t s ts-68
q- -
-PAC+p/- P IB


OTKy.n. a


6 A . PI B + e B (P AC + P d
is=
PAC+PIB+P/
TaK, eCJlH B351Tb .IlaHHble npell.bI1l.YIll.erO npHMepa 17 H npHMeHHTb HeKa-
GeCTBeHHYIo H30Jl5lIJ.I1IO npH cpaBHHTeJIbHO MaJIOH ee TOJIIll.HHe (I5 Chi),
TO nOJIytJHM:
t s = 1),05+
:


 + 0,75 " i A + O,i:3 . t B = O,094t A + O,907t B =


(6. 5)


= 51,7 + 18,1 ::::::: 70°C.


T. e. TeMnepaTypa nOBepxHocTH H30JI5IUHH 6Y.IleT Gpe3MepHo BbICOKOH;
BeJlHKa TaK)!(e OKa3blBaeTC5I Ii nOTepfl TenJIa: no (1.13) 6Y1l.eT q =
= t s p - tB = (70-20) .12 = 600 KKa/l .M- 2 'lac-I, TOrll.a KaK 1I. 0n y-
IR
CTHMa51 nOTep51 TenJia - nopfl.IlKa 200-250 KKa/l .M- 2 'lac-I.
HapaBHe C J... !l,JIfI COBpeMeHHOH TeXHHKIi, a TaK)!(e .IlJI5I )KHJIHlll.Horo
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/ _ KOHllYKTliMeTp: / I - KOHTPOJlb
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npOCTYIO cxeMY; KOH,AYKTHMeTp nOJlY"IaeT CJle,AYIOIlI.ee OCpOpMJleHHe.
npe}K,Ae Bcero He06xoJl.HMO HMeTb HCTO"lHHK TenJla, KOTOpblH n03BO-
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06pa3eu, ]<OTOPOMY npH,AalOT cjJOPMY HJlH KBa,ApaTHOH M:JlH KpyrJlOH
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nO"lTH HCKJIIO"lHTeJlbHO nOJlb3YIOTCSI 3J1eKTpOHarpeBaTeJlSlMH. 3J1eKTpOHa-
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KOTopaSl nJlOTHO npHJleraeT K 06pa3UY. .lJ..TJSI oXJla}KJl.eHHSI npHMeHSlIOT
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npJ!60pa qJlir. 69.


B KOTOpOH U.HPKYJlHPye-r oXJla
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npOXO,ASlIlI.HH "Iepe3 06pa3e1l, "ITO He06xo,AHMO no caMOH H,Aee MeTO,Aa, a
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ero OT OCHOBHoro HarpeBaTeJlSl Ii CJlOeM TenJlOH30JlSlUHOHHoro MaTepH-
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J... B
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l-13.uepeHlle K03q}(IJ/l/{lleHTOB Ten/lOnpOBOOHOCTIl TeXHlI'leCKlIX MaTepllo,wB 121


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BHJIa OTKa3aTbCH OT BBeAemlH nonpaBKII II 1136paTb Jl.pyroii MeTO,1.\,


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J13MepeHue K03q}(IJu/{UeHTOB TenAOnpOBOOHOCTU TeXHUlleCIWX MaTepuaA08 123


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BJIHSIHHe Ha nepeHOC TenJIa B MaTCpHaJIe. LLJISI npHHIJ.HnHaJlbHOll cxeMbI
3TO 06CTOSITeJIbCTBO, KOHeqHO, pOJIH He HrpaeT.
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06ll1.eii: cxeMe qm r. 67.
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cnaeB nOMelIeHbI Ha q:Hr. 73 6YKBaMH a, b, d, f, h, h', g. 3TO qHCJlO TepMo-
nap - MHHHMaJIbHO He06xoJl.HMoe JJ.JlSI I<OHTpOJISI npaBHJIbHOCTH pa-
60TbI npH60pa. TepMonapbI B TOqKaX a H b, pacnOJlOmeHHblx Ha rOpSIqell
H XOJlOJJ.HOii: nOBepxHocTSIX 06pa3lJ.a P, cJlymaT JJ.JlSI H3MepeHHSI TeMnepa-
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napa, JJ.aJOllI.aSI TeMnepaTYPY t g B KaKOH-JIH60 T04Ke 3TOH Ha6HBKH.
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no cpopMYJle


B KOHTpOJIbHO-H3MepHTeJlbHYJO annapaTYPY II (cpHr. 67) BXOJJ.SlT
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q=S=S;= . :; , (6. ll)
rJJ.e I BblpameHO P aMnepax, U - B BOJIbTax.
113MepHB TOJllll.HHY 06pa3IJ.a 0 (B MeTpax), nOJIY4HM H HCKOMoe }..:
A=O,860IU S
t (6.12)


'leCKOMY MeTOJJ.Y. 3JJ.eCb YMeCTHO npHMeHHTb JJ.ByxnOJIJOCHoe BKJlJOqeHHe
TepMonap C OJJ.HHM XOJlOJJ.HbIM cnaeM, HanpHMep no cxeMe cpHr. 74, a,
fJJ.e npHMeHeH lllTenCeJlbHbIH nepeKJlJ04aTeJlb, HJlH no cxeMe cpHr. 74, 6,
rJJ.e nOKa3aH JJ.ByxnOJIJOcHbIH Kyp6eJIbHbIll nepeKJIJO'laTeJlb. Ha cpHr. 74,8
nOKa3aHa cxeMa BKJIJ04eHHSI TepMOCTOJl6HKa, oc06eHHo YJJ.06HaH rJlSI H3Me-
peHHSI MaJlbIX pa3HocTeH TeMnepaTYP b. t. Ha qJHr. 74 pa604He cnaH JJ.Hct>-
cpepeHIJ.HaJIbHbIX TepMonap YCJ10BHO Ha3BaHbI «ropSIqHMH», a TepMocTaTH-
pOBaHHbie cnaH TepMOnap - «XOJlOJJ.HbIMH». B Ka'leCTBe H3MepHTeJlSI
HanpSImeHHll npH TOqHblX TeXHH4eCKHX H3MepeHHSIx nOJlb3YJOTCSI xopo-
lllilM nOTI'nIJ.noMt'TpoM. a npH Tpf'OOBaHHH nOHH)!(f'HHOH TO'lHOCTH-
nHpOMeTpH'leCKHM MHJlJIHBOJIbTMeTpoM.


B KKa/l. M- 1 zpaa -1 'lac-I.




124


Ji.1.MepeHUR u npu6oplJ/


CaMO C060H pa3YMeeTcH, 4To He06xo.D.HMa TllI.aTeJIbHaH rpa.D.YHpoBKa
TepMonap. KOTOpylO CJIe.D.yeT npoBepHTb nOCJIe Kalli.D.OH npO.D.OJIlliHTeJIb-
Hoii cepHH onbITOB, oc06eHHo eCJIH TeMnepaTypa i 1 BbIllle 200° C.
.IT.JIH nO.D..D.eplliaHHH nOCTOHHHbIMH HanpHllieHHi'i Ha KJIeMMaX Harpe-
BaTeJIeiJ: H, HI' H(Jon CJIe.D.yeT npHMeHHTb cTa6HJIH3aTOp HanpHllieHHH;
He06xo.D.HMO 06ecne4HTb nOCTOHHCTBO paCXO.D.a H xopOlllee nepeMelllH-
BaHHe XOJIO.D.HJI bHOH lliH.D.KOCTH.
B 3aBHCliMOCTH oT TeMnepaTypbI i l BbI6HpalOT MaTepHaJI Kop060K,
B KOTopble 3aKJI 104eHbI HarpeBaTeJIH H, HI' H (Jon; nOKa i 1 He npeBOCXO-
.D.HT 400° C, HX H3roTOBJIHIOT H3 MeTaJIJIa, KaK H XOJIO.D.HJIbHYIO Kop06KY K.
2 MeTaJIJIH4eCKHe, .D.OCTaT04HO
MaCCIiBHbIe nJIOCKOCTH nO.D..D.aIOTCH
BeCbMa coBepllleHHoH 06pa60TKe
H. KpoMe TOro, CJIYlliaT. 6JIaroJ],a-
pH BbICOKOH TenJIOnpOBO.D.HOCTH
MeTaJIJIa, BbIpaBHHBaTeJIHMH TeM-
nepaTypbI no nOBepXHOCTHM HC-
nbITblBaeMOro 06pa3IJ.a-nJIOxoro
npoBo.D.HHKa TenJIa. B HHX npo-
.D.eJIblBalOTCH KaHaJIbI .D.JIH BBO.D.a
<DHI'. 75. HenJIOTHOCTH H B03):{YlllHble 3a- TepM03JIeKTpo.D.oB TepMonap.
30pbl B O}jHOnJIaCTHHlJaTOM KOH):{YKTHMeTpe: Cepbe3HbIM IICT04HHKOM OIIlH-
J - B03J1YX; 2 - TenJlOH30JlgTOP; 3 - MeTaJl., 60K npH onpe.D.eJIeHHH ). no 3TOMY
MeTo.IJ:Y, eCJIH MaTepHaJI nJIOT-
HbIH - C 1 >- 800-900 K2 .111- 3 - H MaJIOnOpHCTbIH, HBJIHIOTCH He-
nJIOTHOCTH B nJIOCKOCTHX ero conpHI<ocHoBeHHH C XOJIO.D.HJIbHOH KO-
P06KOii K H C HarpeBaTeJIbHOH H. 1-13-3a HeH36e>KHOH IIlepoxoBaTocTH
nOBepxHoCTeH 06pa3IJ.OB TeXHlI'IeCKHX MaTepHaJIOB, KaK, HanpHMep,
cTpOHTeJIbHblii KHpnH4 (KpaCHbIii), KHpnH4H nYCTOTeJIbie .D.JIH KpynHo-
6JI04HOrO CTpOHTeJIbCTBa (nma «KpecTbHHHH») H T. n., HHOr.D.a 6bIBaeT
04eHb TPY.D.IIO OCYllI.eCTBHTb nJIOTHOe KacaHHe BbIllleynoMHHYTbIX nOBepx-
HocTeH: Melli.IJ:y HHMH nOJIY4aeTcH B03.D.YIIlHbIH 3a30p, KaK 3TO nOKa-
3bIBaeT <pHL 75.
npH60pOB, OCHOBaHHbIX Ha MeTO.D.e O.D.HOH nJIaCTHHI<H. CYllI.eCTByeT
MHoro B pa3JIH4HbIX JIa60paTopHHx pa3HbIx CTpaH, H 3TOT MeTO.D. MOllieT
C4HTaTbCH O.D.HHM H3 HaH60JIee pa3pa60TaHHbIx. B CCCP HX n04eMY-To
npHHHTo Ha3bIBaTb npH60paMH «THlIa 51 K06a», HecMoTpH Ha cBoe06-
pa3He 3Toro nOCJIe.D.HerO, .D.eJIalOllI.t:ro ero MaJIO nOXOlliHM Ha .D.pyrHe.
CxeMa npH60pa 7lI<o6a .D.aHa Ha <pHr. 76.
::hOT npll60p, XOTH H BeCbMa cOBepllleHHbIH H XOpOIIlO npO.D.YMaHHbIH,
MaJIO npHrO.D.eH .D.JIH HcnbITaHHH TeXHH4eCKHX MaTepHaJIOB. OH. Tpe6yeT
elll.e 60JIee TOHKoro 3KcnepHMeHTHpoBaHHH, 4eM 06bI4HbIe npH60pbI.
OTJIH4HTeJIbHaH 4epTa KOH.D.YKTHMeTpH4ecI<oi'1 4aCTH: npHMeHeHHe Mac-
CHBHbIX Me.D.HbIX .D.eTaJIeH .D.JIH BbIpaBHIiBaHHH TeMnepaTYP H MaJIbIe pa3-
MepbI Bcero npH60pa. .IT.JIH KOHTpOJIH pelliHw,a CJIYlliaT lJ.eJIbIX 16 TepMonap.
y C'Tp:1HPHTH' BJ-,TIIIPYIl()
H1nYThI,{ HPfTTInTllncTPTI (\CYIIJ.PCTBJTHPTCH nocpe']:-
CTBOM npOCJIOeK H3 napa<pHHoB C BbICOKOH T04KOH nJIaBJIeHHH, TenJIOBOe


113MepeHue K03tjJtjJUl1UeHTOB TenAonpoBooHOCTU TeXHUlteCKUX MaTepuaAoB 125


conpOTHBJIeHHe KOTOpblX oco60 onpe.D.eJIHeTcH. TeMnepaTypa i 1 He BbIIIle
100°.
TOJIllI.I-IHa 06pa3IJ.a He JJ.OJIlliHa npeBblIIlaTb BO BCHKOM CJIY4ae 4 CM,
HHa4e BpeMH HCnbITaHHH KpaHHe B03paCTaeT; 06pa3lJ.bI C TOJIllI.HHOH
0,8-1 CM He .D.alOT B03MOlliHOCTH T04HO onpe.D.eJIHTb O.


I, I, I , I, I , 1.1, I r I , I ,I
b 5 (DCM


<DHI'. 76. CxeMa npll60pa M. 51 K06a.


I



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Ero H.D.eH nOHHTHa H3 <pHL 77, a. U.eHTpaJIbHbIH OCHOBHOH nJIOCImH
HarpeBaTeJIb H oKpYllieH C .D.BYX CTOpOH .D.BYMH TOlli.D.eCTBeHHbIMH nJIaCTIiH-
KaMH PIli P 2 HCnbITbIBaeMOro MaTepHaJia. CIiCTeMa H3 HarpeBaTeJlH H .D.BYX
nJiaCTIiHOK OKpYllieHa oxpaHHblM npHcnoc06JIeHHeM, COCTOHllI.HM H3 KOJIb-
lJ.eBorO HarpeBaTeJlH H K H .D.BYX O.D.HHaKOBbIX TenJlOH30JIHIJ.IiOHHbIX KO-
JIeIJ. P; H P;. K HHM H K nJiaCTHHKaM PI H P 2 nJlOTHO npHlliaTbI MaCCHBHbIe
O.D.HHaI<OBbIe XOJlO.D.HJIbHbIe Kop06KH K, H K2. 5YKBaMH a, b, c, c', d,
t, f' Ha cpHr. 77, a 0603Ha4eHbI MeCTa 3aJlOllieHHH HeKoTopbIX cnaeB
TepMonap. Ha cpHr. 77, a BHH3Y H306pa}f(eHO ce4eHHe npH60pa nJIOCKO-
CTblO, npoXO.D.HllI.eH 4epe3 ropH4YIO nOBepxHocTb O.D.HOi'I H3 nJlaCTHHOK.
npH60pbI 3Toro THna pacc4HTaHbI 06bI4HO Ha 06pa3lJ.bI KBa.D.paTHOH
<jJOPMbJ.
3TOT MeTO.D. B Ka4eCTBe CTaH.D.apTHOro (.D.JIH t cp = +20° C) npHIUJT
B 1954 r. Melli.IJ:YHapO.D.HbIM 06'be.D.HHeHHeM J1a60paTopHi'1 HcnblTaHHi'1
CTpOHTeJlbHblX MaTepHaJIOB (R I LEM); OH 04eHb 6J1H30K K HaIIleMY OTe-
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HaMH B npe.D.bI.D.YllI.eM naparpacpe (qmr. 77, 6).




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113MepeHue K03tjJtjJUl1UeHTOB Ten_1OnpoBOaHOCTU TeXHllfleCKUX MaTepllaAOB 127


PaCqeTHaH ct>opMYJIa 3TOro MeToJJ.a aHaJIOmqHa (6.11), TOJIbKO BMe-
1
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u:eHTpaJIbHbIM HarpeBaTeJIeM, pacIJpeJJ.eJIHeTCH IJOpOBHY Me}KJJ.Y JJ.BYMH
COBepll1eHHO oJJ.HHaKoBbIMH qaCTHMH KOHJJ.YKTHMeTpa; IJ03TOMY


1 Q* I
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(6. 13)


06a MeToJJ.a IJpH rOJJ.HbI TOJIbKO JJ.JIH OJJ.HOpOJJ.HbIX MaTepHaJIOB; JJ.a}Ke
He60JIbll1aH HeOJJ.HOpOJJ.HOCTb, Bblpa}KalOlQaHCH B BapnaU:HHX IJJIOTHOCTH
H CTPYKT)'pbI MaTepnaJIa OT OJJ.HOll ero TOqKH I< JJ.Pyroi1, BbI3bIBaeT He06xo-
JJ.HMOCTb B qaCTbIX IJOBTOpHblX HCIJbITaHHHX HeCKOJIbKnX 06pa3l!OB, qTO
KpaHHe YJJ../IHHHeT H YCJIO}KHHeT HCIJblTaHne.
3TO OTHOCHTCH K MeToJJ.Y O
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HH6YJJ.b HeoJJ.HopoJJ.HbIX MaTepnaJIOB OH COBepll1eHHO He IJpHrOJJ.eH
B Tex CJIyqaHX, KorJJ.a }KeJIaTeJIbHO IJOJIyqeHHe 60JIee BbI.COKHX cpeJJ.-
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HarpeBaTeJIbHbIMH IJJIHTaMH. LLpyroll THIJ IJpn60pa JJ.JIH 60JIee BbICOKHX
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 7.



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B HeKoTopbIX, peJJ.KHx, CJIyqaHX, KorJJ.a TOJIlQHHa 06pa3u:a MaJIa B a6co.
JIIOTHOM Bblpa}KeHHH (IJOpHJJ.Ka HeCKOJIbKHX MHJIJIHMeTpOB, a OTHOll1eHHe
8/L, I'JJ.
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6e3 oxpaHHoro KOJIbu:a. KOHeqHO, IJpH 3THX YCJIOBHHX npHxoJJ.HTCH 06pa-
lQaTb oc060e BHHMaHH
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3YIOTCH He A, a HMeHHO P [3].
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IJOpHJJ.OK O}KHJJ.aeMbIX IJpH 3TOM 0ll1H60K MO}KHO YCTaHOBHTb IJOCpeJJ.cTBoM
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OT KaKHX llJaKTopoB 3aBHCHT 3Ta 01lJJl6Ka.
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JJ.nMbIH K HH}KHeH IJOBepXHocTH 06pa3u:a, paBHblii Q*, TeM HJIH HHblM CIJO-
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B03JJ.YX:


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128


Jf3MepeHUJ/ U npu60pIJt


I1peHe6pe)KeM HCKpHBJleHlleM JlIIHIIH TenJlOBOrO TOI(3 H 3aBIICI1MOCTblO
TenJlOnpOBO}J.HOCTH OT TeMnepaTypbI.
Tor}J.a pacnpe}J.eJleHHe Te!VmepaTYP Ha 60KOBOH nOBepxHocTH 06-
pa3IJ.a mil (cpllr. 71, a) 6Y}J.eT JlIIHeHHOe, a ):LJlH nOTepll TenJla Q/, T. e.
TenJlOBOrO nOTOKa, nOJlY'IlIM BbIpa)KeHHe
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B CHJJY ynpOlIJ.eHHOrO npe}J.nOJlO)KeHHH 0 TeMnepaTypHoM nOJle MbI nOJlY-
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r):Le
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S M


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(6. 15)


1-13 npH6ml)KeHHblX CPOPMYJI (6.14) H (6.15) BbIBO}J.HM CJle}J.YIOlIJ.He
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lIJ.H Ha 0;
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nOMelIJ.eHHH; TaK, HanpllMep, eCJlH 8 = 20°, TO, C03):LaBaH npH HCnbITaHHH
YCJlOBHH t 2 = 0°, t 1 = 40°, CHJlbHO CHH3HM 3TY 01llH6KY;
3) YBeJlHlJeHHe At npH C06J1IO}J.eHHH HeH3MeHHOCTH tap = 1) t 12
CHH)KaeT 01llH6KY;
4) OHa 6Y):LeT oc06eHHO 3aMeTHa npH OnblTaX C TenJlOH30JlHTOpaMH,
KOr):La A MaJlO, H, Ha060poT, npH 3KcnepHMeHTax C MeTaJlJlaMH alIa CHH-
)KaeTCH;
5) npeHe6pe)KeHHe YTelJKOii TenJla no 601WBOH nOBepXHOCTH oGpa3IJ.a
Be):LeT K nOJlYlJeHHIO 3aHH)KeHHbIX no cpaBHeHHIO C HCTHHHbIM 3H<JlJe-
HHH TenJlOnpOBO}J.HOCTH.
flpu.M.ep 19. O):LHOnJlaCTilHlJaTbIH npH60p, cxeMa KOToporo '}J.aHa Ha
(!mr. 78. npHMeHeH ):LJlH onpe}J.eJleHHH TenJlOBOrO conpOTHBJleHHH TKaHH,
KYCOK KOTOpOH P 3aJlO)KeH Me)K}J.Y OlJeHb TOHKlIM nJlOCKHM HarpeBa-
TeJleM H H JlerKOH MeTaJlJlHlJeCKOii nJlaCTHHKoH; CHH3Y HMeeTCH ):LonOJl-
IIHTf''1I.,Hhlrr H
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nOTOK H3 H-O}J.HOCTOpOHHHI1; ):L.1H h.OHTpOJJH 3TOrO CJlY)KHT ):LHqxpepellIJ.H-


l1sMepeHue K03tjJtjJU/{UeHTOB TenAonpOBOOHOCTU TeXHUIleCKUX MaTepUaAoB 129


;


3J1bHaH TepMonapa HJlH TepMOCTOJl6HK, O):LHH H3 cnaeB KOToporo npH-
KJleeHbI K HH)KHeH CTopOHe HarpeBaTeJlH H, a ):LPyme - K BepXHell
CTopoHe HarpeBaTeJlH Hoon' I1YCTb H3MepeHbI TaK)Ke TeMnepa;YPbl
i 1 = 50°, i 2 = 10°; 8 = 20°. TenJlOBOe conpOTHBJleHHe TKaHH, HaH):LeH-
Hoe HHbIM, He3aBHCHMbIM, MeTO):LOM, P ' 0,1 M 2 fiac epaa KIW/l- 1 .
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BeTCTBHH C pa3MepaMH HarpeBaTeJlH H, Ha KOTOpbIll OH nOJlO)KeH Heno-
cpe):LCTBeHHo, HMeeT CPOPMY KBa):LpaTa co CTOpOHOll L = 20 CM. I1pHMep-
lIaH TOJlll(HHa TKaHI;! 0
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I'fO[ln
<DHr. 78. CxeMa KOH):{YKTHMeTpa .nJlH H3MepeHHH TenJIOBblX conpOTHBJIeHHii TOHKHX CJIOeB
TenJIOH30JlHTOpOB no MeTO):{Y o):{Hoii nJIaCTHHKH 6e3 oxpaHHoro KOJIbua:
p' _ .I10nOJlHHTeJlbHblH CnD" TennoH30nHTopa; A - MeT8nJlH'.leCKHe BblpaBHHB810IllHe TeMnepaTYPHoe none
JlHCTbI. OTlleJlbHO npellCT3BJleH3 npHM3H. H306pa>K3101U3H npH6J1H>KeHHO pacnpelleJleHHe TeMnep3TYP Ha
60KOBOfl nOBepxHocTH mn HcnblTbluaeMoro nOnll w


<I>OPMYJlY (6.13) MmKHO HanHcaTb B BH):Le
o t cp - 6

=4T' !::.t exP.


K03qxpHIJ.HeHT TenJlOOT):LalJH ex B CnOKOHHOM B03):Lyxe OIJ.eHHM I1.H4>-
pOll 10 (cp. C KOHI1.0M npHMepa
 11 rJl. 6). Tor}J.a
5 30-20
1:.- 4 .-. .(0.01;::,-.20 %
10- 200 40 ,_.
OlllH6Ka 6Y):LeT He3HalJHTeJlbHa.
CYlIJ.eCTByeT, KpOMe TKaHeH O):Le)K):LbI, pH}J. MaTepHaJlOB, HanpHMep
rocppHpOBaHHbIH KapTOH, fIlleHCTbIe ac6eCTOBble JlHCTbI H T. n., npH HcnbI-
TaHHH KOTOpblX Ha TenJlOnpOBO;\HOCTb Henocpe):LCTBeHHO Ha npH60pax
onpe):LeJlHeTCH P, a He A. Tor):La BMeCTO CPOPMYJlbl (6.10) HJlH (6.12)
CJle):LyeT nOJlb30BaTbCH CPOPMYJlOH
P =
. (6. 16)
q
OlJeBH):LH,O TaK)Ke, lJTO H3J10)KeHHbIe Bblllle MeTO):LbI n03BOJlHIOT onpe):Le-
JlHTb HenOCpe):LCTBeHHO TenJlOBOe conpOTHBJleHHe MHOrOCJlOHHbIX JlHCTO-
BblX H3):LeJII1H; }J.JlH 3Toro HeT He06xo):LHMOCTH 3HaTb TOJllIJ.HHbI H TenJlO-
npOBO):LHOCTH MaTepHaJlOB OT):LeJlbHbIX CJIOeB. Tor):La B (6.16) nO):L P cJle-
'{YPT nnmllll/
Th 3I{RnB
 TJPHTHOP TPnJlOROf' conpOTHBJJf'HJ.ie ('JlO)KHOrO (,JlOH,
T. e. Ps .
9 l{oHllpanea Z763




130


If 3MepeHUR U npu60pbt


YlMelOTcH nOnblTKH npUMeHUTb K onpeJ].eJleHI1IO TenJJOBblX COnpOTUB-
JleHUH U K03$tJl1Ul1eHTOB TenJlOnpOBOJ].HOCTU CTapbIH CpaBHUTeJlbHbIH
MeTOJ]. XpUCHaHCeHa, npeJ].Ha3I-Ja'IaBIIlHikH J].JlH )K11J].IWCTeH H OCHOBaHHbIH
Ha HaJlUlIl1H «3TaJlOHHOrO» UJlU, JlYlIwe CKa3aTb, C<HOpMaJlbHOrO» MaTe-
pHaJla [8], T. e. MaTepUaJla N; 06J1aJ].alOll.{ero xopowo 113YlIeHHoH H
HeU3MeHHOH TenJlOnpOBOJ].HOCTblO, C KOTOpbIM H CpaBHI1BalOT I1CCJle):Lye-
MbIH MaTepHaJl X. Yl):LeH MeTO):La OlleHh npoCTa H BbITeKaeT H3 q:mr. 79.
06pa3uaM MaTepl1aJlOB npH):LalOT rpopMY nJlaCTHH C O):LHHaKOBbIMU
OCHOBaHUHMH, C TOJlIl.{HHaMH ONH ox; H'\ nJlOTHO npH)KHMaIOT JJ.Pyr K ):LPY-
ry, K nJlOCKoMY HarpeBaTeJIlO
H (MeTaJlJlHlIeCKOH Kop06Ke)
U K nJlOCKOH (oxJla)K):LaeMOH
/( BO):LOH HJlU B03):LYXOM KOMHaTbI)
MeTaJlJlHlIeCKOH nJlHTe K. Ten-
ON JlOBOH nOTOK, C03):LaBaeMbIH
t HarpeBaTeJleM, npOXO):LHT lIepe3
r; 06e nJlaCTHHKH. ECJlU t 1 H t 2 -
TeMnepaTypbI Ha ropHlIeH H
XOJlO):LHOH CTOpOHax 3TOH ):LBYX-
COCTaBHOH nJlaCTHHKH, t'if._
TeMnepaTypa B nJlOCKOCTH HX
conpUKOCHOBeHlHI, TO MbI HMe-
E'M:


. t( .: . '_ -


If


f


<DHL 79. CXeMa cpaBHIITeJlbHoro MeTOJ1a onpe-
J\eJIeHHH K03qx!mUHeHTa TenJIOnpoBo.nHOCTH Ten-
JlOH30JIHI.lHOHHbIX MaTepHaJIOB, no X pHcTHaH-
ceHY.


q=


/1 - i*
Px


i* - i z
PN


a OTCIO):La BbITeKaeT paclIeTHaH rpopMYJla MeTO):La
p = Ox = i 1 - i* P .
x I,x i* - i 2 N


(6. 17)


TaK KaK P N U3BeCTHO (MaTCpHaJl HOpMaJlbHbIif), TO ):LJl5I onpe):LeJle-
HU5I P x , KaK BU}J.HO U3 (6.16), }J.OCTaTOllHO TOJlbKO 113MepUTb TeMnepaTYP-
Hble pa3HocTH t 1 - t* 11 t* - t 2 : 3HaTb TenJloBoM nOTOK HeT He06xoJJ.u-
MOCTH, OTna):LaeT HaJ].06HocTb U B oxpaHHoM KOJlbue.
3TU BbIBO}J.bI cn, paBe}J.JlUBbI }J.a U TO C 60JlbillIlMlI orOBopK3MH, B TOM
CJlYlIae, eCJlII npll BOnJlOll.{eHlI1I 3Toro MeTO}J.a B BII):Le npH60pa 6Y):LYT
C06J1IO):LeHbI CJleJ].YIOIl.{He YCJlOBII5I: 1) TOJlll.{lIHa 0 = Ox + ON ):LBYXCOCTaB-
HOH H3 N 11 X nJlaCTUHKH OlleHb MaJJa H a6COJllOTHO H no OTHOIlleHHIO
K ee OCHOBaHII5IM; 2) rpa):LHeHTbl TeMnepaTYP B 06eHx nJlaCTHHKax Ha-
CTOJlbKO M3J1bI H pa3HocTb TeMnepaTYP t 1 - t 2 HaCTOJlbKO MaJla (HeCKOJlb-
KO rpa):LYCOB), liTO MO)KHO ClIHT3Tb Ax II fW nOCT05lHHbIMH, a pacnpe):LeJle-
HlIe TeMnepaTYP B MaTepHaJlaX X H N JIll HeHHbIM. TaKHe )KeCTKIfe YCJlOBUH
HeB03MO)KHO oCYIIJ.eCTBUTb npll 3KcnepHMeHT3x C TeXHHlIeCKIIMII TenJlO-
H30Jl5lTOp3MH, H n03ToMY nonbITKII npIIMeHHTb 3TOT MeTO):L K HHM KOH-
lIHJlHCb HeYJ].allerr, lIe rOBopH Y)Ke 0 Heonpe}J.eJleHHOCTII npH H3MepeHHH t*
II oueHKe 0 y II 0"". MO)KHO TOJlbKO nOnbITaTbCH npHMeHHTb 3TY MeTO):LHKY
K TK3HHM {cpo c npllMcpOM l
).


/13MepeHue K03tjJtjJUljUeHTOB TenAonpoBooHOCTU TeXHUlteCKUX MaTepuaAofl 131


Co BpeMeH XpHcTHaHceHa (1881 ro):L) 3TOT cpaBHHTeJJbHbIH MeTO}J.
npHMeH5IIOT K )KH):LKOCT5IM, pacnoJlara51 HarpeBaTeJlb cBepxy, a He CHH3Y,
KaK Ha rpl1r. 79. CnOH )KH):LKOCTH TOJlIIJ.HHOH 0 - nOp5l):LKa 1-1,5 MM
npH L -;:::: 120 MM; HOpMaJlblO CJlY)KI1T CTeKJl5IHHaH nJlaCTHHKa [10,
13],



 7. MeTo.n I1J1aCTHHKH I1PH BbICOKHX TeMIIepaTypax
Cpe):LH pa3J1HlIHbIX BapHaHToB HaH60JlbillerO BHHMaHH5I 3aCJlY)KHBaeT
MeTO):L, cxeMa KOToporo H306pa)KeHa Ha rpHr. 80 [16 L YlcnbITblBaeMbIH


c


p


D





H


[


<DHr. 80. CxeMa npH60pa HcnblTareJlbHOii Jla-
60paTopHH Hal.lHOHaJIbHOrO HHCTlJTYTa <l>paHI.lHH
JI,JIH onpe.neJJeHIJH K03ct4JH I.lHeHTa TenJlOnpoBo,n-
BOCTH .no 10000. C (Ha ropHlJeii cTopoHe).


J


06pa3eu P (nJlaCTHHKa) pacnOJlO)KeH Me)KJ].y nJlOCKHM 3J1eKTpHlIecKHM
HarpeBaTeJleM H H CHcTeMoH H3 }J.BYX KOHueHTpHlIecKHx COCY}J.OB, HanOJl-
HeHHblX ):LHCTHJlJlHpOBaHHOH BO}J.oiL BO}J.a }J.OBO):LHTC5I ):LO KHneHHH npH aT-
MocrpepHoM ):LaBJleHHH nO):L BJllI5IHlIeM TenJla, npoxo):L5Ill.{ero OT HarpeBa-
TeJlH lIepe3 06pa3eu. 50KoBa51 H BepXH5I5I lIaCTb ueHTpaJlbHOrO cocY):La C
oKpY)KeHa KHn5lll.{eH BO):LOH 11 ee napoM, KOTOpbIH BMeCTe C lIaCTblO 06.
pa3ua, oKPY)KalOIIJ.eH ero cpe}J.HIOIO lIaCTb, npHJleralOIIJ.YIO K C, IIrpael
TY >Ke pOJlb, KaK H oxpaHHoe KOJlbUO B onHcaHHOM paHee npH60pe ):LJIS'
60Jlee HI13KlIX TeMnepaTYP (
 4 3TOH rJlaBbI).
He'lIPHlH::t nnJl f-Inrn TenJl0f\nrn nnTnK::t, npo....0J\HTTTPfO R yrT:JHoRIIP,.
IlleMC5I pe)KIIMe lIepe3 ueHTpaJlbHYIO qaCTb 06pa3ua, HaXO):L5IIl.{YIOC5I nOl
9*




132


HSMepeHUR U npu60pN


,AHOM cocy,Aa C, HaXO,!{HTCSI no KOJmqeCTBY BO,!{bl, HcnapSHom;eikSI B Teqe-
HHe e,!{HHHLlbl BpeMeHH B cocy,!{e C. ::ha Bo,!{a nOJ1yqaeTCSI KaK KOH,!{eHcaT
napa, BbIXO,!{SIm;ero H3 C qepe3 TPy6KY R, oKpymeHHYIO X0J10,AHJ1bHH-
KOM K.
Cpe,!{HHii: K03qxpHLlHeHT TenJIOnpOBO,!{HOCTH MaTepHaJ1a 06pa3Lla BblqHC-
JISIeTCSI no <popMYJ1e


537G

A cp = 5.tH '


(6. 18)


B KOTOpOii: 8 - TOJ1LLlHHa nJ1aCTHHKH B M; G - KOJIHqeCTBO HcnapSIIO-
LLleHcSI B LleHTpaJ1bHOM cocy,!{e C BO,!{bl B KC'laC- I ; S - nJ10LLla,!{b ee ,!{Ha
B M:!. K03qxpHLlHeHT 537 npe,!{CTaBJ1SIeT c06010 CKpblTYIO TenJ10TY BO,!{bI
npI1 HcnapeHHH no,A aTMoc<pepHbIM ,!{aBJ1eHHeM, Bblpa}KeHHYIO B KKa/l/Kc- l .
B 3aBHCHMOCTH OT THna HarpeBaTeJ1SI H TeMnepaTypa Ha rOpSlqeH
cTOpoHe 06pa3Lla MomeT ,!{OCTHraTb 1000-1200° C H BbIIlle. MorYT 6bITb
.npHMeHeHbI HHXpoMoBbie H HM aHaJ10rHqHble 3J1eKTpOHarpeBaTeJ1H H3
MeTaJ1J1a, CHJ1HTOBble cTepmHH H T. n.
TeMnepaTypa XOJIO,!{HOii: CTOpOHbI 06pa3Lla /2
 100° C.


* *


*


)..
./


MeTO,!{bI nJ1aCTHHKH y,A06HbI ,!{J1S1 HCnbITaHHii: Ha TenJ10npOBO,!{HOCTb
rnep,!{bIX TenJ10H30J1SILlHOHHbIX H CTpOlJTeJ1bHbIX MaTepHaJ10B, TenJ10npo-
BO,!{HOCTb KOTOpbIX He OqeHb BbICOKa. TaK, YCTaHOBJ1eHHbIH Mem,!{YHapo,!{-
HbIM COBem;aHHeM 1954 r. (a TaKme aMepHKaHcKHM 06LLlecTBoM no HcnbI-
TaHHIO MaTepHaJ10B ASTM) MeTO,!{ paCCqHTaH Ha npHMeHeHHe K MaTepHa-
JIaM, A KOTOpbIX He npeBbIIllaeT 1,8 KKa/l M- 1 'lac- l cpaa- 1 (npH 20° C).
TOJILLlHHY 06pa3Lla He paLlHOHaJ1bHO 6paTb 60J1bIlle 4-5 CM, H60 B npo-
THBHOM cJ1yqae Kpaii:He 3aTSIrHBaeTCSI BpeMSI YCTaHOBJ1eHHSI cTaLlHoHap-
Horo TenJIOBOrO pemHMa KOH,!{YKTHMeTpa, Mem,!{y TeM KaK O,!{Ha H3 qaCTO
BCTpeqalOLLlHXCSI OIllH60K HMeHHO H 3aKJ1IO'laeTCSI B TOM, qTO OTCqeTbI nOKa-
3aHHii: npH60pOB CHHMalOT, He ,!{om,!{aBIllHCb CTaLlHOHapHoro pe}KHMa
Bcero KOH,!{YKTHMeTpa.
flpu.M.ep 20. 0YCTb nocpe,!{CTBOM O,!{HOnJ1aCTHHqaTOrO npH60pa ,!{J1SI
onpe,!{eJIeHHSI TenJ10npOBO,!{HOCTH, onHcaHHoro B
 4 H H306pameHHoro
Ha <pHr. 73, H3MepSllOT K03qxpI:lLlHeHT TenJ10npoBo,!{HOCTH nJ10THOrO CTPOH-
TeJ1bHOrO MaTepHaJ1a, TI:Ina 6eToHa, C IllepoxoBaToii: nOBepxHocTblO.
BCJ1e,!{cTBHe 3Toro BnOJ1He B03MO}KHa oIllH6Ka, Ha KOTOPYIO 6bIJ10 YKa3aHo
B KOHLle
 4 (<pHr. 75), BbI3BaHHaSI HeH36e}KHOH HenJ10THOCTblO conpHKoc-
HOBeHHSI nOBepxHocTeii: 06pa3Lla H Kopo60K, C oXJIam,!{aIOLLleii: }KH,!{KO-
CTblO K H C 3JIeKTpOHarpeBaTeJIeM H (<pIJr. 81). HaJ1HqHe HenJ10THOro
KacaHHSI paBHOCHJIbHO, C TOqKH 3peHHSI TenJIOnepe.D.aqH, HaJ1IJ'lIJIO ,!{BYX
TOHKHX B03,!{YlllHbIX C.ROeB. OLleHIJM TOJILLlHHY Ka}K,!{oro 8'
 8. :::::; 0, I MM.
OOCTaBHM ce6e LleJIblO YCTaHOBHTb nopSl,!{OK BbIIlleHa3BaHHoii: OIllH6KH,
eCJ1IJ HCTHHHaSI TenJ10npOBO,!{HOCTb MaTepHaJ1a A = I KKa/l M-] 'lac-]
i'paol, a TOJILLlIJHa o6pa3Lla 8x 4 CM = 0,04 M, npHHSlTaSI paBHoH
raCCTOJUlIllO t) Me>K,AY nUD
p.xHUL HI Mil 11<11 pCDal
JlSl II H XlJJIU)J.I1JILIlIIh<l
K, T. e. 6e3 yqeTa HenJIOTHocTeii: KacaHHSI.


I1sMepeHue K03tjJtjJUl{ueHTOB TenAonpOBOaHOCTU TeXHU'leCKUX MaTepuaAoB 133


B ,AeiiCTBHTeJ1bHOCTH Mbl ,!{OJ1}KHbl oLleHHTb TOJ1IUI1HY MaTepHaJ1a
B t x = 40-0,2 = 39,8 MM (pa3HocTb, Ka3aJ10Cb 6bI, npaKTHqeCKH He
HMelOll.taSI 3HaqeHHSI). OnblT npOH3BO.D.HTCSI npH TeMnepaTypax, 6J1H3KHX
K 20°, npH He3HaqHTeJ1bHOM nepena,!{e TeMnepaTYP 6./ H n03ToMY Mbl
npeHe6peraeM 3aBHCHMOCTblO TenJ10npoBo,AHOCTH B03,!{yxa OT TeMnepa-
TYPbI; npHMeM A p03iJ = 0,022 COOTBeTCTBeHHO / = 25° [10]. TenJ1onpo-
BO,AHOCTb, HaH.D.eHHYIO C OIllII6KOH, 6e3 yqeTa TenJ10BOrO conpOTHBJIeHIISI
B03,!{YlllHbIX CJ10eB


ii' 'f,W
P iJ=
+-"-"
B03 I\B030 "BoOO


0603HaqIIM >"oum/5..
BblBe,!{eM cnepBa
.D.J1SI OLleHKH 0IllII6KII.

 6 rJ1. 2 HMeeM:
t 1 - t 2
q-
- P +P B03 iJ


06m;ylO cjJOPMYJIY
00 06m;eH TeopIIII


9


H


t 1 - t2
- POUlu6 '


r,!{e


o 0',7
/;J=h


'f,
. P oUlu6 =
,
l\oUlu6


a OTCIO,!{a


K


P OUlu6 - P = P poai)'
TaK qTO B 06LLleM cJ1yqae oIllH6Ka MomeT
6bITb OLleHeHa B npoLleHTax ,!{p06blO
P oum 6 - P .100 = P"030 .100 (6. 19)
P P'


<lJHr. 81. K pac'IeTY 01I1H6KH,
BbI3BaHHoii HenJIOTHblM npHJIera-
HHeM 06pa3ua HcnblTblBaeMoro
MaTepHaJIa K nJIOCKOCTHM .neTa-
JIeii npH60poB.


Oepexo,!{SI OT TenJ10BbIX conpOTHBJ1eHHH K K03c1JclJHLlHeHTaM TenJ10-
npoBo,!{HOCTH, J1erKO oLleHIIM II OIllII6KY B A.
B ,!{aHHoM qaCTHOM CJIyqae 6Y,AeM IIMeTb
02.10- 3
PBO.w = '0,022 = 0,0091 (TexH. e,AHH.);


P _ 0,0398 .
- 1 '


j


n03TOMY no (6. 17) nOJ1yqHM ,!{JISI 0lllH6KH B OLleHKe TenJ10BOrO conpo-
TH)3J1eHIJSI 06pa3Lla BeJIIIqIIHY B o
o

 % = 23%, a ,!{J1SI A OUlUlJ HaH,!{eM
o 0,04 00
A OUlU6 = POUlu6 = 0,0398 + 0,0091 = 0,82 BMeCTO 1, .
OnblT BCeLleJIO nO,!{TBep}K.D.aeT npaBIIJ1bHOCTb 3TOii: OLleHKH: IJMeHHO
TaKoro nopSI,!{Ka (20-30%) OIllII6KIJ II nOJ1Y'laIOTCSI npII HeyMeJIOM 06pa:
m;eHIIII co BCeMIJ BapIIaHTaMII npII60poB, OCHOBaHHblX Ha C<MeTo,!{ax O,!{HOH
H ,!{BYX nJIaCTIIHOK».
COBepllleHHo IIHaqe 06CTOI:lT .D.eJIO, eCJ1H npIIXO,!{HTCSI HCnbITbIBaTb
'leIlJIUH3UJIHLlI10HHbl
 Md r
pHaJlbl B 6uJlee Y3KOM l:Mbll:Jle :lIUIO CJIOila,
T. e. MaTepIIaJIbI, TenJIOnpOBO,!{HOCTb KOTOpbIX (npH 20°) He npeBOCXO,!{IJT




134


J13MepeHUR u npu60pIJI


0, ]5-0,20. 3}J.ecb Y}Ke Jlerqe YCTpaHHMbl B03}J.YlllHble llleJlH (HanpHMep,
nocpe}J.CTBOM nO}J.CbmaHHH MeJlKOrO nopolllKa MaTepHaJla, TenJlOnpoBo}J.-
HOCTb KOToporo cpaBHHMa C TenJlOnpoBo}J.HOCTblO caMoro HCnblTbIBaeMOro
MaTepHaJla). a KpOMe Toro, 3TH llleJlH Y}Ke 3HaqHTeJlbHO MeHbllle OTpa-
}KaIOTCH Ha 01lm6Ke H3MepeHHH, KaK BH}J.HO H3 CJle}J.YlOlllero npHMepa.
flpu.M.ep 21. Ha nJlOCKOM npH60pe, 0 KOTOpOM rOBOpHJlOCb B npe}J.bl-
}J.YllleM npHMepe, npoH3Bo}J.HTCH HcnbITaHHe TenJlOH30JlHlJ.HOHHOro MaTe-
pHaJla. Be3 yqeTa BJlHHHHH B03}J.YlllHbIX npOCJlOeK 6blJlO nOJlyqeHO
}J.JlH TeX }Ke TeMnepaTypHblX YCJlOBHH t 1 H (2' npH TOH }Ke TOJlIllHHe 0
4 CM A = 0,08.
OlJ.eHHM 01llH6KY B H3MepeHHH, 06ycJloBJleHHYlO 3TOH npHqHHoH.
Haxo}J.HM P owu6 =
:
: = 0,5, a 3aTeM HCTHHHoe
P = POWll6 - P 8030 = 0,5 - 0,009]
(H60 3}J.eCb P 8030-TO }Ke, qTO H B npe}J.bl}J.YllleM npHMepe), T. e. P=0,491.
OocJle 3Toro JlerKO onpe}J.eJlHM H HCTHHHYIO TenJlOnpoBo}J.HOCTb Ax =
o 398.10- 2
= P = '0,491 = 0,08]; 01llH6Ka 3Ta - 3a npe}J.eJlaMH TOqHOCTH
TeXHHqeCKHX H3MepeHHH TenJlOnpoBo}J.HOCTH.
B 3THX paCqeTaX MbI npeHe6perJlH 3aBHCHMOCTblO K03cpcpHlJ.HeHTOB
TenJlOnpOBO}J.HOCTH OT TeMnepaTypbl - }J.JlH npocToTbI paCl.JeTa. TaK
KaK 1.8030 B03paCTaeT (H OqeHb 3aMeTHO) C TeMnepaTYPOH, TO MO}KeT
nOKa3aTbCH Ha nepBbIH B3rJlH}J., qTO paCCqHTaHHaH Bblllle 01llH6Ka
6Y}J.eT He TaK Y}Ke 3HaI.JHTeJlbHa; 3TO HeBepHO: H onbITbl, H npHKH}J.OqHble
paCl.JeTbI nOKa3bIBa1OT, qTO H npH nOBblllleHHblX TeMnepaTypax }J.eJlo 06-
CTOHT He JlYl.Jllle. ECJlH }KeJlaTeJlbHO Yl.JeCTb 3aBHCHMOCTb 1.8030 OT TeM-
nepaTypbI, CJle}J.yeT 06paTHTbCH K Ta6J1HlJ.aM; XOTH 3Ta 3aBHCHMOCTb HeJlH-
HeHHaH, HO B HHTepBaJle 0-200°C C TOqHOCTblO, }J.OCTaTOqHOH }J.JlH TeXH}l-
qeCKH x paCqeTOB [10 1. MO}KHO nOJlaraTb
A 803Q ;:::;:; 0,0205 (] + 0,28. I
O ) .



 8. MeTo}J. TPy6bl
LIano npe}J.cTaBJlHeT 60.TlblllOH npaKTHl.JeCKHH HHTepec npH HCnblTaHHH
Ha TenJlOnpoBo}J.HOCTb TenJlOH30JlHlJ.HOHHOro MaTepHaJla nO}J.oHTH KaK MmK-
HO 6J1H}Ke K YCJlOBHHM, KOTopble HMelOT MeCTO npH 3KCnJlyaTalJ.HH. O}J.HHM
H3 MeTo}J.oB, }J.alOllJ.HX TaKYIO B03MO}KHOCTb, CJlY}KHT MeTO}J. TPy6bl, npH-
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140


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(6. 25)


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HOCTH. .D,HaMeTp BHYTpeHHeH MeTaJ1JIHqeCKOH TPy6bI T BbI6HpalOT no-
pH)J.Ka 6-15 CM; HaXO)J.HILlYIOCH BHYTPH Hee Tpy6y R HHor)J.a HanOJIHHIOT
nopOlllKOM TpeneJ1a HJIH )J.HaTOMHTa [16]; CJ10H HCnbITblBaeMOH H30J1HUHH
TOJ1Il1.HHOH )J.O 7 CM.
MeTO)J. pa3pa60TaH npeHMYIlI.ecTBeHHo )J.JIH TeMnepaTYP t 1 = 300-
350° C.



 9. MeTo)J. lllapa


06a BbIllleonHcaHHbIX MeTO)J.a MaJIO npHro)J.HbI )J.J1H nopolllKo06pa3-
HbIX, cbmyqHX H HeKoTopbIX B0J10KHHCTbIX MaTepHaJIOB, HaXO)J.flILlHX
umpoKoe npHMeHeHHe Ha npaKTHKe. DO
ToMY )J.JIH HcnbITaHHH Ha TenJ10-
npoBO)J.HOCTb nO)J.06Horo pO)J.a MaTepHaJIOB nOJIb3YIOTCH MeTO)J.OM lllapa,
H)J.eH KOTOpOro HCHa H3 <pHr. 86.
3J1eKTpHqeCKHH HarpeBaTeJIb H no-
MeIll.eH BHYTPH MeTaJ1JIHqeCKOrO no-
J1oro lllapa S'; K(jHueHTpHqHO C HHM
pacn0J10)KeHa lllapOBaH MeTaJIJ1HqeC-
KaH 060J10qKa S, a npoCTpaHCTBO
Me)K)J.Y HeH H BHYTpeHHHM lllapoM
F 3anOJIHeHO HcnbITblBaeMbIM MaTepHa-
J10M. B TOqKaX M 1 H M2' paccToH-
HHe KOTOpbIX OT 06ILlero ueHTpa
lllapdB S' H S CYTb R 1 H R2' Ha-
XO)J.flTCH cnaH TepMonap )J.JIH -H3Me-
peHHH TeMnepaTYP B 311iX TOqKaX
t 1 H t 2 . Tor)J.a cpe)J.HHH K03<Mm-
UHeHT TenJ10npoBo)J.HOCTH Me)K)J.Y
TeMnepaTypaMH t 1 H t 2 6Y)J.eT HaH-
)J.eH no <PoPMYJ1e (2.16) HJ1H
1 ( 1 1 )
A _ 2; D; -
 Q*
C'p- 1 1 -/ 2
3)J.ecb Q*-nOJIHOe KOJ1HqeCTBO TenJ1a, BbI)J.eJIHeMOe 3J1eKTpOHarpena-
TeJ1eM Ha e)J.HHHuy BpeMeHH.
DpeHMYIlI.ecTBaMH 3Toro MeTo)J.a HBJ1 fleTCH , Bo-nepBbIX, OTCYTCTBHe
napa3HTHbIX nOTepb, TaK KaK Bce TenJIO OT HarpeBaTeJ1f1 npOXO)J.HT CKB03b
06p a3e u MaTepHaJIa, HMelOILlHH 3)J.ecb <POPMY lllapoBoro CJIOH; BO-BTOPbIX,
B03MO)KHOCTb H3 o)J.Horo OnblTa HaHTH 3aBHCHMOCTb K03<pcp H U H eHTa
TenJIOnpoBo)J.HOCTH OT TeMnepaTypbI, B TOM CJ1yqae, eCJIH pa3MepbI npH-
60pa n03BOJIHIOT pa3MecTHTb BHYTPH Hero 3 (HJ1H 60JIee) cnaH TepMonap.
.D,JIH lllapOB MaJ10rO )J.HaMeTpa np
xo)J.HTCH OrpaHHqHTbCH TOJIbKO )J.BYMH
rpynnRMH Tf'rMl')nRp;
 ('naif n£'pBOIf rr
'nm.I YKpCnJ1CIIW 118 nOBepXIIOCTil
BHYTpeHHero, BTOpOH - Ha nOBepXHOCTH HaPY)KHOrO lllapa. TeMne-


F


C1>Hr. 86. CxeMa MeTo.na wapa:
F - cjJJl8HLlbI, COeJlMHHlOlI.lMe 0 OJIMO LleJloe JIBS
nOJlyrnapMA. 06pa3YIOII.lMe HapY>KHYIO rnapooylO
MeTannH1.J.eCKYro o6ono ' -u<y; H - 9neKTpOHarpe-
naTenb; P - HccnellyeMbdt MaTepHan; SI- BHy -
TpeHHIIH MeTa.:rnHI.JeCH811 060nOI.JKa; S- BHelIIHHe
nonYllIapHH; M I' M z - MeCTa 3anO>KeHHH
cnaeo TepMonap.




142


J!3MepeHUR II npll60pbt


113MepeHue K03tjJtjJUlIUeHTOB TenAOnpOBOaHOCTIl TeXl-!1l'leCIWX MaTepUaAoB 143


PaCClJl-1TaeM
:lliHY L CTOpOHbI :,HOro Ky6a, nplf KOTOpOH TeMnepaTypa
Ha ero HapY>KHOH nOBepxHocTH t n He 6y
eT npeBOCXO
HTb 50° C. npek
nOJlO>KHM, lJTO: a) pa3MepbI lllapOBoro npH60pa (cxeMa Ha qmr. 86) -
Dl = 0,23 M, D 2 = 0,60 M; 6) TeMnepaTypbI Ha BHYTpeHHeH H HapY>KHOH
nOBepxHoc;HX t 1 = 800°, t 2 = 600°; B) HcnbITblBaeMbIH MaTepHaJl-
lllaMoroBbIH KaMeHb,
JlH KOToporo MO>KHO opHeHTHpOBOlJHO ClJHTaTb A =
= Acp = 0,8 KKa/l M- 1 llae- 1 cpaiJ- 1 . D,JlH 3aCbmKH
liaTOMHTOM
npHMeM An (HaPY>KHbIH CJlOH = 0,09.
3aMeHJ.-IM Ky6 wapOM, KOTOpblH Ha qmr. 87 nOKa3aH nyrrKTHpoM,

HaMeTp KOToporo Dn paseH HCKOMO

JlHHe Ky6a; 3TO CYIUeCTBeHHO
He H3MeHHT Halllero paClJeTa, r
e
MbI HMeeM B BH
Y YCTaHOBHTb
TeXHHlJeCKYJO TOlJHOCTb H HaHTH
.nopH
OK BeJlHlJHHbl Dw
B YCTaHOBHBweMCH .cOCTOH-
HHH O
HH H TOT >Ke nOTOK npo-
HH3bIBaeT 06a wapoBbIx CJlOH H3
waMOTa H H3
HaTOMHTa, H MbI
HMeeM no q>opMYJle (6. 23):
Q* = 27tA (1 1 - (2) = 27tA H (12 - (n)
I I 2 1 ·
75;- D 2 D 2
 Dn


ECTb MeTO
, B KOTOpOM HcnOJlb3yeTcH 60Jlee CJlO>KHbIH cJlYlJafi CTaLlHO-
HapHQrO TeMnepaTypHOrO nOJlH; H
eH ero HC1Ia H3 q>HL 88.
0eTaJlJlHlJeCKHH HIlI.HK B q>opMe npHMoyrOJlbHOrO napaJlJleJlenHne
a
a'b'e'd' 06J10
eH no BceM CBOHM weCTH rpaHHM nJlHTaMH HJlH JlHCTaMH
HcnbITbIBaeMoro MaTepHaJia P, KOTopbIe CHapY>KH nJlOTHO nOKpbITbl MeTaJl-
JlHlJeCKHMH JlHCTaMH, 06pa3YJOIUHMH KO>KYX abed (npHMoyrOJlbHblH napaJl-
JleJlenHne
, no
06HblH BHYTpeHHeMY C napaJlJleJlbHbIMIf eMY rpaHHMH).
BHYTpH pacnOJlO>KeH 3J1eKTpOHarpeBaTeJlb H, C03
aJOIUHH TenJlOBOH
nOTOK Q*, KOTOpbIH LleJlHKOM, 6e3 nOTepb, nepexo
HT OT nOBepxHo-
CTH a'b'c.'d'., HMeJOIlI.eH TeM- p
nepaTYPY t, lJepe3 CJloY.:
MaTepHaJla TOJlIUHHOH °
(noBcJO
Y o
HHaKoBoH) K
nOBepxHocTH abed, TeMne-
paTypa KOTOpOH paBHa . t 2 .
nYCTb H3BeCTeH K03q>q>H-
LlHeHT q>OpMbI CJlOH L *,
Tor
a no q>opMYJle (2.18),
H3MepHB 3J1eKTpHlJecKHM
cnoc060M Q*,HaH
eM HCKO-
Moe:


--
..-
..-
.-
/
,
,
I
I


--
-....,
....
"
....
....
,
\
\
I


..J
,


I
I
I
,
,
.-
.-
..-


..J


\
\
\
,
....
"
,
'....
......


c1>nr. 87. MeTo.n llIapa B o!jJopMJleHIIH BaH-
PHHcYMa npHMeHHTeJlbHO K BblCOKHM TeM'
nepaTypaM.


,.


L
r-


Q*
"J... p = L*(t 1 -t 2 )


(6. 26)


a oTCJO
a nOJlYlJaeTCH ypaBHe-
HHe
JlH onpe
eJleHHH HCKOMoro
Dn: .


c1>Hr. 88. MeTOJ1 SlIl.lI1Ka:


, " p_ HCnbITbIBaeM311 TennOM30nSIllHH; S Ii S' - ee lIapymHall H
0603Ha lJHM LI, L2' L3 - UHYTpeHHHH nOBepXHOCTH; H - 9neKTpOHarpeBaTenb.

JlHHbI pe6ep BHYTpeHHero
napaJlJleJlenHne
a, S' -CYMMY nJlollw
eii ero llleCTH rpaHeH, "2:.L' -CYMMY
. 1

JlHH Bcex
BeHa
LlaTH pe6ep; eCJlH Bce pa3MepbI L' >5°, TO, KaK no-
Ka3aJll-l JIeHrMJOp, A
aMc H MaHKJI [10], C
OCTaTOlJHbIM npH6J1H>Ke-
HHeM L * MO>KHO BbIlJHCJlHTb no q>opMYJle:
L* = s; + 0,54"2:. L' + -}o. (6.27)


1 I. ( 1 1 ) AH (t 2 - (H)
D 2 - D H = 75;- D 2 . Alfl-(2)


HJlH



 _
_ ( 1 1 ) 0,09(600-50)
0,60 D H - 0,23 - 0,60 ' 0,8.200 .
oTKy
a D H = 1,19 M,
PYrHMH CJlOBaMH - TOJlIUHHa CJlOH
liaTOMHTa

OJl>KHa 6bITb nOpH.l\Ka 30 eM.
MOIlI.HOCTb, pa3BHBaeMaH HarpeBaTeJleM, nOJlYlJaeTCH paBHOH
Q * 2r..0,8.200 3 1
= 2 6
1 = 75 KKa/l llae- 1 = _ 86 .375 em = 437 em.
, u,


ECJlH O
HH H3


1
BHYTpeHHHX pa3MepOB < 5 °
L* =
 + 0,465
 L' + 0,35a.


1
a
PYrHe >'5°, TO
(6. 28)


'1
HaKoHeLl, eCJlH Bce TPH BHYTpeHHHx pa3Mepa <50' TO
L* =- 0,791f s
s



 10. MeTo.n SJIlI.HKa (Box-Method)
Bo Bcex npe
bl
YIUHX MeTo
ax H MHOrOlJHCJleHHbIX BapH8HTax npH-
60POB, Ha HHX oCHoBaHHbIx, 6bIJIH HCnOJlb30BaHbi TPH npocTelfwHx
CJlYlJaH cTaLlHoHapHoro nOJIH TeMnepaTYP, BCJle
CTBHe Gero H K03

H-
LlHeHT q>OpMbl. MO>KeT OhITh JlPrKO nOIlY4f'H no 0l1.Hnij H1 rpnrMYJI, nrI-l-
Be.l\eHHbIX B
 5 rJl. 2.


(6. 29)


MTaK, 3TOT MeTO
 cOBepweHHo aHaJlOrHlJell MeTO.l\Y mapa H 06J1a
aeT
TeM >Ke
OCTOHHCTBOM, KaK H nOCJle
HHH: napa3HTHbIe TenJlOBbIe nOTepH
OTCYTCTBYJOT.
OCHoBHaH npe.l\nOCblJlKa MeTo.na COCTOHT B
onYIUeHHI-I, lJTO HapY>KHaH
II BHYTpeHHHH nOBepXHOCTl1 oS H oS HBJIHlOrCH l130repMl14eCh,l1Ml1; eCJIH :l1U




144


H3Mepel-lllJ! u npll60pbl


He BnOJIHe cTporo oCYIlLeCTBJIHeTCH Ha npaKTHKe ,l{a)j{e ,l{JIH TaKOll H,l{eaJIb-
HOll I!>0PMbI, KaK Illap, TO 3,l{eCb - B CJIY'lae napaJIJIeJIenHne,l{a - ero
yrJIbI BbI3bIBalOT HepaBHOMepHOCTb pacnpe,l{eJIeHHH TeMnepaTYP no S
H S', qTO MO)j{eT nOBeCTH K 3aMeTHbIM OIllH6KaM.


* *


*


PaCCMOTpeHHbIe 3,l{eCb MeTO,l{bI - Ba)j{HellIllHe H HaH60JIee pa3pa60-
TaHHbIe H3 MeTO,l{OB CTaUHOHapHoro TenJIOBOrO nOTOKa ,l{JIH npHMoro
onpe,l{eJIeHHH K031!>cpHUHeHTOB TenJIOnpOBO,l{HOCTH H TenJIOBbIX conponm-
JIeHHH ,l{H3JIeKTpHKOB Bo06IlLe H TeXHH'leCKHX TenJIOH30JIHUHOHHbIX H
CTpOHTeJlbHbIX MaTepHaJIOB, B qaCTHOCTH. OHH npHrO,l{HbI ,l{JIH MaTepHa-
JIOB, BH,l{HMaH nJIOTHOCTb (06"beMHbIll Bec) KOTOpbIX KOJIe6JIeTCH B IllHpOKHX
npe,l{eJiax - H B COOTBeTCTBHH C 3THM TenJIOnpOBO,l{HOCTb 3aKJlIO'laeTCH
B npe,l{eJiax OT 0,025 ,l{0 1,8 KKaJl .M- 1 'lac- l epaiJ- 1 (npH 20°).
D,JIH MaCCHBHbIX ropHbIx nopo,l{ BpO,l{e HOpHTOB, Y KOTOpbIX A-qHCJlO
nOpH,l{Ka 2 H BbIIlle, npHMeHeHHe 3THX MeTO,l{OB (MbI pa3YMeeM MeTO,l{bI
nJiaCTHHKH) CTaHOBHTCH BeCbMa TPY,l{HbIM; Tpe6yeTcH pa3pa60TKa oc060
TOHKOll, ,l{OporoCToHIlLell TeXHHKH 3KcnepHMeHTa.
O,l{HOll H3 OTJIHqHTeJIbHbIX 'lepT TeXHHKH 3KcnepHMeHTa BO Bcex BbIIlle-
onHcaHHbIX MeTO,l{aX HBJIHeTCH CTpeMJleHHe BbIpaBHHTb TeMnepaTypbI
Ha Tex .noBepxHocTHX KOH,l{YKTHMeTpa, Me)j{,l{Y KOTOpbIMH npoTeKaeT
TenJIOBOH nOTOK Q*. D,JIH :onoro BCIO,l{Y, r,l{e MO)j{HO, BBO,l{HT MaCCHBHbIe
MeTaJIJIH'leCKHe «BbIpaBHHBaIOIlLHe» nJIHTbI, TPy6bI H T. n., paCC'lHTblBaH
Ha BbICOKYIO TenJIOnpOBO,l{HOCTb MeTaJlJlOB. 3To npe,l{ycMoTpeHo H BaCT
BKC 7458 H B Me)j{,l{YHapO,l{HOM CTaH,l{apTe Ha MeTO,l{ ,l{BYX nJiaCTHHOK,
B TPy6e BaH-PHHCYMa H B IllapOBbIX npH60pax 60JIbIllOrO ,l{HaMeTpa:
TOJIIlLHHbl CTeHOK ,l{eJiaIOTCH nopH,l{Ka 2 .M.M, BHYTpeHHHll Illap ,l{eJiaeTCH
JlHTbIM TOJICTOCTeHHbIM H T. ,l{.
OO,l{'lepKHeM eIlLe O,l{HO 06CTOHTeJIbCTBO, Ha KOTOpoe 6bIJlO YKa3aHo
paHbIlle - B
 5 3TOll rJIaBbI: MeTO,l{bI ,l{alOT Ha,l{e)j{HbIe pe3YJIbTaTbI,
TOJIbKO eCJIH HCnbIThIBaeMbIll MaTepHaJi 06JIa,l{aeT Heqpe3MepHo KPynHbIMH
nopaMH H paBHoMepHoll CTPYKTYPOll.


rJIABA 7


onPE
EnEHME K03$$M
MEHTA TEnnOnpOBO
HOCTM
METAnnOB no METO
AM CTA
MOHAPHoro TEnnOBoro
nOTOKA



 1. npaKTH'ieCKOe 3HaIJeHHe TenJIOnpoBo,ll.HOCTH MeTaJIJIOB
3HaHHe TenJ10BbIX CBOllCTB MeTaJIJ10B He06xo,l{HMO npH peIlleHHH pH,l{a
BonpocoB H3 06JIaCTH MaIllHHoCTpoeHHH H npH60poCTpoeHHH. OpHBe,l{eM
,l{JIH HJIJ1IOCTpaUHH HeCKOJIbKO npHMepoB.
MeTaJIJIHqeCKHe 'laCTH MHornx TepMHqeCKHX MaIllHH nO,l{BepralOTcH
,l{elICTBHIO nepeMeHHbIx TeMnepaTYp: TaK, B ,l{ByxTaKTHoM ,l{H3eJIb-MOTOpe
npH 100 060poTax B MHHYTY npH Ka)j{,l{OM 060poTe TeMnepaTypa BHYTpeH-
Hell nOBepXHOCTH CTeHKH UHJ1HH,l{pa KOJIe6JIeTCH OK0J10 CBoell Cpe,l{Hell
TeMnepaTypbI Me)j{,l{Y + 14 ° H _8° C (npH Cpe,l{Hell TeMnepaType ra30B

1500° C). OTCIO,l{a B03HHKalOT ,l{Ba Bonpoca: a) KaK OTpa)j{aIOTCH 3TH
nepeMeHHbIe BIIeIllHHe YCJ10BHH Ha TeMnepaTypHOM nOJIe cTeHKH? 2) K8Jme
HanpH>KeHHH B03HHKalOT B MaTepHaJIe CTeHKH BCJ1e,l{CTBHe TeMnepaTypHbIX
rpa,l{HeHTOB B Hell? D,JIH peIl1eHHH HX He06xo,l{HMO 3HaTb TenJIOnpOBO,l{-
HOCTb H TenJIOeMKOCTb MaTepHaJia. B CJIY'lae BbIIl1eynoMHHYToro ,l{H3eJIb-
MOTopa BHYTPH ero CTeHKH B03HHKaIOT, BCJ1e,l{CTBHe ,l{a)j{e TaKHX He3Ha'lH-
TeJIbHbIX KOJIe6aHHll TeMnepaTypbI (nopH,l{Ka 10 rpa,l{YCOB), ,l{OnOJIHHTeJ1b-
HbIe HanpH)j{eHHH nepeMeHHoro 3HaKa (HopMaJIbHbIe H TaHreHUHaJIbHbIe),
KOTopbIe MorYT OKa3aTbCH onaCHbIMH ,l{J1H ueJ10CTH MaIllHHbI. Ka)j{,l{bIll
rpa,l{Yc KOJIe6aHHH TeMnepaTypbI BbI3bIBaeT ,l{OnOJIHHTeJIbHOe HanpH)j{eHHe,
npH6JIH3HTeJIbHO paBHoe
E B ( r- )
_ I . --;-- . ; t ACj= b ,
-'I r J.C"(


r,l{e E - MO,l{YJIb IOHra, v - qHCJ10 OyaccoHa H
 - J1HHellHbIll K03<Mm-
UHeHT paCIl1HpeHHH MaTepHaJia [13 L
BbIpa)j{eHHeV Aq ,BCTpe'laIOIlLeeCH npH TenJIOBbIX paC'leTaX, A. B. JIbI-
KOB Ha3bIBaeT «aKTHBHOCTblO» MaTepHaJIa, repMaHcKHe TenJIOl!>H3HKH -
«K03<p<pHUHeHToM npoHHKHoBeHHH TenJIa» (Warmeeindringzahl). mOT
K031!>cpHUHeHT BBe,l{eH B npaKTIIKY paC'leTOB rpe6epOM B 1921 r. BMecTO
Hero npoIlLe BBeCTH 60JIee HarJIH,l{HbIH napaMeTp - Ko::xpcpHUHeHT TeMne-
prn)"ponpOBO.l\IIOCTII n, IIPnOCp(H{CTRPHHO B"I{0'{<m!1!H B ypaRHPHlIP TPnJlO-
npOBO,l{HOCTH £PYPbe [eM. (1.35) H (1.36) L


10 KOHllpaTbeB 2763




146


J!3MepeHUJ! U npU60pbl


OnpeaeAeHue IW3tjJtjJUI{IleHTa TenAOnpOBOaHOCTU MeTaAA08


147


3TO TOJ1bKO H,AeH MeTO,Aa; O<p0pMJ1eHHe ero MO)KeT 6bITB OqeHb pa3-
Ho06pa3HbIM. O,AHO H3 HHX nOKa3aHO Ha <pHr. 89.
TenJ1o, pa3BHBaeMce 3J1eKTpHqeCKHM HarpeBaTeJ1eM b, nO,ABO)I,lITCSI
CHH3Y K KOHUY HcnbITblBaeMoro CTep>KHH
a, HM€IOIUerO )J.JIHHY 40 CM H TCJ1IUHHY
2 CM, H OTBO)J.HTCH cBepxy BC,ACCTpYHHbIM
KaJ10pHMeTpoM c; nOBbIllleHHe TeMnepaTY-
pbI BO,AbI H3MepSleTCSI nOCpe,ACTBOM TepMO-
MeTpOB n H o. COBepllleHHO TO )Ke na)J.e-
HHe TeMnepaTypbI, KaK B cceBOM Hanpa- P
BJ1eHHH B HCnbITblBaeMOM CTep)KHe, OCY-
IUeCTBJ1HeTCH B oxpaHHOM KOJ1bue g npH --
nOMOIlLH OXJ1a,AHTeJ1bHOrO 3MeeBHKa h;
,AJIH KOHTpOJ1H CJ1Y)KHT TepMOMeTp p.
5YKBaMH d, e, f 0603HaqeHbI cnaH Tep-
Monap, nOMeIlLeHHbIe B pa3J1HqHbIX Me-
CTax HCCJ1e,AyeMoro CTep)KHH a; m-
TenJ10H30J1S1UHOHHbIH MaTepHaJ1.
TenJ10IJOH nOTOK, npOXO,AHIlLHH qepe3
CTep)KeHb, H3MepHJ1CH no MeTo,AY CTPYH-
HOro KaJ10pHMeTpa [6]. .D,J1H 3Toro CJ1e-
,AyeT 3HaTb pacxo,A oXJ1a>K,AaIOIlLeH BO,Abl,
npoTeKaIOIlLeH qepe3 ueHTpaJ1bHbIH KaJ10-
pHMeTp C, H nOBbIllleHHe ee TeMnepaTypbr.
3TOT MeTO,A 6bIJ1 pa3pa60TaH .D,)K. B.
.D,oHaJ1b,ACOHOM, ,AJ1S1 TeMnepaTYP ,AO
400° C H BbIlile.
EMY npHcyIUH Bce 3Kcnep'HMeHTaJ1b-
HbIe TPY,AHOCTH, CBH3aHHbIe C npHMeHe-
HHeM CTPYHHoro, «npOTOqHOro», no Tep-
MHH0J10rHH M. M. flonoBa [6], KaJ10pH-
MeTpa; nO,A06HO BbIlileynoMHHYTbIM aHa-
J10rHqHblM MeTO,AaM, B qaCTHOCTH TeM,
KOTopbIe pa3pa60TaHbI HaUHOHaJ1bHOH
<pH3HQeCKOH J1a60paTOpHeH AHrJ1HH II 4],
OH )J.aCT Y,AOBJ1eTBOpHTeJ1bHbIe pe3YJ1bTaTbI
B PYKax HCKYCHbIX 3KcnepHMeHTaTopoB.


BeJ1HQHHbI a H b CBH3aHbI COOTHOllleHHeM
b = V Acy = Cj Va = CVOlVa. (7. I)
B ueJ1HX .cHH)KeHHH TenJ10BbIX HanpH)KeHHH B ,AeTaJ1HX ,ABHrareJ1eH
BHYTpeHHero cropaHHH, B ra30BbIX Typ6HHax H T. ,A. CTpeMHTCH npHMe-
HHTb ,AJ1H HX H3rOTOBJ1eHHH MeTaJ1J1bI C BbICOKOH TenJ10npOBO,AHOCTbIO;
HanpHMep, Y)Ke ,AaBHO (npHMepHo 30 J1eT Ha3a,A) UHJ1HH,ApbI ,ABHraTeJ1eH
BHYTpeHHero cropaHHSI H3roTOBJ1S1IOTCSI H3 aJ1IOMHHHeBbIX CnJ1aBOB.
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peH XCJ10,AHJ1bHHKOB H TOMY nO,A06HbIX YCTPOHCTB CTpeM5ITC5I npHMeHHTb
MeTaJ1J1bI C BbICOKHM A. HanpHMep, B TenJ10BbIX YCTpoHCTBax aTOMHblX
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vb MeTO,AOB onpe,AeJ1eHH5I K03<p<pHUHeHTa TenJ10npOBO,AHocrn MeTaJ1-
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 5 H 7,
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nOCTOHHHOH TeMnepaType t (HanpHMep, nocpe,ACTBOM norpY)KeHHSI HX
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OnpeaeAeHUe IW3tjJtjJUI{IleHTa TenAOnpOBOaHOCTU MeTaAAOB


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TenJ1a B,AOJ1b OCH.
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B Cepe,AHHe CTepmHH, T. e. Ha paCCTOHHHH L OT ero KOHUa O. TeMnepa-
t


f1pe,AbI,AYIllee paBeHCTBO MOlliHO npe,ACTaBHTb B BH.lI.e:


( d3 ) _ ( d3 ) =-!:J....l.
dx x-tl dx x "


d3 F( ) U
0603HaqHM dx = X H npHMeHHM K J1eBOH qaCTH npe,Abl.ll.YllL ero
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Bq_===l


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 <: I.
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L


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, B qaCTHOCTH H npH

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a - HcnblTblBaeMblH CTep}f{{'Hb. KOHllbl KOToporo 0 H B nO.lUlep>KH-
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TO


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M N
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3aKOHY (<!>lir. 92).




150


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151


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Cepe,AHHe A H npHHHMaH BO BHHMaHHe, 'lTO no 3aKOHY OMa
U m - U = I fJ L S x = i (L - x) p,


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A -
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(7. 2)


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t m


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O'lepe,Ab HarpeBaeMYlO, nO,A06HO TOMY KaK 3TO 6bIJ10 OCYILlecTBJ1eHO
B paHee onHcaHHOM npH60pe D.oHaJ1b,ACOHa; 3TO n03B0J1HJ10 CHH3HTb
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pOll CTeneHH YCTpaHHTb 60KoBbIe nOTepH; ,AHaMeTp cTepmHH 6bIJ1 YMeHb-
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npUMPp 23. f1pHMeHHSI MeTO
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rJIABA 8


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B lllapoBoM HarpeBaTeJ1e).
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ElIHHCTBeHHbI'\1 CTIOCOf)OM R MPTO
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153


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BbIpaBmiBaHHe TeMnepaTypbI HH3a H BepXa X0J10,AIiJ1bHOH Kop06KH.
TaIWH cnoc06 nOKa3an Ha Q:JHr. 93, a H 6.
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YCTPOHCTB, BeCbMa BeJ1IiKa, TaK KaK Bce npH60pbI 06J1a,AaIOT orpoMI
oH
TepMHQeCKOH HHepLlI1ei1 H HX cTaLlHoHapHblH pe)KHM ,AOCTHraeTCH Kpalme
Me,AJ1eHHO, H60 B KOHeQHOM CQeTe. KOrJ
a Y)Ke, Ka3aJ10Cb 6bI, pe)KHM YCTa-
HOBHJ1CSI (0 QeM CY,AHT no nOKa33HHHM HeMHOrHX TepMonap), CIiCTeMa
B ,AeHCTBHTeJ1bHOCTH Bce eILle «nO,An0J13aeT» K cTaLlHoHapHoMY pe)KHMY,
CTpeMHCb K HeMY no 3KcnoHeHLlHaJ1bHoMY 3aKOHY. Me)K,AY TeM Bce pac-
'1PTbI TIO 9THM MPTO,\;JM OC'HOR;JHhl H;J Vp;JRHf'HI'f!X CT:1lI1iOH1JpHOrO n'nJ1O-
BOrO pe)KHMa. OTclO).\a H B03MO)KHOCTb ).\OBOJ1bHO rpy6bIx OlllH6oK.




154


H3MepelWR u npll60pbl


H3!>lepeHW! IW3ljJqJlll{UeHTOB a, A, C


155


KOHe'IHO, YMeHbliJaH ra6apHTbI 06pa3LloB, HanpHMep .l{OBO.l{H TOJ1-
ILlHHY nJ1aCTHHOK B nJ10CKHX npH60pax .l{0 HeMHomx MHJ1J1HMeTpOB H .l{a)Ke
.l{0 0,5-1 MM, MO)KHO 6bIJ10 6bl 3H8'IHTeJ1bHO COKp8THTb .l{J1HTeJ1bHOCTb
onbITa, K8K 3TO .l{eJ18J1H 3. rpHcpqmT H KeH B HaLlHOHaJ1bHOH cpH3H'IeCKOH
J1860paTopHH AHrJ1HH [14], HO TaKoH BbIXO.l{ H3 38TpY.l{HeHHSI COBceM
He rO.l{HTCH nO'ITH .l{J1H Bcex TeXHH'IeeKHX M8TepH8J10B, oc06eHHO CTPOH-
TeJIbHbIx. fl03TOMY HCnbITaHHe npH O.l{HOH K8KOH-J1H60 Cpe.l{HeH TeMne-
parype no MeTO.l{8M CTaLlHOHapHoro nOTOKa OTHHMaeT B J1Y'IWeM cJ1y'Iae
8 'IJC. 8 06bI'IHO HeCKOJ1bKO .l{HeM.
CJ1e.l{yeT elll.e He 3a6bIBaTb 0 He06xo.l{HMOCm nOBTopHbIX H KOHTpOJ1b-
HbIX onbITOB .l{J1H J]OJ1Y'IeHHH Cpe.l{HHX 'Il-\CJ10BbIX .l{8HHbIX .l{J1H A, 'ITo6bI
06HapY)KHTb HJ1H HCKJ1IO'IHTb CJ1Y'IaHHbIe oWH6KH. B pe3YJ1bTaTe .l{ocm-
raeMaH TO'IHOCTb onpe.l{eJ1eHHH A MO)KeT 6bITb OLleHeHa B 6J18rOnpHHTHbIX
CJ1Y'IaHX, T. e. B xopowo 060pY.l{OBaHHOH .l{J1H TO'IHbIX p860T J1a60p8TOpHH,
f.l{e pa60T81OT HCKycHbIe 3KcnepHMeHT8TopbI, LlHcppOH 0,5-1 %; onblTHbIH
HcnbITaTeJ1b B TeXHH'IeCKOH J1a60paTopHH H3MepHeT A C norpeWHOCTblO
3-7%. 3m LlHcpPbI OTHOCHTCH K TeMnepaTypaM B6J1H3H KOMHaTHbIX
20-40°; no Mepe nOBbIweHHH Cpe.l{HeH TeMnepaTypbI 06p.a3Ll8 norpew-
HOCTb H3MepeHHH B03paCTaeT; HaHJ1Y'IWaH .l{OCTH)KHMaH TO'IHOCTb H3Me-
peHHH A npH 1000 0 C BPH.l{ J1H MO)KeT 6bITb OLleHeH8 LlHcppOM 3%, Bcero
BepOHTHee, B Cpe.l{HeM, C'IHTaTb ee 5 % .
K TaKoMY 38KJ1IO'IeHHIO npHBO.l{HT MHOrOJ1eTHHH OnblT cneLlHaJ1HCTOB
no TenJ10BbIM TeXHH'IeCKHM H TO'IHbIM H3MepeHHHM: A. <P. 110cpcpe [II J,
3. rpHcpcpHTa [12 J, M. 5IK068 [10], M. fl. CTaLleHKo H aBTop8 3TOH
KHHrH.
OxapaKTepH30BaHHoe n0J10)KeHHe BellleH 38CTaBHJ10 HCCJ1e.l{OB8TeJ1eH
Y)Ke BCKope nOCJ1e C03.l{aHHH <PYPbe (1822 r.) TeopHH TenJ10npOBO.l{HOCTH
06p8THTbCH K nOHCKaM MeTO.l{OB HecTaLlHoHapHoro TenJ10BOrO nOTOKa.
B J1I06oM H3 MbICJ1HMbIX MeTO.l{OB 3Tora pO.l{a HeH36e)KHO npHXO.l{HTCH
paCCM8TpHBaTb He TOJ1bKO K03qxpHLlHeHT TenJ1(mpOBO.l{HOCTH A MaTepHaJ1a,
HO .l{OnOJ1HHTeJ1bHO eILle II ero Y.l{eJ1bHYIO TenJ10eMKOC'Ib C H 06'beMHbIH
Bec 1, nOToMY 'ITO TeMnepaTypHoe nOJ1e TeJIa B cJ1Y'Iae HecTaLlHoHapHoro
TenJ10BOrO pe)KHM8 M8TeMaTH'IeCKH BbIpa)K8eTCH, KaK MbI BH.l{eJ1H B rJ1. I,
ypaBHeHHeM (I. 32), a CIO.l{a BXO.l{HT Bce TPH BeJ1H'IHHbI-A, C, 1.
3TO yp8BHeHHe ynpoILlaeTcH, KOr.l{8 3m BeJ1H'IHHbI, B .l{8HHbIX YCJ10BH-
HX OnblTa, MO)KHO C'IHT8Tb He3aBHCHILlHMH OT TeMnep8TypbI. Bo Bcex
MeTO.l{8X HecTaLlHoHapHoro TenJ10BOrO nOTOKa, HMeHHO T8Koe npe.l{n0J10-
)KeHHe H .l{eJ1aIOT, 'IT06bI H36e)K8Tb HenpeO.l{OJ1HMbIX npH cOBpeMeHHoM
COCTOHHHH M8TeM8THKH TPY.l{ilocTeM peweHHH 38.l{a'IH. 113J10)KeHHe HeKO"
TOpbIX 'IaCTeH TeopHH TenJIOnpOBO.l{HOCTH, C.l{eJ1aHHOe B rJ1. 4 H 5, .l{aHO
TaK)Ke B npe.l{n0J10)KemiH nOCTOHHCTBa A, c, 1'.
TOf.l{a ypaBHeHHe TenJ10rrpoBo)J.HOCTH <PYPbe npHMeT BH.l{


saHbI Me)K.l{y C060H, a HMeHHO


A = acy.


(8.2)


C'IHT8H 1 H3BeCTHbIM, MO)KeM CKa3aTb, 'ITO .l{J1H nOJ1Y'IeHHH u Bcex Tpex
TenJ10BbIX xapaKTepHcTHK M8TepHaJ1a - A, a, C .l{OCTaTO(IHO HaHTH KaKHe-
HH6Y.l{b )J.Be H3 HHX: A H C HJ1H C H a HJ1H aHA. HH)Ke MbI YBH.l{HM, 'ITO
HeKoTopbIe H3 MeTO.l{oB HeCTaLlHoHapHoro nOTOKa .l{alOT B03MO)KHOCTb O.l{HO-
BpeMeHHoro onpe.l{eJ1eHHH KaKOH-J1H60 H3 3THX Tpex nap.



 2. 0 cpH3UIJeCKUX BeJIHIJHHaX A, c, a
<PH3H'IeCKHH CMbICJ1 K03cpcpHLlHeHTa TenJ10npoBo)J.HOCTH A YK838H
B Ha'IaJ1e Y'Ie6HHKa. PaCCMOTpl-\M .l{Be .l{pyme x8paKTepHcTHKH TepMH'Ie-
CKHX CBOHCTB MaTepHaJ1 - TeMnep8TyponpOBO.l{HOCTb BeILleCTB8 H era
TenJ10eMKOCTb.
TeMnep8TyponpOBO.l{HOCTb x8p8KTepH3yeT cnoc06HoCTb M8TepHaJ1a
u u all
nOBbIW8Tb CBOIO TeMnepaTYPY C 60J1bWeH IIJ1H MeHbweH CKOpOCTblO "'"(h'
no.l{ )J.eHcTBHeM npHTeKalOILlero TenJ1a (.l{J1H onpe.l{eJ1eHHOCTH rOBopHM
o nOBbIweHHH TeMnepaTYPbl).
ECJ1H B KaKOM-J1H60 CJ10e M8TepH8J18 npoHcxo)J.HT nOBbIweHHe TeM-
nep8TYPbI, TO CKOpOCTb 3Toro nOBbIll1eHHH 6Y)J.eT, npe)K)J.e Bcero, onpe.l{e-
J1HTbCH TeM, KaKoe KOJ1H'IeCTBO TenJ1a nepe.l{aeTCH 3TOMY CJ1010 B e)J.HHHLlY
BpeMeHH OT coce)J.HHX C HHM CJ10eB. 3TO nOCJ1e.l{Hee KOJ1H'IeCTBO nponop-
LlHOHaJ1bHO TenJ10npOBO.l{HOCTH, a CJ1e.l{OBaTeJ1bHO, CKOpOCTb nOBbIll1eHHSI
TeMnep8TypbI nponopLlHOHaJ1bHa A. C .l{pyroH CTOpOHbI, 'IeM 60J1bIlle
TenJ10eMKOCTb e)J.HHHLlbI 06'beM8 M8TepHaJ1a, KOTOPYIO MbI 0603Ha'IllM C vo !
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6Y.l{eT nOBbIll1eHHe TeMnepaTypbI paccM8TpHBaeMoro CJ10H; CJ1e.l{OB8--.
TeJ1bHO, CKOpOCTb nOBbIweHHH TeMnepaTypbI ero 06paTHo nponopLlHo-
HaJ1bHa c vo !. OTCIO.l{8 MbI npHxo)J.HM K 38KJ1lO'IeHH10, 'I!'o CBOHCTBO,
xapaKTepHoe .l{J1H nOBe)J.eHHH MaTepHaJ18 npH H3MeHHIOILleHCH TeMnep8-
Type ero, MO)KeT 6bITb npe]J,CTaBJ1eHO cpOPMYJ10H


A
a=k-,
cvol


(8.3)


f.l{e k - K03qxpHLlHeHT nponopLlHOHaJ1bHOCTIL
flpHMeM k p8BHblM e)J.HHHLle, a BMeCTO c vo ! BBe.l{eM y)J.eJ1bHYIO TenJ10-
eMKOCTb C,l BH)J.HMYIO)Ke nJ10THO
Tb MaTepHaJla (HJ1H ero «06beMHbIll Bee»)
0603Ha'IHM 1; c vo ! = c1'; H3 (8.3) nOJ1Y'IHTCH
A
a=-
q'


au 2
(h = av u,


(8. I)


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113 3TOH cpJpMYJ1bI BH.l{HO, 'ITO e.l{HHHLl8 TeMnep8TyponpOBO)J.HOCTH
onpeJ{eJ1HeTCH 'Iepe3 e.l{HHHLlbI TenJ10npOBO.l{HOCTH, TenJ10eMKOCTH H nJ10T-


B KOTOpOM a npell('T::IB.TJHeT ('OOOH npOCTYIO M
Tf'l\1RTHqp('KYIO K('Il\1nHH::I-
LlHIO H3 A, C, 1 (I. 36); HT8K, BeJ1H'IHHbI A, a, c, l' He He3aBHCHMbl. a CBSJ-


1 C lJaCTO Ha3b1BalOT O.nHHM CJlOBOM (<TenJIOeMKOCTb», onYCKaH 3nHTe'T «y.n-eJIbHaH».




1.56


H31>lepeHUR U npu60pbl


H3MepeHUR K03tjJtjJU/{UeHTDB a. A, C


157


HOCTH. B TeXHHLJeCKOH CHCTeMe e
HHHU pa3MepHocTb y
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eMKOCTH C 6y
eT
[C) = ""all "F-1cpaiJ-l H [c vaZ ] = "FJrt- 3 cpaiJ-\ (8.4)
a n03TOMY, Bocnonb30BaBllJJJCb 3aBJJCHMOCTHMH (1.25) H (8.2), nonYLJHM
pa3MepHoCTb TeMnepaTyponpoBO
HOCTH
[a] = Jrt 2 "ac- l . (8.5)
B npaKTHKe BCTpeLJaeTCH Heo6xo
HMOCTb 3HaTb TeMnepaTyponpoBo
-
HOCTb MaTepHana H ero TennonpOBO
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a 3Hmme nocne
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60pe no
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yneM
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BO
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OBaHHH LJHCTblX
MeTannOB H cnnaBOB, KepaMHKH H MeTannOKepaMHKH (CTp. 147-148).
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BO>K
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e Tenna, MeXaHHLJeCKOH
pa60TbI. B cHny 3aKOHa coxpaHeHlIH 3HepmH HMeeM:
Q = 6.U + W,
r
e Q - 3HepmH', nO
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eHHaH K Teny B BH
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AU - npHpoCT ero BHYTpeHHeH 3HepmH U;
W - npoH3Be
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bl
OT 0
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ero TeMneparypbl Ha dt. l1iVIeeM:


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= C (p, t) = Cp,t.
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a peLJb
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o t 2 ) II nO
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6. Q = C I f M. M
t. 2 '


(8.7)


r
e At = t 2 iI, a Ct,.f_ 0603HaLJaeT «cpe}J,HIOIO y
enbHYIO Tenno-
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y TeMnepaTypaMH t 1 H t 2 »; OHa onpe
enHeTCH
<popMynoH


CI,. f, =


I-
I cdt
t,
/2 - t]


(8.8)


dQ = cMdt.


(8.6)


BemlLJHHY C - <PYHKUHIO TeMnepaTypbl C = f(t) - Ha3blBaIOT u {(HCTHH-
HOH y
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a
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113 Ta6n. 4 BH
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enbHoH
TennoeMKOCTblO 06na
aeT Bo
a, llJHpOKO npHMeHHeMaH B KaLJeCTBe Belll.e-
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Bonpoc 6bW no
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D,JIH CYXIIX TeXHHLJeCKHX MaTeplianoB CnO>KHOrO COCTaBa (HanpHMep,
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eHCTBHTenbHa <popMyna
CMellJeHIIH: ecnII MaTeplian COCTOltT 113 pa3nllLJHbiX BeIlLecTB, y
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BeJIp.tJllHa C 11 eCTb y
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1 CKa3aHHoe OTHOCHTCH K 06bl4HOii BOJ1e (npHpo.nHblH COCTaB): BXOJ1HIl.lHii B ee COCTaB
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3HalJHTeJJbHO Bblwe.




158


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H3MepeHUR K03ljJljJuIlueHToB a, >.., C


159


T a6AuIla 4
YlI,eJlbHble Tl'nJlOCMKOCTH C HeKoTopblX ynoTpe6HTeJIbHblX B npaKTHKc
Ten1l0H30JlSlUHOHHblX CTpOHTCJlbHblX MaTepHaJlOB lI,JlSI HHTepBaJla TeMnepaTYP 0-20°C


Ha3B8HHe MaTepHa
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KHpnHlJH MarHe3HTOBble
KHpnHlJH orHeynopHble
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KHpnHlJH XpOMHToBble
llHaToMoBblH H HHI»Y30P-
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fpaHHTbl (B 3aBHCHMO-
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Ii TpenCJlbl .
CTCKJlHHHaH BaTa, BOH-
1IOK, UlepCTb .


YAenbH3R I
Tenno.
eMKOCTb C


0.20-0.22
0.24-0.23
0,1£5
0.225
0,195
0,18
0,20-0,22
0.20-0,21
0.19
0.16-0.19
0,20
0,19
0,21
0,20-0.25
0,20
0.22
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0.175
0.174
0,205
0.17
0,20
0.23
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C = CX I + CX2 + . .. ]
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0.18
0.165
0.21
0,19
0,2
0.195
0.18
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Y.Qe.nbHaH Ten.noeMKOCTb B.na)j{HbIX MaTepHa.noB npH YMepeHHbIx
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npH t > 0 C BJI = C cyx (1 - (J)) + O) } (8. 10)
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HanoMHHM, 'lTO BeJIH'lHHbI Cl, C2 . . . iIe 3aBHCHT OT CTeneHH ynJIOT-
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CHHbI, TOp<pa H T. n., <popMy.na (8.10) CTaHOBHTCH HenpaBH.nbHoU; He06xo-
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K B.na)j{HbIM MaTepHa.naM npHMeHHMa <popMy.na (8.10).
flpli npHKH.n;O'lHbIX paC'leTaX MO)j{HO C'lHTaTb:


0,30-0.38


0,32-0,33


0,37-0.38


c = 0,2 J1JIH HcOpraHHlJeCKHX TenJlOH30JIHUHOHHblX H CTpO-
HTeJlbHbIX MaTCpHaJlOB;
c = 0,4 J1J1H OprallHlJeCKHX 61'3 npHMeceH lIeopraHHKOB;
c = 0,35 AJIH OprallHlJCCKHX C npHMecblO HeopraHHKOB.
3aBUCHMOCTb y.n;e.nbHOH Ten.noeMKOCTH OT TeMnepaTypbI pa3.nH'lHa
.n;.n H pa3HbIX MaTepHaJIOB: B nepBOM npH6.nH)j{eHHH ee MO)j{HO C'lHTaTb
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c=co(I+
i) (8.11)
B npe.n;eJIax npHMepHo .n;o 500° C.
D,.nH TeXHH'lecKoH KepaMJ.-IKH H KHpnH'la K03<p<pHuHeHT
c, KOTOpbIM
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(0-500°) nOJIyqaeTcH:
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0 )'
K OpraHH'leCKHM MaTepHa.naM MO)j{HO npHMeHHTb TY )j{e <POPMYJIY, HO
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 = (1 -+- 2) . 10- 3 rpaA. -1.


0.26
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cpellH.
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'5 :E
co

(j-




IG2


H3MepeHUJ! U npu60ptJI


npHMeHHB (4. 18) )J.Ba}K)J.bI, nOJlyqaeIII:
a'Lo = c; ( L 1 If m' )
A . 0 a'


a" Lo = (p ( L 1 / m" ) .
A . 0 a


3.QeCh m' H m" - TeMnbl OXJla}!(.QeHHH 06pa3ua 13 nepBOM H B'rOpOM
onhlTe; oqeBH.QHO, m' =1= m". Ka}!(.Qoe 1-13 ql-lCeJl m', m" MhI onpejJ,e-
JlHeM TaK, KaK 3TO OnHCaHO HI-I}!(e 13
 4. B pe3YJlbTaTe 06a HanHcaHHbIX
Bbllue ypaBHeHHH npejJ,CTaBJlHIOT C060IO )J.Ba ypaBHeHHH C jJ,BYMH HeH3Ben-
HbIMH a H )., KOTopbIe H 6YjJ,YT HaiijJ,eHbI nYTeM IIX COBMeCTHoro pelIIeHHH. 1



 4. OnpeJJ.eJleHHe TeMna OXJl3}KJJ.eHHSI m
Bce MeTOjJ,bI HMeIOT OjJ,HY 06ll1.YIO qepTY - BejJ,eHHe onhlTa 130 Bcex
HIiX cOBepllleHHo OjJ,IIHaKOBO. OnhlT }!(e 3aKJlIOqaeTCH 13 TOM, qTO 06pa3-
t!HK HCCJlejJ,yeMoro MaTepHaJla, 13 CJIyqae He06xojJ,HMOCTH (eCJIH 3TO-
cbmyqHH HJlH BOJlOKHHCTblH MaTepHaJl) nOMelll.eHHblll B}!(eCTKYIO 060JlOqKY,
oXJla}!(jJ,aeTcH HJlH HarpeBaeTcH 13 cpe-
)J.e nocToHHHOH TeMnepaTypbI B - np'"
C06J1IOjJ,NIHH YCJIOBHH(*). npH 3TOM Ha-
6J1IOjJ,aIOT H3MeHeHHe TeMnepaTypbI U 13
KaKOH-JlH60 cpHKcHpoBaHHoH TOqKe M
TeJla, OTMeqaH MOMeHTbl BpeMeHH 't H
B cooTBeTcTBYIOllI.He HM nOKa3aHHH
npH60pa, CJIY}J{alll.ero )J.JlH H3MepeHHH
TeMnepaTypbl u; H3MepfiloT TaK}!(e TeM-
t nepaTYPY cpe)J.bI B.
Yl3MepeHHe U H B MO}!(HO H ueJle-
co06pa3HO 3aMeHHTh H3MepeHHeM
pa3HocTH


LnU


tgjJ.m


P,


Pn


'J


to


'i>Hr. 94. 3KcnepHMeHTaJIbHOe onpe-
J1eJJeHHe TeMDa perYJIHpllOrO OXJJa>K-
J1ellI1H (I1JJI1 H1JrpeBaIlI1H) CI1CTeMbI m.


U - B = &.


(8. 12)


ECJIH no )J.aHHhIM 3THX Ha6J1IO)J.eHHH nOCTpOHTb nOJlYJlOrapHcpMH-
qeCKHH rpacpHK OXJla}!()J.eHHH HJlH HarpeBaHHfI, OTKJla)J.blBafi no OCH
a6CUHCC T, a no OCH 0pJJ.IIHaT In & (cpHr. 94), TO ero qaCTh AB, COOT-
BeTCTBY IO llI. 3 f1 perYJlflpHOMY pe}J{J1MY, 6Y)J.eT npfiMaH, ypaBHeHHe KOTO-
pOH, COrJlaCHO OCHOBHOMY 3aKOHY perYJlflpHOrO pe}!(HMa (nepBoro pO)J.a),
6Y)J.eT


In & = -m't + g (x, Z, z).


(8. 13)


Ha cpHr. 94 KpY}!(KaMH 0603HaqeHbi 3KcnepHMeHTaJlbHbie TO'IKH,
cooTBeTcTBYlOllI.He HpperYJI flPHOMY pe}!(HMY, KpecnmaMH - TO'IKH,
OTHOCHllI.HeCfI K perYJlflpHoMY pe}!(lIMY. ECJIH OnblT npoBe)J.eH npaBHJlbHO,


1 ::fro - IIJI
fI MeTOll,8, l!.olUpblii Mll hllll IIdJIJUIL MCllI.AUM .AUYA aJlufJa. 011 pa3pd-
60TaH B. H. OJIeHIIHKOM.


H3MepeHUJ! K03tjJtjJuqueHToB a, A, C


163


UHlI )J.OJl}!(Hbl Jleqb Ha npHMYIO. YrJloBofi ee K05cpcpHuHeHT H eCTb B3HTbifi
CO 3HaKOM MHHYC TeMn OXJla}!()J.eHlIH.
B3HB Ha HeH )J.Be KaKHe-HH6Y)J.b TOqKH PI H P II C Koop)J.lIHaTaMH
TI' In &1 II 'tll' In &11' no cpopMYJle
m= lu&l-ln&\I (8.14)
't\l-'tI


BhIqllCJlHM TeMn OXJla}!()J.eHHH m.
.LLJlfI 3Toro, KaK OTCIO)J.a CJIe)J.yeT, npHHUHnllaJlhHO rOBopH, )J.OCTa-
TOqHO TOJlbKO OTMenITh )J.Be TOqKlI KpHBOH OXJla}!()J.eHHH H )J.Ba MOMeHTa
BpeMeHH. Ha npaKTlIKe Mbl qalll.e Bcero H3MepHeM TeMnepaTYPY )J.JlH pfl)J.a
MOMeHTOB BpeMeHH 't i < T2 < Ta < T4 < . . .. fpacpHK CTpOHTCfI
Ha MHJlJlHMeTpOBKe HJlH KJleTqaTOH 6YMare.
::trOT nplieM BblrO)J.eH 13 )J.BYX OTHOllleHHHX. Bo-nepBbIX, JlerKO YCTa-
HaBJlHBaeTCH MOMeHT npeKpalll.eHHH lIpperYJlHpHOrO H HacTynJleHHH
perYJlHpHOrO pe}!(HMa; BO-BTOPbIX, 60JlhlllOe KOJlHqeCTBO 3KcnepHMeH-
TaJlbHbIX TOqeK n03BOJlHeT C ropa3)J.0 JlyqllleH TOqHOCThIO HaHTli m, qeM
Ha OCHOBaHHH H3MepeHHH TOJlhKO 13 )J.BYX TOqKax. 06bIqHO npll npaBHJlh-
HOH nOCTaHOBKe OnblTa 3KcnepHMeHTaJlbHbie TOqKH TOqHO pacnOJIaraIOTCfI
no npHMOH, eCJIH nOJlh30BaThCH 06bIqHOH KJleTqaTOH u 6YMarOH, H60
TOqHOCTh HaHeceHlIH ceTKH KBa)J.paTOB npH COBpeMeHHOH TeXHlIKe H3ro:
TOBJleHHH KJleTqaTOM 6YMarH BeCbMa Ii!eJlHKa. HapaBHe C 06bIKHOBeHHOH
MHJlJllIMeTpOBOH Mbl ycnelIIHo npHMeHfleM 1I nOJlYJlorapllcpMHqeCKYIO
6YMary.
H3MepeHHe BpeMeHH. B nOJJ.aBJlflIOllI.eM 60JlhlllHHCTBe cJlyqaeB npaK-
THKH m He npeBbllllaeT 50-100 'lac-I, H n03TOMY OTMeTKa MOMeHTOB
BpeMeHH He npe)J.CTaBJlfleT TpY)J.HOCTeH; )J.OCTaTOqeH ceKYH)J.OMep HJlH
)J.a}!(e xopOlllHe qaCbl C ceKYH)J.HOH CTpeJiKOH.
npH 6blCTpO npOTeKaIOllI.HX npoueccax, Kor)J.a m - qHCJIO nopSl)J.Ka
150-200 'lac-I, He06xo)J.HMO npHMeHHTh xpoHorpaQ:>, Ha JleHTe KOT
-
poro OTMeqaIOTCH MOMeHTbl npOXO}!()J.eHHH YKa3aTeJlH np1l60pa - 3all-
qHKa raJlhBaHOMeTpa - qepe3 YJJ.06HO Q:>HKcHPyeMhIe lllTpHXlI lllKaJIbI
np1l60pa, HanpHMep qepe3 ueJible ero )J.eJleHHfI. 06pa60TKa 3
nHcH
Ha JleHTe OCYllI.eCTBJlHeTCfI 6e3 TpY)J.a; m onpe)J.eJlHeTCH C 60JlblIIOH TOq-
HOCTbIO.


"



 5. H3MepeHHe TeMnepaTYP (nepBbIH BapHaHT)
.LLJlfI H3MepeHHfI TeMnepaTypbl U, KOTopaH H3MeHfleTCH C TeqeHHeM
BpeMeHH H npHToM 13 O)J.HY CTOPOHY, T. e. MOHOTOHHO (eCJlH IICKJlIOqHTb
H3 paccMoTpeHHH HpperYJlHpm>lll pe}!(HM, 130 BpeMH KOToporo B03MO}!(HO
H He MOHOTOHHoe H3MeHeHHe U), MbI nOJlb3yeMcH qaw.e Bcero TepMonapaMH
H TOJlbKO 13 HeKOTophIX CJIyqaHX npHMeHHeM PTYTHbIe CTeKJl5IHHbIe Tep-
MOMeTpbI. HeKOTopble H3 3KcnepHMeHTaTopOB npl-lMeHflJlH MHHHaTIOp-
Hble 3J1eKTpHqeClme TepMOMeTpbl conpOTHBJleHHfI, H JJ.OBOJl
HO ycnelllHo;
KOHeqHO. 3TH TepMOMeTpbI J].onVCKaIOT. Bo06w.e rOBopH, 60JlblllVIO TO'!-
HOCTb H3MepeHlHi, qeM Bce )J.pyrHe, OJ].HaKO rpOM03J].KOCTb TpeOYIOllI.eiicSJ
3)J.eCb 3J1eKTpOH3MepHTeJlbHOH annapaTypbl 3aCTaBJIfleT Hac B03)J.ep}!(H-
11*




Jf3MepeHUJI U npU60pbt


H3MepeHUJI K.03t!Jl/Ju/{ueHTOB a, A, C


165


164


1 YKa3aHHe OTHOCHTe1IbHO NOHTHpOBKH TepMonap .naHO B rJl. 9
 5, n. 2.


rO)J,Ha TOJJbKO )J,JJH KpaTKoBpeMeHHbIX I-I3Mepemd% TeMnepaTYP, 6JJI-I3KI-IX
K MaKCI-IMaJJbHO .n.JJH Hee .n.onycTi-lMOH TeMnepaType, a BCHKoe .n.JJI-ITeJJbHOe
(I-I .n.aLKe nOBTopHoe KpaTKOBpeMeHHoe) npe6bIBaHi-le ee npI-l BbICOKI-IX TeM-
nepaTypax Bbl3bIBaeT He06paTi-lMbie I-I3MeHeHHH TepM03JJeKTpo.n.oB,
BCJJe)J,CTBI-Ie qero TepMOnapa CTaHOBI-ITCH npI-lro.n.HoH TOJJbKO .n.JJH rpy6bIx
TeXHI-IqeCKI-IX, HO OTHIO.n.b He .n.JJH TOqHblX I-I3MepeHi-lH.
3KCnepI-lMeHTaTopbI He Bcer.n.a y.n.eJJHIOT .n.OJJLKHOe BHI-IMaHi-le XI-IMH-
qeCKOH I-I cpI-l3I-1qeCKOH O.n.HOpO.n.HOCTI-I TepOM03JJeKTpo.n.OB, 3a6bIBaH 0 TOM,
qTO )J,aLKe I-IX pe3KI-IH I-I 3JJ OM , CJIa60e nepeKpyqI-lBaHI-Ie I-I T. n. HBJJHIOTCH
HCTOqHI-IKOM napa3I-1THblX 3JJeKTpo.n.BI-ILKYllI.I-IX CI-IJJ.
nepeKJJ, IOqaTeJlI-l Kyp6eJJI-I I-I npOqHe .n.eTaJJI-I 3JJeKTpOI-l3MepI-lTeJlbHOrO
YCTpOHCTBa He .n.OJJLKHbl BBO.n.I-ITb B uenb TepMOnapbI HenOCTOHHHblX H
60JJblllI-lX COnpOTI-IBJJeHHH. TeMnepaTYPY cB060.QHoro KOHua ueJJeCO-
06pa3HO no.n..n.epLKI-IBaTb Ha ypOBHe ° I-IJJI-I 20° C C TOqHOCTblO.n.O
0,02-0,05°.
TepMonapbI CJIe.n.yeT TllI.aTeJJbHO oTrpa.n.YHpoBaTb B KOM6I-1HaUI-lI-l C no-
TeHUI-lOMeTpOM, JJI-I60 C XOpOlllI-lM nI-lpOMeTpI-lqeCKI-IM MI-IJJJJI-IBOJJbTMeTpOM,
I-IJJI-I, elll.e JJyqllle, C 3epKaJJbHbiM raJJbBaHOMeTpOM.
HeJlb3H 060HTI-ICb 6e3 rpa.n.YI-IpOBKI-I YCTaHOBKI-I, nOJJaraHCb Ha CTaH-
.n.apTHble Ta6JJI-IUbi )J,JJH TepMonap, TaK KaK B3aI-lM03aMeHHeMOCTb TepMO-
nap elll.e He HaCTOJJbKO COBepllleHHa, qT06bI 06eCneqI-l o Tb He0 6xo .n.I-IMYIO
TOqHOCTb npI-l I-I3MepeHI-IHX, Tpe6YIOllI.I-Ix nOBblllleHHOH TOqHOCT
.
npI-l OnbITaX C MeTaJJJJaMI-I I-I 6JJI-I3KI-IMI-I K HHM no TenJJOBblM CBOI-lCTBaM
MaTepI-laJJaMI-I npouecc npOTeKaeT TaK 6bICTpO, qTO npI-lMeHHTb nOTeHUI-lO-
MeTp CTaHOBI-ITCH HeB03MOLKHbIM; B 3TI-IX CJIyqaHX npI-lXo.n.I-ITCH npI-l6e-
raTb K MaJJO I-IHepUI-IOHHOMY 3epKaJJbHOMY raJJbBaHOMeTpy, CTPYHHOMY
raJJbBaHOMeTpy I-I OCUI-IJJJJorpacpI-lpOBaHi-llO. npI-l I-ICCJle.n.OBaHI-IHX no
3aKaJJKe CTaJJbHblX 3arOTOBOK MaJJblX pa3MepOB 6bIJJ npI-lMeHeH CTPYH-
HbIH raJJbBaHOMeTp C OnTI-IqeCKOH 3anI-lCblO nOKa3aHI-IH, BOJIbcppaMOBblH
BOJJOCOK KOToporo I-IMeJJ .n.HaMeTp TOJJbKO 0,0075 MM.

 6. H3MepeHHe TeMnepaTYP noCpe]l.CTBOM ]l.HcJ>cJ>epeHlJ.I-taJIbHOH
TepMonap
 (BTOpOH BapHaHT)
LLJJH nOCTpOeHI-IH nOJJYJJOrapI-lcpMI-IqeCKOrO rpacpI-lKa perYJJHpHOrO
peLKI-IMa .n.OCTaTOqHO 3HaTb BeJlI-lqI-lHY TeMnepaTypffoH pa3HOCTI-I {}. H HeT
He06xo.n.I-IMOCTH I-I3MepHTb no OT.n.eJJbHOCTI-! U H 6, KaK 3"F0 HaMI-I 6bIJJO
npo.n.eJJaHO B npe.n.bI.n.YllI.eM naparpacpe. LLJJH I-I3MepeHHH pa3HOCTI-I {} OqeHb
y.n.o6Ha .n.mpcpepeHUI-IaJJbHaH TepMonapa, npI-lCoe.n.I-IHeHHaH K qYBCTBI-I

TeJJbHOMY raJJbBaHOMeTpy MarHI-IT03JJeKTpI-lqeCKOrO TI-Ina no 06bIqHOI-l
cxeMe, KOTopaH I-I306paLKeHa Ha cpI-lr. 95. 5YKBOH E 3.n.eCb 0603HaqeHa
cpe.n.a, B KOTOpylO norpYLKeHbl KaJJOpI-lMeTp F
 TepMO
JJeKTpo.n.bI .n.I-Icp-
cpepeHUI-IaJJbHoi'f TepMonapbI A I-I B, O.n.I-IH cnaI-l KOTOpOI-l M H'lJXO.n.I-ITCH
npH TeMnepaType U, a .n.PyroH - N npI-l 6. B TOqKaX m I-I n TepM03.neK-
TpO.n.bI npI-lCoe.n.I-IHeHbl K Me.n.HbIM npoBo.n.aM C, I-I.n.YllI.I-IM K ra.nbBaHO-
MeTpy Q.
npH ymWpf'nlTf'HHH Rf'C'f-,M;J qVRC'TRHTf'JlhHOrO r::l.nhR;JHOMf'Tpa MOLKeT
OKa3aTbCH He06xo.n.I-IMhIM nOHI-I3I-1Tb ero qYBcTBlfTeJJbHOCTb, oc06eHHo B


BaTbCS! OT peKoMeH.n.aUI-II-I MeTo.n.OB, OCHOBaHHbIX Ha npi-lMeHeHI-IH TepMo-
MeTpoB ConpOTI-IBJJeHi-lH.
npe.n.nOqreHI-ISI 3aCJIY}I{I-IBaeT TepM03J1eKTpI-lqeCKI-IH MeTO.n., MeLK.n.y
npoqI-lM, I-I nOTOMY, qTO nplJ: Bbl60pe TOHKl;X TepM03JJeKTpo.n.oB H HK
paUI-IOHaJJbHOH MOHTI-IpOBKe llCKaLKeHHe TeMnepaTypHoro nOJIH KaJlOpI-l-
MeTpa COBceM HeBeJJI-IKO I-I He BJlI-IHeT Ha TOqHOCTb I-I3MepeHI-IH 1 , qero
HeJlb3H CKa3aTb 0 )J,pyrHX MeTo.n.ax I-I3MepeHI-IH, npH KOTOpbIX Te!IJlOqYB-
CTBI-ITeJlbHaH qaCTb npH60pa I-IMeeT TenJlOeMKOCTb I-I pa3Mepbl. Bo06ll1.e
rOBopH, CpaBHI-IMbIe C TenJJOeMKOCTblO I-I pa3MepaMI-I Toro TeJJa, BHYTPb-
KOTOpOro 3Ta TenJJOqYBCTBI-ITeJlbHaH qaCTb BBO.n.I-ITCH.
npI-lMeHHeMbl
 HaMH KaJJOpi-lMeTpbl I-IMelOT 06blqHO He60JJblllI-le pa3-
MepbI; MaTepHaJlbl, I-I3 KOTOpbIX OHH COCTOHT, 3aqaCTYIO 06JJa.n.a1OT He3Ha-
qI-lTeJJbHbIM 06'beMHbIM BeCOM. 1, a CJIe.n.OBaTeJJbHO, I-I MaJJOH 06'beMHOH
TenJJOeMKOCTblO c vo1 ; n03TOMY PTYTHble CTeKJJHHHble TepMoMeTpbI MO}KHO
npI-lMeHHTb B Tex CJIyqaHX, Kor.n.a MaTepI-laJJ, BHYTPb KOToporo BBO.n.I-ITCH
TepMoMeTp, I-IMeeT 06'beMHbIH Bec He HI-I}Ke 6(0-700 KF/M 3 , a .n.I-IaMeTp
lllapi-lKa TepMoMeTpa no KpaHHeH Mepe B nHTb-llleCTb pa3 MeHblIIe HaI-l-
MeHblllero pa3Mepa KaJJOpi-lMeTpa.
npI-l YMeJJOM npI-lMeHeHI-II-I PTYTHblX TepMoMeTpoB TOqHOCTb H3Me-
peHHH MO}l{eT 6bITb He HI-I}Ke 2-3 %, .n.a}Ke eCJlH ynoTpe6JJHTb TeXHI-I-
qeCKI-Ie I-IHCTpYMeHTbl C HaI-lMeHblllI-lMI-I no.n.pa3.n.eJJemfHMI-I lllKaJlbl Ha
0,5-1,0° C. JIyqllle Bcero 6paTb Te TepMoMeTpbI, Y KOTOpbIX Xo.n. no-
npaBKH B I-I3MepHeMoH 06JJaCTI-I TeMnepaTYP, T. e. B6JJI-I3H t, OTJJH-
qaeTCH nJJaBHOCTblO H KOTopbIe He 06HapY}KHBaIOT 3aMeTHoro «MepTBoro
xo.n.a». IllapI-lKlJ (pe3epByapbI) He .n.OJl}KHbl 6bITb qpe3MepHO MaCCHBHblMI-I
H .n.OJJ}KHbl I-IMeTb UHJJI-IH.n.pI-lqeCKYIO HJJI-I CJIa60 KOHHqecKYIO <tOPMY C
YToHblIIeHHeM KHH3Y.
HecMoTpH Ha npocTOTY 060I-lx npI-l.MeHHeMbIx HaMH MeTo.n.OB, He06xo-
.n.HMO 06paTHTb oc060e BHI-IMaHi-le Ha TeXHi-lKY 3KCnepI-lMeHTa, npeHe6pe}Ke-
HI-Ie )J,eTaJJHMI-I KOTOpOH, Ha nepBblH B3rJJH.n. He I-IMelOllI.I-IMI-I 3HaqeHI-IH,
BJleqeT 3a C060H rpy6bIe 01llI-l6KH B H3MepeHI-II-I TeMnepaTYP U H 6, a TeM
60JJee HX pa3HOCTi-l. I1MeHHo 3TI-IM 06CTOHTeJJbCTBOM 06'bHCHHeTcH cYllI. e -
cTBYlOllI.ee .n.o CI-IX nop .n.a}Ke cpe.n.I-I cneUI-IaJJHCTOB no TenJJOBblM I-I3Mepe-
HI-IHM HenpaBHJJbHOe MHeHi-le 06 3KCnepI-lMeHTaJJbHOH cTopoHe MeTo.n.I-IKI-I
perYJJHpHOrO pe}l{I-IMa.
npI-l I-I3MepeHI-II-I TeMnepaTYP U H 6 TepMOnapaMI-I MbI 06bIqHO npHMe-
HHeM TepM03J1eKTpo.n.bI TOJllll.I-IHOH OT 0,10 .n.o 0,65 MM, qalll.e Bcero 0,3-
0,4 MM. BbI60p MeTa.nJJOB TepMonapbI onpe.n.eJJHeTCH TeMnepaTypHblM
ypoBHeM 6; )J,JlH (J He BbllIIe 400 0 C MO}KHO npI-lMeHHTb Me.n.HO-KOHCTaHTa-
HOBbie HJJH' Me.n.HO-KOneJleBble TepMonapbI, .n.o 800 0 -xpOMeJJbaJJIOMeJle-
Bble, .n.o 1300 0 - nJJaTi-lHOpo.n.I-IH-nJJaTi-lHOBble.
PeKoMeH.n.yeMble HaMH HaI-lBbIClllI-le npe.n.eJlbl npHMeHeHI-IH TepMonap
3HaqHTeJlbHO HI-I}Ke YKa3bIBaeMbix B JJI-ITepaType, B qaCTHocTI-I TeX HaI-l-
BblClllI-lX TeMnepaTYP, KOTopbIe .n.aHbI .n.JlH OTeqeCTBeHHblX cTaH.n.apTHblx
repMonap B ocpI-lIlI-la.nbHblx Ta6JJI-Iuax. LLeJJo B TOM, qTO TepMonapa npI-l-




166


H3MepeHUJI U npU60pbt


H3MepeHUJI K03tjJtjJUliueHTOB a, A, C


167


Haqa.nbHblH MOMeHT, KOr,lJ.a pa3HocTb {} Bemma, TOK i, TeKYllI.l-IH qepe3
ra.nbBaHoMeTp, 3Haql-lTe.neH 1-1 MO}KeT 6b1Tb onaceH )J..nH ue.nOCTI-I I-IHCTPY-
MeHTa; C :nOM UeJJblO B uenb TepMonapbl nOCJIe)J.OBaTe.nbHO C HI-IM BK.nIO-
qaeTCH Mara31-1H conpOTHB.neHI-IH, KOTOpblH n03Bo.nHeT BK.nlOql-lTb conpo-
TI-IB.neHl-le RM' 1-13MeHSISI ero no }Ke.naHHIO, 1-1 TeM CHI-I31-1Tb CI-I.ny TOKa i.
3TOT BTOpOH Bapl-laRT H3MepeHliH TeMnepaTYP I-IMeeT cepbe3Hoe npe-
I-IMYllI.eCTBO nepe)J. nepBblM: OH n03Bo.nSleT 3Haq1-lTe.nbHO nOBblCI-ITb qYB-
CTBI-ITeJIbHOCTb 1-13MepeHHH 1-1 ynpOCTI-ITb BblqHCJIIITe.nbHble onepaIlHH 1-1
H36aB.nHeT OT He06xo)J.I-IMOCTI-I rpa)J.Yl-lpOBaTb TepMonapy, KaK :no YCMa-
Tpl-lBaeTCH 1I3 )J.aJIbHeHIIII-IX paCCY}K)J.eHI-IH.
A C
m


npl-lqeM K03cpqmuHeHT nponopul-IOHa.nbHOCTH k' np3KTHqeCKH He 3aBI-I

CHT OT Ko.ne6aHI-IH TeMnepaTypbl ra.nbBaHOMeTpa, T. e. OT Ko.ne6aHHH
TeMnepaTypbl nOMelll.eHI-IH, r)J.e HaXO)J.HTCH npH60pbl.
C )J.Pyroii CTOpOHbI, npHMeHHSI 3aKOH OMa K uenH TepMonapbl, B
KOTOPO!! )J.eHcTByeT 3. )J.. C,. paBHaSl ED' no.nyqaeM
i= r
DRr ' (B.17)


B


A


c


T'.n.e Rr - COnpOTI-IB.neHl-le ra.nbBaHoMeTpa; r - conpOTlm.neHHe BHelIl-
l:eH uenH, paBHoe cYMMe conpOTHBJIeHHfI: R T - TepMonapbl, Rn - CO-
e)J.HHHTe.nbHblx npoBO)J.oB H RJ;f - Mara3HHa conpOTHB.neHHH:
r=RT+Rn+R M .
lb conocTaB.neHHH CPOPMY.n (8. I5), (8. I6), (8. I7) HaXO)J.HM CJIe)J.YIO-
llI.YIO 3aBHClIMOCTb Me}K)J.Y <p H TeMnepaTypHO!! pa3HocTbi0 {j- = u - 6:
k' -
<p = R F'(fl} &.
r+ r
nYCTb OTCqeT D no IIlKa.ne ra.nbBaHoMeTpa, cooTBeT
TBYlOllI.HH yr.ny
nOBopoTa <p, nponopuHoHa.neH 3TOMY yr.ny, T. e. D = k" <po 3TO .nerKO
oCYlll.ecTB.nHeTcH B 3epKa.nbHblx ra.nbBaHoMeTpax npH )J.ocTaTOqv HOM Y)J.a-
.neAlm IIlKa.nbl OT ra.nbBaHoMeTpa H.nH npH npHMeHeHHH KpyroBoH IIlKa.nbl,
npHqeM nponopuHoHa.nbHOCTb coxpaHHeTcH )J.a}Ke npH OqeHb Ma.nbiX
CH.nax TOKa - nopH)J.Ka 10- 9 a. B 6o.nee rpy6b1x MarHHT03.neKTpHqe-
CKHX npH60pax nponopuHoHa.nbHOCTb co6.nIO)J.aeTcH B CH.ny caMoro
YCTpOMCTBa npH60pa Hero paBHOMepHOH IIlKa.nbl; OHa HapYlIlaeTCH
TO.nbKO )J..nH TOqeK IIlKa.nbl, 6.nH3KHX K HY.nIO, ec.nH Hy.nb COOTBeTcTByeT
OTCYTCTBHIO TOKa B npH60pe.
113 )J.BYX nOCJIe)J.HHX paBeHcTB BblTeKaeT, qTO
D = k'!l" F' ({!-} &
r+Rr


n


RM


N(e) -


E


4>Hr. 95. CxeMa H3MepeHHH TeMTiepaTypHoii pa3HOCTH U - 6
TlOCpe.ncTBoM J1H4>4>epeHUHaJIbHOH TepMonapbl B COe.l\lHlellHH C
MarHHT03JIeKTpHlJeCKHM raJibBallOMeTpoM.


CorJIaCHO TeopHH )J.l-lcpcpepeHUHaJIbHOH repMonapbl, repM03.neKTpo-
)J.BH}KYllI.aH CH.na ED' pa3sHBaeMaH B ee uenH, COCTaBJIeHHOH no cxeMe
cpHr. 95, )J.aHa tPOpMy.nOH
ED = (u - B) (

 )&=&. (8. 15)
3)J.ecb E - 3. .n. C. TepMonapbl H3 MeTa.n.nOB A 1-1 B, O)J.I-IH cnaH
KOTOpOH .no)J.)J.ep}KHBaeTCH npH nOCTOHHHOH TeMnepaType 6 0 (06blqHO 0
I-I.nl-l 20° - CM. npe)J.bl)J.Ylll.HiI
 5), a )J.pyroH ---.: I-IMeeT 1I3MeHHIOlll.YlOCH
TeMnepaTYPY u, & = u - 6; CI-IMBo.nHqeCKH
E = E AB (&, 6) = F (&).
B npaBoH qaCTM paBeHcTBa (8. 15) CTOHT npOH3BOl!HaH OT E no 3,
T. e. F'({j-}, OTHeCeHHaH K 3H3'1eHHIO & = tJ., npnqeM ij. eCTb TeMnepaTypa,
.ne}KaillaH Me)!{)J.y 0 1-1 U - 6.
0603HaqHM qepe3 <p yro.n OTK.nOHeHHH nO)J.BH}KHOH CHCWMbI. Hanpl-l-
Mep paMKI-I ra.nbBaHoMeTpa, OT ee no.nO}KeHHH paBHoBecHH, cooTBeTcTBY-
IC'IllHH CH.ne TOKa i, npoxo)J.HIllero qepe3 ra.nbBaHoMeTp.
Cor.nacHo TeOpHI-I ra.nbBaHoMeTpa, <p J1 i npHMo nponopuHOHa.nbHbl;
If = k'i, (8.16)


H.nH npolll.e


D=k&,


(8. 18)


r)J.e k - K03cptPHUlieHT nponopuHoHa.nbHOCTH, CTpYKTypa KOToporo
)J.aHa cpOpMy.nOH


k =
!l"- F' ({j-} .
r + Rr
ECJII-I YCJIOBHH onblTa He H3MeHHIOTCH, TO Be.nHqHHbl k' k", r, 1-1 Rr


OCTalOTCH TaK}Ke HeH:ilMeHHbIMH. To }Ke caMoe MO}J{!I0 CKa3aTb 1-1 0 npo-
H3BO)J.HOH F'(J}, eCJIH pa3HocTb TeMnepaTYP {} TaKOBa, qTO npoH3Bo)J.'
HVIO F' ( {J.) = dE MO}KHO CqHTaTb nOCTOHHHOH (npaJ{THqeCKI-I E MeHHeTCH
. d!t
.nHHeHHo C {j-}. B 3TOM cJIyqae I-IMeeT MeCTO Ba}KHOe C TOqKH 3peHHH Tn-




168


/f.j"tepeHUJ! U npuoopp"


HHKI-I H3MepeHHH CJIe}J.CTBHe: nOCKO.nbKY Ha npOTH)!(eHI-IH OnbITa k
OCTaeTCH nOCTOHHHbIM, cpOPMY.ny (8. 14) MO>KHO 3aMeHHTb ropa3}J.0 60.nee
npocTOH:


InDI-InDTI
m=
"11- "I


(8. 19)


(TaK KaK 1n k COKpalll.aeTcH).
C.ne}J.oBaTeJIbHO, npHMeHHH }J..nH H
MepeHHH TeMnepaTYP BTOpOH
BapHaHT, MbI H36eraeM B 60.nblIlHHcTBe CJIY1.JaeB He06xo}J.HMOCTH
pa-
}J.YHpoBaTb TepMonapy H no.nY1.JaeM B03MO>KHOCTb HaH.nY1.JlIlerO Hcno.nb30-
BaHHH 1.JYBcTBHTe.nbHocTH ra.nbBaHoMeTpa. KpoMe TOro, 3}J.eCb He Hrpae-r
pO.nH HeCTa6H.nbHOCTb :meKTpO}J.OB, BbI3BaHHaH I-IX neperpeBaHl-leM,
KOTopaH, KaK YKa3blBa.nOCb paHee, HMeeT CYllI.eCTBeHHoe 3Ha1.JeHHe }J..nH
T01.JHOCTH H3MepeHHH & no nepBOMY BapHaHTY.
00 npl-l1.JHHe 3THX oc06eHHOCTell BToporo BapHaHTa OH BOlIle.n BO
Bce06ll1.ee ynoTpe6.neHHe. nepBblM BapHaHTOM MbI no.nb3yeMcH ropa3}J.0
pe>Ke, npeHMYllI.eCTBeHHO Kor}J.a OKa3bIBaeTCH B03MO)!(HbIM npHMeHHTb
pTYTHbIe CTeK.nHHHble TepMOMeTpbl H.nH )!(e Kor}J.a no KOHCTPYKTHBHblM
C006pa>KeHHHM npHMeHeHHe }J.HcpcpepeHl.lHa.nbHOH TepMonapbI Hel.leJIe-
co06pa3HO.
B 06ll1.eM c.nY1.Jae, Kor}J.a pa3HOCTb TeMnepaTYP (3-) Be.nHKa H T. 3. 11.. c.
E H3MeHHeTCH C TeMnepaTypoi-i HemlHelIHO, Bblpa>KeHHe (8. 19) CJIe11.yeT
nepenHcaTb B 60.nee 06ll1.eM BH}J.e:
F' (61)
In DI-ln Du - In p' (8 )
m= . II


fnABA 9
nEPBblA METOJ( PEfYJUIPHOfO PE)I(HMA



 1. !eopeTH'IeCKHe OCHOBbl nepBoro MeT01I.a


npe11. no .nO)!(HM, qTO H3 Hcnb1TblBaeMoro MaTepHa.na H3rOTOB.neH
06pa3el.l, K03cpcpHl.lHeHT cpOpMbl KOToporo K H3BeCTeH. nO}lBeprHeM 06pa-
3eIJ. ox.na)!(}J.eHI-lIO H.nH HarpeBaHHlO, npHqeM C03}J.a}J.HM TaKYIO 06cTaHoBKY
OnblTa, qT06bI C06.nIO}J.a.nI-lCb YCJIOBHH (4. 5) H (*) (
 4, r.n. 4), T. e.
nycTb


e = const,


(J.
 00.


(**)


Onpe}J.e.nI-lM 3KcnepHMeHTa.nbHo TeMn ox.na>K}J.eHHH m = moo
(r.n. 8); Tor}J.a Ha OCHOBaHHH 06ll1.ei-i TeopeMbI (
6, r.n. 4) HMeeM (4. 19),
T. e. HaXO}J.HM TeMnepaTyponpoBo}J.HOCTb MaTepHa.na no cpopMy.ne
a=Kmoo. (9.1)


"2 -"I


(8. 20)


B COOTBeTCTBHH C TO.nbKO qTO H3.n0>KeHHOH TeopHeH MbI }J.O.n)!(HbI pac-
no.naraTb cpe}J.oH E nocToHHHOH TeMnepaTypbl e, qTO npaKTHqeCKI-I oCY-
ruecTB.nHeTCH C nOMOlll.blO TepMocTaTa, n03Bo.nHlOllI.ero 11.0CTaTOqHO
}J.o.nroe BpeMH nO}J.}J.ep)!(HBaTb TeMnepaTYPY. 3Toro elll.e He}J.OCTaToqHO;
He06xo}J.HMO. qT06bI 6bI.n0 06ecne1.JeHO c06.nIO}J.eHHe BToporo H3 YCJIOBHH
(**).
Y)!(e }J.aBHO (OKO.nO 1930 r.) OnblTHbIM nYTeM 6bI.n0 06Hapy)!(eHO, 1.JTO
O}J.HI-I H Te )!(e YCJIOBHH ox.na>K}J.eHHH - B O}J.HOH H TOH )!(e BaHHe, C O}J.HHM
H TeM )!(e nepeMelIlHBaHl-leM - npH HcnbITaHHH 06pa3IJ.OB O}J.HHX MaTepH-
a.nOB }J.alOT Bno.nHe npHeM.neMbIe pe3y.nb1'aTbI, a }J..nH }J.PyrHx - HBHO
01IlH60qHbIe, T. e. YCJIOBl-le (**). B 3TOM CJIyqae He BbIllo.nHHeTCH. no-
3TOMY CJIe}J.yeT BBeCTH 06ll1.Hll MeTO}J. OlieH,KH K03cpcpHlil-leHTa Ten.nOOT}J.a1.JH,
npH KOTOpOM }J..nH }J.aHHoro 06pa3lia 6Y}J.eT BbIllO.nHHTbCH YCJIOBHe (**),
HB.nHlOllI.eeCH He06xo}J.HMOll npe}J.nOCbI.nKOH }J.JIH npaBH.nbHoro npHMe-
HeHHH MeTO}J.a aKa.nopHMeTpa.


C.ne}J.OBaTe.nbHO, npH onpe}J.e.neHHH TeMna pery.nslpHoro oX.na>K}J.eHHH
TeJla, TeMnepaTypa KOTop
ro H3MeHHeTCH B lIlHpOKOM HHTepBa.ne, He06-
XO}J.HMO no.nb30BaTbCH rpa}J.YHpOBaHHOH TepMonapOH H BblqHCJIHTb m no
cpopMy.ne


In {h - In {III
m-
- "2-"1 .


(8. 21)


CYllI.eCTBeHHeHlIlHM YCJIOBHeM npaBH.nbHoH pa60TbI cxeMbl cpHr. 95.
HB.nHeTCH paBeHCTBO ieMnepaTYP MeCT npHcoe}J.HHeHHH m H n TepMO-
3.neKTpO}J.OB K Me}J.HbIM npOBO}J.aM; 3TH TeMnepaTypbI MorYT 6bITb KaKl-le
yrO;J:HO, .nHlIlb 6bI OHH 6bI.n1-l paBHbI Me>K}J.Y C060H.
npH H3MepeHHH 3- nOCpe}J.CTBOM Me}J.HO-KOHCTaHTaHOBOH H.nH Me}J.HO-
KOne.neBOll TepMonapbI 3TO YCJIOBHe OTna}J.aeT, eCJIH 3a TepM03.neKTpo}J. A
B3HTb Me}J.b, T. e. C.
XIJTH no caMoH cym }J.HcpcpepeHl.lHa.nbHoro MeTo.n.a 1-13MepeHHH TeMne-
paTYP HeT He06xo}J.HMOCTI-I H3MepHTb 8, TeM He MeHee peKOMeH}J.yeTcH
KOHTpo.nl-lpOBaTb TeMnepaTYPy 8 cpe}J.bl E C nOMOlll.blO OT}J.e.nbHoro
npH60pa, KOTOpbIH He CJIY>KI-IT }J..nH H3MepeHHH, a HrpaeT .nHlIlb po.nb
'IHAHKaTopa TeMnepaTypbI H n03Bo.nHeT CJle}J.HTb 3a ee nOCTOHHCTBOM.



 2. nOHSITHe 06 (J.-6ecKOHe'lHOCTH
06bIqHO CqI-lTaIOT, qTO npH Bi nopH}J.Ka 50-70 MO>KHO Bce paCqeTbI
BeCTH, npe.n.no.naraH, qTO YCJIOBHe (**) c06.n , lO}J.eHO T. e. 1.JTO Ha Ha-
PY>KHOH nOBepXHOCTI-I S 06pa3l.la nO}J.}J.ep>KHBaeTCH 3a}J.aHHaH TeMnepa-
Typa, paBlwR t (TaI{ IIn3LmaCMI,IC «KparBLlcI II.n1l «rpalllitlIll>lr YC.nODlIJI
nepBoro pOA8» - eM. (2) 1-1 (8 )).




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HHIO (Bce TO'-lKH JJe)l{aT no o,n:HY CTOPOHY JJI060H npHMOH, npOBO)J.HMOH
'-Iepe3 ,n:Be KaKHe-JJH60 H3 HHX), TO 3TO CJlY)I{HT YKa3aHHeM Ha KaKYIO-TO
01llH6KY npH Be)J.eHHH onblTa HJJH HeBblnOJJHeHHe YCJlOBHH a. = 00.
OnblT He06xo,n:HMO nepe)J.eJlaTb, H3MeHHB HeCKOJJbKO 06CTaHOBKY 3Kcne-
pHMeHTa.
npli'-lHHa liCKpHBJJeHHH rpacpHKa MO)l{eT 6blTb pa3J1li'-lHaH: HaJJH'-IHe
KOHBeKu,HOHHbIX TOKOB B B03,n:YlllHbJX BKJlIO'-IeHHHX, Bbl)J.eJJeHHe CKpbl-
ThlX TenJJOT, BII6pau,HH H T. ,n:. EecnopH)J.O'-lHOe pacnOJJO)l{eHHe TO'-leK
'-IaCTO CJlY)I{HT YKa3aHHeM Ha HenOJJa)J.KH B TepM03JJ€KTpH'-IeCKOH u,enw
B03MO)l{HbI 3aMblKaHHSl B nJloxo H30JJHpOBaHHbJX MeCTax, '-ITO CJlY'-IaeTCH .
npH BJJa)l{HOH aTMoccpepe nOMelll.eHHH HJJH HapYllleHHH u,eJJOCTli npo-
. BOJJO'-leK TepMonapJ>I, li T. ,n:.
n03TOMY CJle,n:yeT oc06eHHO Tlll.aTeJJbHO c06HpaTb 3JJeKTpH'-IeCKYIO
cxeMY YCTaHOBKH, He B3HpaH Ha ee npOCTOTY; HY)I{HO nOMHHTb, '-ITO MbI
liMeeM ,n:eJJO C KpaHHe CJla6bIMH TOKaMH, He )J.OCTHraIOlll.HMH '-IaCTO )J.a}J{e
1 Ma.
I1Hor,n:a rpacpHK nOJJY'-IaeTCH B BH,n:e JJOMaHOii JJHHHH, COCTOHlll.eH H3
)J.BYX npHMblx; B orpoMHoM 60JJblllHHCTBe CJlY'-IaeB 3TO 06'bHCHHeTcH npo-
HHKHOBel-meM BO,n:bI BHYTPb MaTepHaJJa, BCJle,n:cTBHe '-Iero ero TeMnepaTYPo-
npoBo
HO:::Tb pe3Ko MeHHeT CBOIO BeJlH'-IHHY (06bI'-IHO na,n:aeT).
Dpe)J.l1oJJoMliM, '-ITO rpacpliK nOJJY'-IHJJCH y,n:oBJJeTBOpHTeJJbHOrO BH,n:a.
3TO ,n:aeT rapaHTHIO. '-ITO onbIT 6bIJJ npoBe,n:eH npaBHJlbHO, HO He )J.aeT
elll.e npaBa 6e3 )J.onOJJHHTeJJbHOrO pa360pa Bcex 06CTOHTeJJbCTB onbITa
npnMeHHTb paC'-IeTHYIO q)OPMYJJY MeTo,n:a (9. 1): )J.eJlo B TOM, lITO OHa GCHO'
BaHa Ha HeKOTopbIX ,n:onOJJHHTeJJbHbJX npe,n:nOJJO)l{eHHHX, KOTOpbJe
10.'1>KHbI nblTh ()rYIITPrTR.lIPHhI R nponecce onblTa: HaJJH'-IHe )l{e npHMOJlH-
H
llHoro rpaqmKa 6y,n:eT HMeTb MeCTO ,n:a)l{e li npH HeCOOJJlOj.eHl:Il:I l:IX.




184


H3MepeHuJl u npU(j0pbl


nepBbtiJ. MeTOa pezyAJlpHOZO pe:JfCtlllta


185


H60 3aKOH perYJHlpH3aUHH TeMnepaTypHOrO pe)lHlMa panpOCTpaHHeTCH,
KaK Mbl Y}I{e rOBOpHJlH, Ha UmpOKHll KJlaCC HBJleHHiL
3TH npe)J.nOJlmKeHHH cJIe)J.YJOllI.He:
1) K03<p<PHUHeHT TenJIo06MeHa ex cTpeMHTcH K 6eCKOHelJHOCTH;
2) BO Bcex TOlJKaX HapY}I{HOH nOBepxHocTH HcnbITblBaeMoro 06pa3ua
YCJIOBH5I TenJIo06MeHa C oKPY}I{aJOllI.eii: cpe)J.oH O)J.HHaKOBbI;
3) H3MepHTeJIbHbIH HHCTpYMeHT He HCKa)KaeT 3aMeTHo pacnpe)J.eJIe-
HH5I TeMnepaTYP B 06pa3ue.
HY}I{HO C03)J.aTb TaKYJO 06CTaHOBKY' OnblTa, lJT06bl 3TH npe)J.nOJIO}l{e-
HHH OCYllI.eCTBJIHJIHCb C )J.OCTaTOlJHoi\ TOlJHOCTbJO; KaK 31'0 C)J.eJlaTb.
YKa3aHO Bblille. npeHe6pe)KeIme 3THMH YKa3aHHHMH Be.l(eT K 3HalJH-
TeJIbHblM OIllH6KaM B onpe)J.eJleHHH a.


B caMOM )J.eJle, npe)J.nOJIO)KHM, lJTO O.l1.HH H TOT )l{e aKaJIOpl1MeTp
HanOJIHeH )J.Ba)l{)J.bl HCCJle)J.yeMbIM MaTepHaJIOM, TaK lITO n
OTHOCTb er

Ha6HBKH O)J.HH pa3 xapaKTepH3yeTcH 06'beMHbIM neCOM 1, a )J.Pyrol1
pa3 - 06'beMHbIM BeCOM 1". CooTBeTcTBYJOllI.He 3THM pa3JIHlJHbiM n
oT:
HOCTHM TenJlOnpoBo)J.
OCTb H TeMnepaTyponpoBo)J.HOCTb 0603HallHM A ,a
H A', a". npOH3Be)J.H )J.Ba onblTa npH pa3Hbix .1', n0,;1lYlJHM pa3JIHlJHbIe
TeMnbl OXJlaiK)J.eHI1H, KOTopble nYCTb 6Y)J.YT m 11 m, COOTBeTCTBeHHO.
vb <POPMY.'J (8.2) H (9. 1), npl1MeHHH I1X K 3TH
 )J.BYM onblTaM, nOJIYlIHM:
'J...' = a'cj' = Km'Cj';
'J..." = a"c'( = Km"cl",


a OTCJO)J.a



 8. OnpeJleJIeHHe TenJlOnpOBOJlHOCTH A Ha OCHOBaHI11-1 pe3YJlbTaTOB
1-13MepeHH5I TeMnepaTyponpoBo)J.HOCTH
B CHJIY (8.2) JlJIH onpe)J.eJIeHHH A, Kor)J.a a Y}I{e Hai1)J.eHo, Tpe6yeTcH
HaiiTH CHI'
OnpeJleJIeHHe 06'beMHOrO Beca 06pa3ua npOH3BO)J.HTCH C 60JlbillOH
TOllHOCTbJO nYTeM B
meIllHBaHI1H 06pa3Qa H )J.eJleHH5I ero Beca P Ha 113-
BeCTHblH Y}I{e 06'beM aKaJIOpHMeTpa V:
p
I=V'
YJJ.eJlbHa51 TeUJIOeMKOCTb MaTepHaJia C MO}l{eT 6b1Tb onpeJJ.eJleHa H3
oc06oro onblTa (XOTH 6b1 npH npHMeHemIH BTOpOro MeToJJ.a perYJI5Ip-
HOro pe}l{HMa); npOlll.e BOCnOJlb30BaTbCH Ta6J1. 10 JJ.JlH TenJlOeMKOCTeH,
liTO, KOHellHo, MeHee TOllHO, HC BO MHomx CJlYlJaHX npaKTHKH OKa3b1-
BaeTCH JJ.OCT8TOllHbUt,1. llJlH npeJJ.BapHTeJlbHblX nOJJ.clIeToB MO)l{HO rpy60
npHHHMaTb YJJ.eJlbHYJO TenJlOeMKOCTb CYXHX HeopraHHlIecKHx MaTepHa-
JIOB paBHoii B cpeJJ.HeM 0,2. a CYXHX OpraHHlJeCKHX 0,35-0,40 KKWl!K2- 1
2paa- ' (CM.
 2 rJI. 8).


A"
V


m'J if
m'l"


(9.3)


B npaBoii lJaCTH <POPMYJIbl (9.3) CTOHT BemllJHHbI, H3BeCTHble 113
OnblTa, a n03TOMY OHa )J.aeT TOllHoe YKa3aHHe 0 TOM, KaK MeHHeTC5I
TenJlOnpOBOJlHOCTb MaTepHaJia npH eto ynJIOTHeHHH,
ECJIH H3BeCTHbi YJleJIbHbie TenJIOeMKOCTH C 1 H CII JlBYX pa3JIHlJHbiX
MaTepHaJIOB l H ", 06'beMHble Beca, TenJIOnpOBO)J.HOCTH H TeMnepaTYpo-
npOBOJlHOCTH KOTOpbIX CYTb 11' 111 A I' A II' a 1 H all COOTBeTCTBeHHO, TO,
HCnbITblBa51 HX B OJlHOM H TOM )l{e (HJIH B O)J.HHaKOBblX) aKaJIOpHMeTpe H
H3MepHB TeMnbI HX OXJ1a)l{)J.eHHH m l H m ll , MO)l{eM cpaBHHTb H HX TenJIO

H30JIHUHOHHble KalleCTBa, T. e. A I' A II' TaK KaK H3 Tex }l{e ypaBHeHHH
(8. 2) H (9. 1) BblTeKaeT:
AI = Km1c III ; All =- Kmll.clIjn'


n03TOMY



 9. 0 HeKoTopblX cpaBHHTeJIbHblX UCUblTaHU5IX C nOMOllJ,blO aKaJIOpUMeTpa
Bce CKOJIbKO-HH6YJlb 3<p<peKTHBHble TenJIOH30.1I5ITOpbI 06JIa.l1.aJOT Bbl-
COKoii nopHcTOCTbJO, H HX 06'beMHbIii Bec 1 nOJlBep}l{eH )J.OBOJIbHO IllHpOKHM
K0J1e6aHH5IM, 06YCJIOBJIeHHbJM K0J1e6aHH5IMH nopHCToCTH. 3TH K0J1e6a-
HH5I, eCTecTBeHHo, HMeJOT 60JlbIllYJO BeJIHlJHHY )J.JlH HOBbJX MaTepHaJ10B
TeXHOJIOrHlJeCKHii npouecc H3rOTOBJIeHH5I KOTOpblX H COCTaB HCXOJlHOr

Cblpb51 He B nOJIHoii Mepe onpe)J.eJIHJIHcb. OTCJOJla H KOJIe6aHH5I B TenJIO-
npOBO)J.HOCTH A.
YBeJ1HlIeHHe 06'beMHOrO BeCa )J.aHHoro MaTepHaJ1a Bbl3bIBaeT nOBblIlle-
HHe ero K03<p<p H U H eHTa TenJ10npOBO)J.HOCTH; 31'0 nOBbIIlleHHe 3aBHCHT 01'
pO)J.a MaTepH3J1a H nO
Jle)l{HT OC060MY HCCJIe)J.OBaHHJO B KaIK)J.OM OT)J.eJlb-
HOM CJIYlJae. BbInOJIHHTb TaKoe HCCJle)J.OBaHHe J1erKO C nOMOllI.bIO aKaJ10-
pHMeTpa, npHlleM HPT HPnf)'(n
H'>1()(,TIf :maTb YJ\PJII>IIYIO TCIlJ10CMKOCTb C
!rtaTepH3JI3.



 _ m l ", .
 . 1!....
f'lI - m lloo clI "1 II
OTCJO)J.a BH)J.HO, lJTO )J.JlH CpaBHHTeJlbHbIX HCCJle)J.OBaHHH HeT .)J.aIKe
He06xo)J.HMOCTH 3HaTb K03<p<PHI.J,HeHT <pOpMbJ aKaJIOpHMeTpa: MO)l{HO
Bocn0J1b30BaTbCH COCY)J.OM J1J060ii <pOPMbJ, HanpHMep CTeKJIHHHOii Ko.h60H.


(9.4)



 10. Pa3Mepbl H cfJopMa npoCTeiiIllHx aKaJlOpHMeTpOB
Pa3MepbJ H <popMa aKaJIOpHMeTpa BbJ6Hp3JOTCH B COOTBeTCTBHH co
cBoi\cTBaMH HcnblTbIBaeMoro MaTepHaJ1a. JJ.JIH 06bllJHbiX nopoIllKo06pa3-
HbIX, BOJIOKHH CTblX , neHOnJIaCTOB, neH06eToHOB, H30JIHUHOHHbIX KHpnH-
lIeH H TOMY nO)J.06HbJX TenJIOH30JIHUHOHHbIX MaTepHaJIOB O)J.HOpO)J.HOH
CTPYKTypbI MbI npHMeHHeM aKaJ10pHMeTpbI Tpex <pOpM: IllapOBoii, UHJIHH-
)J.pHlJeCKOii H npH3MaTHlJeCKOii (B BH)J.e KBa)J.paTHoii npH3MbI HJIH B BH)J.e
npHMoyroJIbHOrO napaJIJ1eJIenHne)J.a). YIx npHMepHbJe pa3MepbI )J.aHbI
B'Ta6JI. 6.
Pa3MepbI TepMOCTaTa B, KOTOPOMY ueJIeC006pa3Hee Bcero npH)J.aTb
UHJIHH)J.pHlIeCKYJO <PoPMY, )J.OJ1)1{HbI 6bITb B COOTBeTCTBHH C pa3MepaMH
dl
dJlU!JIIMeTpa \', cu CTcnCIILIO CI U npe,J.ua p II TC.l Llloro lIarrena, C()
CBOHCTBaMH MaTepHaJI3.




186


H3MepeHUJ} u npu60pbl


n epBbliJ. Me TOO pezyARpHOZO pe:JfCII.lla


187


T a6AllljU 6


J],JHI


npHMoyrOJl bHoro napaJlJleJlemme.n:a C
1
K= 1 1 1 ) '
'1';2 ( L
 + l! + l!
123


pe6paMH Ll' L2' L3


Pa3Mepbl ynoTpe6HTC1IbHbiX aKaJlOpHMeTpOB B caHTHMeTpaX


(9.8)


UHJlIIHJ1pHlJeCKHe D=4. 5 7
Z=6 7 10
Z] =4 5 5
DpH3MaTH'leCKHe Z2=5 5 6,5
Z3=8 10 12
WapoBble I D=5 I 6 I 8


K =

'1';2 .


JI.,nH cpOpM CJIO)l{HbJX oqepTaHHlf MO)l{HO BOCnOJIb30BaTbCH MO.n:eJlHpO-
BaHHeM; H3 «HopMaJIbHorO» HJIH «3TaJIOHHOrO» TenJIOH30JIHTOpa - rHnca,
BOCKa H T. n. - T. e. Bel.lleCTBa, 06JIa.n:aJOl.llero CTa6HJlbHbIMH H H3BeCT-
HblMH a, ).., C, H3rOTOBJIHJOT Mo.n:eJlb, KonHpyJOI.llYJO B 3a.n:aHHOM MaClllTa6e
o6-beKT, K03cpcpHu,HeHT cpOpMbI K KOToporo Tpe6yeTcSI onpe.n:eJlHTb.
OXJIa)l{.n:aH Mo.n:eJlb B TaKHX YCJlOBHHX, qTo6bJ 6bIJIO 06eCneqeHO YCJIO-
BHe (A **), onpe.n:eJIHJOT H3 3Toro onbITa TeMn perYJISlpHOrO OXJIa)l{.n:eHHH
m H no cpopMYJIe (9. I), r.n:e a H3BeCTHO (H60 MaTepHaJI - HOpMaJIbHbJM),
BbIqHCJlHIOT K03cpcpHu,HeHT cpOpMbI Mo.n:eJlH K MOiJ ' nOCJIe
noro K03cpcpH-
llHeHT cpOpMbJ 06'beKTa K 6y.n:eT HaH.n:eH H3 paBeHcTBa
K = n 2 K MO (J, (9.9)
eCJIH JIHHeHHbIe pa3MepbI Mo.n:eJlH B n pa3 MeHbllle pa3MepoB 06'beKTa.
BTOpOH 3KcnepHMeHTaJlbHbJti npHeM, npHro.n:HbIH .n:JlH )l{eCTKOH 060-
JIOqKH JIJ060H cpOpMbJ, OCHOBaH Ha CJle.n:YJOl.lleM npocToM co06pa)l{eHHH.
nYCTb HMeeTCH 060JIOQKa HOpMaJIbHOM cpoPMbl, T. e. TaKaH, K03<pqm-
u,HeHT cpOpMbI KOTOpOH H3BeCTeH (HanpHMep, lllap); 0603m:qHM ero Kit"
HanOJIHHM O.n:HHM H TcM )l{e nopOlilKOM H COBepllleHHO o.n:HHaKOBbIM
06pa30M - npH' o.iJ.HHaKoBoM 'I - aKaJIOpHMeTp HOpMaJIbHbIH II aKaJ1.Q-
pliMeTp TapHpyeMbIfi, K03cpcpHuHeHT cpOpMbJ KOToporo K Tpe6yeTcH
onpe.n:eJIHTb. 3aCTaBJIHH HX OXJIa)l{.n:aTbCH B YC;TJOBHHX (**) npH O.n:HOH
H TOM )l{e TeMnepaType, Haxo.n:HM H3 cooTBeTcTBYJOI.llHX rpaqmKoB TeMnbJ
oXJIa)l{.n:eHHH m HOO 11 moo. DJIarOAapH TO)l{.n:ecTBeHHocTH MaTepHaJIa H
cnoc06a HanOJIHeHl-IH Mbl HMeeM ocHOBaHHe CQHTaTb TeMnepaTyponpoBo.n:-
HOCTb 0.n:HH3KOBOH B 060HX onbITax. n03TOMY nOJIYQaeTCH ypaBHeHHe
a = Kmoo = K"Ill"oo, H3 KOToporo Haxo.n:HM HCKOMbIII


LI:JlH aKaJIOpHMeTpoB, pa3MepbI KOTOpbJX YKa3aHbI B Ta6J1. 6, K03cpcpH-
ltHeHT cpOpMbI He npeBocxo.n:HT 2 G.M 2 , H npH HarpeBe 06pa3u,oB Ha 10-20°
BbIlile t
 06'beM JIe.n:HHoH BaHHbI .n:OJI)I{eH 6bITb npHMepHO 3-5 /t, 06'beM
BO.n:51Hc?H - OT 8 .n:o 15 /t. ECJIH orp.aHHQHTb npe.n:BapHTeJlbHbIH no.n:orpeB
5-10, TO 6y.n:YT .n:OCTaTOQHbI pa3MepbI 1,5-3 /t H 5-8 /t COOT-
EeTCTBeHHO. '



 11. OnpeJleJIeHHe K03<J><J>HqHeHTa <J>OPMbl K
LI:JIH pH.n:a cpOpM K MO)l{HO HaHTH npH nOMOI.llH CPOPMYJI, HCXO.n:H H3
pe3YJIbTaTOB 06
epa 06pa3u,a HCnbITblBaeMoro MaTepHaJIa. ECJlH MaTe-
pHaJI - cbmYQmf HJIH 06pa3eu, nO)J.OrHaH no.n: pa3MepbI aKaJIOpHMeTpa,
TO )J.JlHHbJ OTpe3KOB, onpe!].e.TJHJOI.llHX pa3MepbI H CPOPMY 06pa3u,a, .n:OJl-
)l{HbI 6bITb OTHeceHbI K BHYTpeHHHM pa3MepaM aKaJIOpliMeTpa.
113 3THX cpOpM 3)J.ecb MbI YKa)l{eM TOJIbKO TPH, caMbIe npocTbIe.
LI:m: lllapa C pa.n:HYCOM R


(9.5)


K m"oo
=K-.
H moo


(9. 10)


LLJIH ltHJIHH.n:pa C pa)J.HYCOM R H BbICOTOH Z


K= I
( ;; r+( ; r'


(9.6)


r.n:e Xo - HaHMeHblllHH KopeHb DecceJIeBoH CPYHKU,HH nepBoro po.n:a
nopH)J.Ka HYJIb, Xo = 2,4048.. n03TOMY cpopMYJIa (9.6) MO)l{eT 6bITb
npe!].cTaB
eHa TaK:


K-;::::;


1
fi,7R3 D,P7
J?2+V


(9.7)




BTOpOiJ. MeTOa peeYAJlpHOZO pe:JICUMa. JIa.U6aalwAopw<leTp 189


fJJABAIO
BTOpoff METO.D. PEfYJHIPHOfO PE)I01MA.
nAM6.D.AKAnOPHMETP


.llJlH peaJlH3aLl.HH H3J10)l{eHHorO MeToJ].a He06xoJ].HMO, npe)l{J].e Bcero.
paCnOJlaraTb TepMocTaToM - B03J].YlllHbIM HJlH ra30BbIM. B I{aqeCTBe
TaKOBoro MO)l{HO npHMeHHTb «KaMepy cnOKOr!HOrO B03J].yxa» [3]. .llJlH
pa60T npH TeMnepaTypax BbIlile KOMHaTHoil cJleJ].yeT npHMeHHTb 3J1eK-
TpHqeCKHH HarpeB. BecbMa L1.eJleC006pa3Ho nOMeCnlT
 BHYTPb KaMepbI
J].onOJlHHTeJlbHYJO L1.HJlHHJ].pHqecKYJO CTeHKY l:!3 KpacHoH MeJ].H HJlH aJlJO-
MHHHH; OHa nOBbICHT TenJlOeMKOCTb BceH YCTaHOBKH H C03J].aCT 6J1aro-
J].apH xopolileH TenJlOnpoBoJ].HOCTH MeTaJlJla ll30TepMHqecKYJO nOBepx-
HOCTb, qTO, B CBOJO OqepeJ].b, 06ecneqHTb paBHoMepHocTb TeMnepaTypbI
B03J].yxa BHYTPH KaMepbI.
.llJlH 3KcnepHMeHToB npH HH3KHX TeMnepaTypax He06xoJ].llMO no-
CTpOHTb cneLl.HaJlbHYJO KaMepy (MeHblllHx pa3MepoB), oXJla)l{J].aeMYJO



 1. nepBbIu BapHaHT MeTOJla Hero 3KcnepHMeHTaJIbHOe OCYI.I\eCTBJIeHHe
npeJ].nOJl
)I{HM, qTO nocpe)J.CTBOM nepBoro MeTOJ].a perYJlHpHOro
pe)l{HMa HaHJ].eHa TeMnepaTyponpOBO.l1.HOCTb a HcnbITblBaeMoro MaTe-
pHaJla. TorJ].a ero TenJlOnpoBOJ].HOCTb MO)l{eT 6bITb onpeJ].eJleHa nocpeJ].-
CTBOM BToporo MeTO)J.a perYJlHpHOrO pe)l{HMa, KOTOpblH 3aKJlJOqaeTCH
B cJle
YJOw.eM. nYCTb H3 3Toro MaTepHaJla H3rOTOBJleH 06pa3eIJ. onpeJ].e-
Jle
HOlf cpOpMbI H nYCTb OH OXJla)l{J].aeTCH (lfJlH HarpeBaeTcH) B ra3006pa3-
HOlf cpe)J.e npH nOCTOHI;!HbIX rpaHHqHblX YCJIOBHHX, T. e. 6 = const.
ex = const. npHMepoM TOMY MO)l{eT CJIY)I{lfTb OXJla)l{J].eHHe npe)J.BapH-
TeJl
HO HarpeToro L1.HJllfHJ].pa B Ka
epe cnoKoHHoro B03J].yxa, HaXOJ].H-
IlI.elfCH B KOMHaTe C YCTaHoBlfBlllelfcH TeMnepaTYPoH.
npe)J.nOJlO)l{HM, qTO, BBe.l{H BHYTPb 06pa3L1.a KaKOH-JlH60 H3MepH-
TeJlb TeMnepaTypbI, Mbl lf3 Ha6J1JOJ].eHHH HaJ]. XO)J.OM OXJla)l{J].eHlfH ero
HalllJlH m (CM.
 4 rJl. 8).
nplfMueHlfM Ten
pb K 3TOMY HBJleHlfJO CPOPMYJlY (4. 18) H npeJ].cTaBHM
KpIITepHlf EHO (BI) B pa3BepHYToM BHJ].e; MbI nOJlyqlfM:
}._ a.Lo 1
- 'f' (p) l
p=Lo V: J


w


<tllr 108. fOpll30HTaJJbHaH Tpy6a C BbIHY}KJ1eHHOii IlHPKYJIHUHeH
B03J1yxa J1J1H JlaM6JlaKa_
OpHMeTpa- CTpeJJKOH W YKa3aHo HanpaB'
JJeHlle B03J1YlllHoro nOTOKa


rJ].e


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(10.2)


npOH3Be)J.H, npH )J.aHHoH TeMnepaType 6, OIlbIT no OXJ1a)l{,TIeHHIO UJ1l1
HarpeBaHulO 06pa3ua B YCJ10BHHX npaKTHlIeCKH 6ecKoHelIHoro ex, KaK
pa3'bHCHeHO B rJ1. 9, MbI HaH)J.eM TeMnepaTyponpOBO)J.HOCTb MaTe-
pHaJ1a a (lIeMY cooTBeTcTByeT npaKTlilIeCKH TeMn OXJ1a)l{.n:eHHH m = moo).
- .ll.aJ1ee, npOH3Be.n:eM BTOpof! onblT C 3T11M 06pa3u,oM B YCJlOBl-!SlX KO-
HelIHoro a: H onpe)J.eJ1HM 3TO a: C I10MOlll.blO aJ1bcpaKaJ10pHMeTpa, KaK 3TO
onHCaHO HH)I{e - B rJ1. 11, nOCJ1e qero HaXO)J.HM BbIIIHCJle
UfeM napa-
MeTp M no cpopMyne


K
M=-.m
a '


(10.3)


(a.i)N = ('1)x


B npaBoH lIaCTH KOTOpOH CTOHT H3BeCTHbIe BeJ1HqHHbl (B caMOM .n:eJle, K
H3BeCTHO, a HaH,TIeHO H3 npe.n:bl)J.Ylll.ero OnblTa npH ex ---+- 00, m - H3
)J.aHHoro onblTa - npH a: = KOH
qHOMY qHCJ1Y).
3HaH M H HMeH YHHBepCaJ1bHYIO 3aBHCHMOCTb Me)l{)J.y M H H, Ta6YJ1H-
pOBaHHYIO B Ta6J1. 2, HaXO)J.HM H; a TaK KaK H, a: H L H3BeCTHbl, onpe-
.n:eJ1HeM H HCKOMblH K03cpcpHu,HeHT TenJ10npoBo.n:HOCTH
I. -
L (I() 1)


r.n:e 1) - nO.TIO)l{I-ITeJ1bHOe qHCJ10, KOTopoe OQeHb MaJ10 MeHHeTCH, Kor.n:a
U. s npHHHMaeT 3HalIeHHSI, 6J1H3KHe K B. n03TOMY )J.J1H oCYlll.eCTBJ1eHHH
YCJ10BHSI


He06xoJUfMO II .QOCT3TOlIHO. 'ITo6b1 6b1J10


ON = ox.


13 KOHJlpaTbeB 2763




Jf3MepeHUf/ U npu60pbt


BTOpOU MeTOO pezyAJlpHoeO pe
UMa JIaJ.t60aKaAOpUMeTp


195


194


T 6 2 u evol
a )!{e Ta JI. n03BOJl5IeT HalfTH c vol H C = '"1' eCJlH BOCnOJl L30-
BaTbCH KpHTepHeM qr, paccMaTpHBaH ero KaK CPYHKU.HJO M; Cvol pacclJ\1-
Tb!BaeTCH no cpopMYJle


He6pelJb If, BO-BTOPbIX, lJTO TOJllll.HHa 060JlOlJKH MaJla no cpaBHeHHJO C
HaIfMeHbllIIfM JlHHeHHblM pa3MepOM 06pa3u.a (T. e. 3TO - «TOHKaH Me-
TaJlJlHlJeCKaH» 060JlOlJKa).
Tor.na BMeCTO \ 10. 4} .nJlH A nOJlYlJaeM


W a
Cvol=T'm'


(10. 5)


A= mL (
 _ C 0 6 0 /l )
H m S'


( 10. 6)


KOTopaH HBJlHeTCH IfHalJe nepenHcaHHoH OCHOBHOH CPOPMYJlOH (4. 16)
TeopHH perYJlHpHOrO pe}l{HMa o.nHopoJiHoro H30TponHoro TeJla \1 nOJlY-
lJaeTCH H3 (4. 16) no 3aMeHe B HeH nOJlHOH TenJlOeMKOCTH TeJla C lJepe3
VCvol = Vq If no BBe.neHHH I Ha OCHOBaHHH (l0. 2).
OlJeBH.n Ho , lJTO B npaBOH lJaCTH paBeHCTBa (l0. 5) CTOHT BeJlIflJHHbl I,
a, m, H3BeCTHble H3 Onb!Ta H If3 06Mepa 06pa3u. a .


a BMeCTO (l0.5) .nJlSl C vol
C = £ = SlF ( ...::.. _ C 0 60/l )
vol 'W V nz S


(10. 7)



 4. POJIb 060JlOIJKH
DpH onpe.neJleHHH TenJlOnpoBo.nHOCTH nopoulKo06pa3Hbl>' ilia repHa-
JlOB If TenJlOH30JlHTOpOB, II MeJOllI.I-1X MaJlbIH 06'beMHbIH Bec, I1X He06xo.nHMO
3aKJlJOlJaTb B >KeCTKYJO 060JlOlJKy l . 3THM H36eraJOT HapyweHHH L1.eJlOCTII
xpyn.Koro 06pa3u.a II KOHBeKLl.HH HapY>KHOrO B03.nyxa CKB03b nopb! MaTe-
pHaJla (eCJlII 3TO - He3aMKHYTble nOPbl, lJTO lJaCTO 6bIBaeT Ha npaKTIIKe).
TenJlOeMKOCTb 060JlOlJKII B 3TIIX CJlYlJaHX 6b1BaeT HaCTOJlbKO BeJlIlKa,


cI>opMYJla (l0. 3) .nJlH BbllJHCJleHHH a OCTaeTCH 6e3 I13MeHeHHH, nOTOMY
lJTO OHa OTHOCHTCH K onbITY B YCJlOBH HX a
 00, Kor.na 060JlOlJKa Y>Ke
nepeCTaeT BJlHHTb Ha TeMn OXJla>K.neHIIH.
TeMnepa1'YPI:Joe nOJle B o6pa3u.e, 060JlOlJKe H oKPY}I{aJOllI.eH cpe.ne
npe.nCTaBJleHO Ha cpHr. 109.


-Y-.


A B M C D


x'



 5. BbIBO.n npeJlblJlYIl.\HX cfJOPMYJI
0603HalJHM lJepe3 &v H &s I136bITOlJHble TeMnepaTypbl - cpeJ],HfOJO
06'beMHYJO H cpe.nHJOJO nOBepxHocTHYIO 06pa3u.a. B CHJlY c.neJlaHHblX
Bblwe npe.nnOJlO>KeHHH 3Ta nOCJle.nHHH - Ta >Ke, lJTO H TeMnepaTypa tt o6o .ll
060JlOlJKH.
HanHweM ypaBHeHHe 3aKOHa coxpaHeHIIH 3HeprHH .nJlH 6eCKOHelJHO
MaJlOrO 'npOMe)!{YTOlJHOrO BpeMeHH B't, B TelJeHIIe KOToporo nYCTb'cpeJ],-
ilHH TeMnepaTypa TeJla &v ynaJ],eT Ha BeJllIlJIIHY Bit'll' a 060JlOlJKH
Ha' B3- o6o .ll; 3TO KOJlHlJeCTBO TenJla Bce npoH.neT B cpe.ny CKB03b nOBepx-
HOCTb S. D03TOMY
- (CB&v + Co6o.llB3-o6o.ll) = as'&O!fO.ll.B't,
. -r.ne 0: - ocpe.nHeHHblH no nOBepxHocTII S K03cpcpIlLl.I1eHT TenJlOOT.naIIH.
n n 3 s .
3aMeTHM, lJTO U'o60.. = U's H lJTO BeJlIllJHHa r = 'Ii" - CM. (4. 17) -
v .
He 3aBHCIfT OT BpeMeHIf 't; 3aMeHHM B npe.nbl.nYllI.eM paBeHCTBe B3- o6o .ll
1
lJepe3 W s II B&v lJepe3 \iT . B3-s; nOJlYlJHM
(
 + C 060 .ll) B&s = -o:S. &s' B't.


c r1


8


ABdIi
<!JHr. 109. TeJlo (TBepJ\oe, nopHcToe HJJH nopolllKoo6pa3Hoe) B }KeCTKOii MCTaJ1JII\'IeCKOH
HJlH TenJlOH30mlIJ.HOHHOii TOHKOH 060JlO'lKe H pacnpcJ\eJleHHe TeMnepaTYP BJ10JIb ero ce'le-
HHH XX'; A, B, M, C, D - TOlJKH B TeJle H B 060JlO'lKC; abmed - TeMnepaTypHaH
KpHBaH.


lJTO npeHe6pe>KeHIIe ee BJlHHHIIeM He.nOnYCTIIMO; npe.nbl.nYllI.I1e paClJeT-
Hble CPOPMYJlb! .nOJl>KHbl 6bITb 3aMeHeHbi HOBbIMH, K KOTOpblM Mbl CeHlJaC
H nepeH.neM.
0603HalJHM CHMBOJlOM C o6o .ll nOJlHYJO TenJlOeMKOCTb 060JlOlJKII II npe.n-
nOJlO}l{HM, BO-nepBblX, lJTO rpa.nIleHTOM TeMnepaTypbl BHYTPII 060JlOlJKH
no cpaBHeHIIJO C rpa.nHeHTaMH TeMnepaTypb! BHYTPH 06pa3u.a MO}l{HO npe-


JcnOMHHM, lJTO B CHJlY OCHOBHoro cBoiIcTBa perYJlHpHOrO pe>KHMa
(,&8
-=-m
&st. '


KaK 3TO CJle.nyeT "3 cpopMYJI (4.9), (4. 10), (4. II) nocJle HX .nHcppepeH-
llHpoBaHHH no 't; Tor.na npe.nweCTBYlOllI.aH cpopMYJIa o6paTHTcH B
m (
 + C 060 ..) = as. (lO.
)


1 CJIe.nyer OTMeTHTb, lJTO TaKoro pOJ\a BblcoKo34>cpeKTHI;Hble nopHcTble l
IIJtuH.iU'
.IlHTOpbl C MaJJblM 061>eMHblM BeCOM Haxo.nHT Bce 60J1bWee pacnponpaHeHHe B TCXHHKe.


13-




196


Jf3MepeHUR U npU60pbt


BTOpOi1 MeTOa peeYAflpHOZO pe:HCUMa Jlal>16aaKaAOpUJ.Ip.Tp


197


npOCTOe ee npe06p330B3H1-1e, nOLITH OLleBHJ!.Hoe, IIPHBOJ!.Hl K qJOpMYJle
(10. 7), 3 H3 :;nOH nOCJleJ!.HeH nOJlYLIaeTCH H <POPMYJl3 (10. 6) J!.JlH p3cLleTa)..,
CJleJ!.YIOllI.HM nYTeM.
A
B (10. 7) 33MeHHeM c vol Llepe3 a' a - TeMnepaTyponpoBoJ!.HOCTb a
Llepe3 Km//vI B CHJlY onpeJ!.eJleHIiH KpHTepHH /vI, J!.aHHoro <POPMYJlOH
(4.20), H npHXOJ!.I-IM K paBeHcTBY
)..,= Km .
 (
 _ C U 60A )
M I m S .


TO


K = 0,935.10- 4 .M 2 H L = i = 0,955.10- 2 .M.


no <popMYJle (10.3) H3XOJ!.HM
O,93f'
M= 575.1,15 = 0,187.
,


K
3aMeHI-IB T Llepe3 L 1-1 'IJ!//vI Llepe3 l/H nOJlYLlHM paBeHcTBo (10.6).
flpuMep 26. OnpeJ!.eJlHIOTCH TenJlOBble K03<P<1mu,HeHTbl XHMHLleCKH
LlHCToro H3<pT3J1HHa npl-l TeMnep3Type 20°. H3<pT3J1HH, H3MeJlbLleHHblH
B TOHKHH OJ!.HOpOJ!.HblH nopollloK, H3CbmaH B Jl3TYHHblH U,HJlHHJ!.P, BHY-
TpeHHHe pa3Mepbl KOToporo: BblCOTa Zl = 10,00 CM, J!.H3MeTp Dl =
= 4.88 CM. KOHcTaHT3 060JlOLIKH BblLlHCJleH3 Ha OCHOB3HHH J!.3HHbIX ee
B3BelllHBaHHH H 06Mepa ee HapY>KHOH nOBepXHOCTH S H HaMJ!.eH3 paB-
HOH


no Ta6J1. 6, 3HaH M, HaXOJ!.HM H = 0,22, <popMYJla >Ke (l0. 6) J!.3eT


A - 1,15.0,955.10- 2 ( 3,75 _ ° 761 ) = ° 125
- 0,22 1,15' ,.


C-

OA =0,761KlwA M- 2 "paa-1,


no TOM >Ke Ta6J1Hue 3HaH M = 0,187, HaXOJ!.HM 'If == 0,856 H no
<popMYJle (10. 7) onpeJ!.eJlHeM
. 0,856
c vol = 0,98 .2,5.100=218


H OTCIOJ!.3 YJ!.eJlbH3H TenJlOeMKOCTb (He 3aBHCSlllI. 3 H OT 06'beMHOra BeC3)


npHHHM3H C JlaTYHH paBHoH 0,092 KKaA &-1 i'paa- I .
OJlOTHOCTb nopolllK3 Ha<pTaJlHHa 'I = 727,5 Ki'M- 3 .
OpH TaKOM 'I H3 onblTa HaJ!. OXJla>KJ!.eHHeM B3HTOH np06bl nopOlllK3
HaqrraJlHHa B YCJlOBHHX ex -+- 00 nOJlYLleH3 era TeMnepaTyponpoBoJ!.-
HOCTb:


218
C = 727,5 = 0,3.


a = 5,75.1O- 4 M 2 "ac- 1 .



ha uH<ppa C TOLIHOCTblO J!.O 1 % COBn3J!.aeT C JlHTepaTypHblMH J!.3HHbIMH,
nOJlYLleHHbIMH cOBepllleHHo HHblM MeTOJ!.OM.
Pa30op3HHblil npHMep 6blJl' H3MH B3HT H3 pSlJ!.3 MHOrOLlHCJleHHblX
OnblTOB J!.JlH HJlJlIOCTp3U,HH Toro, LITO MeTOJ!.HK3 n03BOJlHeT nOJlytJnTb
XOPOlllYIO TOLIHOCTb, npHLIeM OJ!.HOBpeMeHHO H3 J!.BYX OnblTOB onpelle-
JlHIOTCH 06a K03qxpnu,ueHTa: a H A HJlH a H c.
BJlHHHHe 060JlOLIKH. B npoueHTHoM OTHOllleHUH, MO>KeT 6bITb Ha-
rJlSlJ!.HO OX3p3KTepH30BaHo, CCJlH <POPMYJlY (10.8) nepemlcaTb B BHJ!.e


D.aJlee npoH3BoJ!.HM onblT HaJ!. ero OXJl3>KJ!.eHHeM B K3Mepe cnoKoii:-
Horo B03J!.yxa, npHLIeM H3MepeH K03cpq:muHeHT TenJlOOTJ!.aLlH
cx= 3,75 KiWA M- 2 1.LUc- 1 epaa- 1 ,
BblLlHCJlHM C nOMOllI.blO KpHTepHeB M H H H YHHBepCaJlbHOM CBH3H
Me>K.n.y HHMH TenJlOeMKOCTb C H TenJlOnpoBoJ!.HOCTb A, YLI, HTbIBaH LITO
OnblT B B03J!.yxe J!.aJl m = 1,15 '-lac-I.
npe>KJ!.e Bcero BblLlHCJlHeM b H t. H3 OCHOB3HHI1 J!.aHHbIX 06Mepa
HMeeM:


mC I m C 0 60A
a<j>S = -
'-S


(10.9)


1
K


'Jt2
Z2

1


5,783
R



9,87
100


5,783
_ I,m (' ,,-2,
5,96


CneJ!.OB3TeJlbHO, 6e3p33MepHaH BeJlHLlHHa : . C
OA X3p3KTepH3yeT
OlllH6KY, KOTopaH npOHCXOJ!.HT, eCJlH npeHe6peLib pOJlblO 060JlOLlKH;
H J!.eHCTBHTeJlbHO, eCJlH OHa paBHa HYJlIO, <POPMYJl3 (10.9) 06pallI.aeTCH
B OCHOBHYIO CPOPMYJlY, Bblpa>K31OllI.YIO TeMn perYJlHpHOrO OXJl3>KlleHHH
Toro >Ke TeJl3, HO 6e3 060JlOLIKH.
ECJlH B npHBeJ!.eHHOM Bblwe npl-lMepe He npHHHM3Tb B pacLieT 060-
JlOLlKY, TO Ollll-l6K3 COCT3BHJl3 6bl

:

 .O,7l>l,IUUo" = 2J,3° v .


t _
 _ 7tR
Z] _ Rl 1
- S - 2'1tR]Z] +2'1tRi - 2' I +R]/Zl


HJlH


I
t = 1,22 1 + 0,244 ' 10- 2 M = 0,98.M' 1O- 2 .M.


TaK KaK




198


Jf311lepeHUR u npu60pbl


B .n:PyrHx CJlY4aHX OHa MO}j(eT .n:OX0.AHTb .AO 40-50%; Hao6opoT,
HMeH .n:eJlo C nJlOTHblMH MaTepHaJlaMH (60Jlb1llOe 1), MO}j(HO elO npeHe-
6pe%.


rnABA 11


onPE.lI.EJ1EHI1E K03<J><J>l1l1.I1EHTOB TEnJ100T.lI.A411.
AJ1b<J>AKAJ10PI1METPW


, j.
_' CI{/
{.o :'j1


! t"

:
h


f
...\'t8.

C.'
'
Q
,
:.

-:
t
ft_



<lJHr. 110. LLHJlHH.npH'IecKHii JlaM6J13K3JIOpHMeTp:
N - UHJlHH.lp H3 MeT8..na C H3BeCTHoA TenJlOeMKOCTbIQ ('If <::< I); X - o6pa3eu HCCJleJ1yeMoro M8TepH8J18
B DH.:te O.D.HH3KOBoro no BHeWHHM pa3MepaM C N UHJlHH1I.pa MJlH >KeCTK3H MeT3nnW..leCK3H 060JlOq:K3
BHYTPb KOTOpOH nOMell!eH HCCJleJ1yeMbJH M8TepH8J1. '



 1. Koacl)(lmu.weHTbl TenJlOOT)laQI1 KOHBeKu.l1eH 11 113J1YQeHl1eM


)\


N


Dpe}j(.n: e 4eM nepeXO)lHTb K MeTO)laM onpe.AeJleHHH KOacpqmuHeHTOB
TenJlOOT)laqH, HanOMHHM, 4TO TenJlOBaH :meprHH nepe)laeTCH B cpe.n:y
TpeMf! npHHIJ.HnHaJlbHO pa3J1H4HbIMH nYTHMH: KOHBeKTHBHbIM, KOH.n:YK-
THBHblM H JlY4eHCnYCKaHHeM (rJl. 1). KaK npaBHJlO, Bce TPH npo
ecca
OCYl.lleCTBJlHIOTCH o.n:HOBpeMeHHO, HO B pa3HblX CJlY4a
x Y)leJlbHbIH Bec
HX pa3J1H4eH. HanpHMep, TeJlO, HarpeTOe .AO BblCOKOH TeMnepaTypbl H
HaXO)lHl.lleeCH B ra30BOH cpe)le, B OCHOBHOM OT.AaeT TenJlO JlyqeHcnYCKa-
HHeM. To }j(e TeJlO B }j(H.AKOH cpe.Ae OT.n:aeT TenJlO 3a C4eT KOHBeKIJ.HH H
KOH.AYKIJ.HH. B o6061.lleHHbIX cpopMYJlaX THna (I. 8)-(1. 12), 0 KOTOpblX
pe4b IllJla B nepBOH rJlaBe, Y4HTbIBalOTCH TOJlbKO )lBa" MexaH
3Ma nepe-
Hoca TenJla - KOHBeKTHBHblH H KOH.n:YKTHBHbIH. HaH.AeHHbIH no 3THM
cpopMYJlaM K03cpcpHIJ.HeHT TenJlOOTJI,a4H npHHHTo Ha3bIBaTb KOHBeKTHB-
HblM KoacpcpHIJ.HeHTOM TenJlOOTJI,aqH (a:,,). Ta 4aCTb 3HeprHH, KOTopaH
nepeHocHTcH JlY4eHcnycKaHHeM C eJI,HHHIJ.bI nJlOl.lla.n:H B e.n:HHHuy BpeMeHH
npH pa3HocTH TeMnepaTYP Me}j(JI,Y nOBepxHocTblO TeJla H cpe.n: oH , paB-
HOH OJI,HOMY rpaJI,Ycy, eCTb TaK Ha3bIBaeMblH Ko3cj)cpHUHeHT TenJlOOTJI,a4H
JlyqeHcnycKaHHeM (a: ...). CYMMa 3Toro K03cpcpHIJ.HeHTa TenJlOOT.n:aqH H
_KOHBeKTHBHoro K03cpcpHUHeHTa (a: K) Ha3bIBaeTCH nOJlHblM K03<pcjJHIJ.HeHTOM
TenJlOOTJI,a4H


DpHMeHHBIllHeCH HaMH B OnblTe npHMepa KaJlOpHMeTpbI npe.n:cTaBJleHbI
Ha <PHr. 110: N - JI,JlH onpe)leJleHHH a: - H3 JlaTYHH H X - JlaM6.n:a-
KaJlOpHMeTp, B KOTOpblH HaCDmaJlCH Ha<pTaJlHH.


* *


*


11: npe.n:blJI,Yl.llero MbI BHJI,HM, KaKHe IllHpOKHe nepcneKTHBbI Hcnbl'
TaRIm pa3J1H4Hb1X no cpopMe H no MaTepHaJlY 06pa3IJ.OB OTKpblBaIOT KPH'
TepHaJlbHbIe BeJlU4HHbl M H H.
D.JlH onpeJI,eJleHHH a:... MO}j(HO, npH MaJlblX pa3HOCTHX u -11 BOCnOJlb-
30BaTbCH <POPMYJlOH II. 19), a Heo6xo).\HMble 3Ha4eHHH :oa<PCPHUHeHTa
H3J1Y4eHHH C B3HTb H3 Ta6J1. I. ECJ1H TeMnepaTypbl Us H 8 3Haq!I-
TeJlbHO OTJlH4alOTCH .n:Pyr OT .n:Pyra, CJleJI,yeT HCXOJI,HTb H3 OCHOBHOH
<POPMYJlbI (I. 16) H BeCTH paC4eT no cxeMe, no).\po6HO H3JIO}j(eHHOH B
npHMepe 18
 I rJl. 6, npHMeHHH <POp MYJI bl (6.3) H (6.4); 3aMeTHM,
KCTaTH, 4TO «cpaKTop» f Ta6YJlHpOBaH. 3JI,eCb no.n: T H T CJle.n:yeT nOHH-
MaTb Ul + 273,2 H 8 + 273,2. 0


a: = rJ. K + 0:....


CMblCJI ero 6blJl H3MH paCKpblT paHee - B rJl. I.
3KcnepHMeHTaJlbHble HCCJle){OBaHHH 4aCTO CTaBHT TaK, 4TO onpe,ne-
JlHeTCH I1MeHHO 3TOT nOJlHblH HJlH cYMMapHblH Koacp<pHIJ.HeHT TenJlOOT-
JI,a4H [2, 19], a n03ToMY HCKOMue 7. K nOJlY4alOT KaK


a: K = a: - a:....


B TOM cJlyqae, eCJlH BeJlH4HHa C .n:JlH .n:aHHoH nOBepxHocTH HeH3B


CTHa. ee Heo6xo)lHMO onpeJ1.eJlHTb 3KcnepHMeHTaJlbHblM nYTeM; npocTolf
MeTO)\ onHCaH a MOHorpaqJHH alHUpa [3 J.




200


113.\lepeHU!1 u npU60pbl


DnpeiJeAeHue K03cpcplll(UeHTOB TenAooToa'tu. A AbcpaKa_10pU.MeTpbl


201



 2. OnpeJl,eJleHHe KoaqJljJHIJ,HeHTa TenJioOTJI,alJH nO MeTO)l.y
CTalJ,HoHapHoro TenJlOBOrO pe*HMa
Cnoc06bI H3M.epeHlHI K03cpcpm.{HeHTa TenJIOOT.l(aqH no MeTO.l(Y CTaUHO- '
HapHoro TenJIOBoro pe)KHMa BeCbMa pa3Ho06pa3Hbl H Bbl60p cnoc06a
onpe.l(eJ15JeTC5I B l(a)K.l(OM OT.l(eJIbHOM cJIyqae KOHKpeTHoH 06CTaHOBKoH
OnblTa.
003TOMY 3.l(eCb orpallHql1MC5I pacCMoTpeHHeM TOJIbKO npHHUHna
MeTO.l(a.
Ha OCHOBaHHH 3aKOHa HblOTOH3 (I. 14) MOIl{HOCTb, paCCe5lHlIa51
TeJIOM B }fUJ.l(KYIO HJIH ra3006pa3HYlO cpe.l(Y, on pe.l(eJI 51 eTCH CJIe.l(YIOIl{HM
06pa30M:


MOlll.HOCTb B HarpeBaTeJIe, .l(06HBaTbC5I pa3JIHqHbiX 3HaqeHHH TeMne:
paTypbl Ha nOBepXHOCTH HCCJIe.l(yeMoro 06beKTa. OpH 3TOM Ha.l(O Ka)K.l(bIH
pa3 .l(O)KH.l(aTbOI HaCTynJIeHH5I CTaUHOHapHoro pe)KHMa H TOr.l(a Y)Ke


5


P = (J. (ts- 6)S,
r.l(e (c; H B - TeMnepaTypbl nOBepXHOCTH TeJIa H Cpe.l(bl.
OTCIO.l(a IIOJIyqaeM ,g.n51 K03tpcpliUMeHTa TenJIOOT,gaqII Bblpa)heHMe
p
0: = S (t s - Ii) . (I I. I)
TaKHM 06pa30M, .'I.JI5J onpe,geJIellllH K03lpqHIlJJleHTa TenJIOOT,gaqM no
CTaUMOHapHOMY MeTO,gy Heo6xo){tlMO: ]) ,gO)K,gaTbCH HaCTvnJIeHH5I B TeJIe
naUHOHapHoro pe)KHMa; 2) H3MepHTb nOJIHYIO MOIl{HOCTb P, pacceH-
BacMYIO TeJIOM; 3) H3MepHTb pacnpe,geJIeHl1e Tel\mepa-ryp Ha nOBepx-
II0CTH t s (xs. lJs, zs) H TeMnepaTYPY BHemHeti cpe,!{bl B, a TaKllie 3HaTb
nOJIHYIO TenJIOoT,gaIOIl{YIO nOBepxHocTb TeJIa S.
MeTo,gbl H3MepeHH5J MOIl{HOCTH P BeCbMa pa3Ho06pa3Hbi H onpe,ge-
.'{eJI5JIOTC5I KOHKpeTHoH 3 a,'{a1lei,'j H 06CTaHoBKoi-i onblTa. HanpHMep,
flpM H3yqeHHH TenJIOOT,gaqH TPy6bl IlJIM wapa on bIT MOlliHO nOCTaBHTb TaK.
Ha MeTaJIJIHqeCKOH TPy6e (mape) COOTBeTCTBYIOW,HX pa3MepOB MOHTH-
PyeT':51 BHYTPH TeJIa 3JIeKTpOHarpeBaTeJIb, a Ha nOBepXHOCTH 3a,geJIbl-
BaIOTC5I -repMonapbl, KaK 3TO nOKa3aHO Ha cpMr. III H 112. MOW,HOCTb
p
cceHBaeMa51 Tpy60H (wapoM) B cTauHoHapHoM pe)KHMe, paBHa MOW,

1I0
TH, Bbl,geJIHBWeHC5I B 3.1]eKTpOHarpeBaTeJIe, H MOllieT 6bITb JIerKO 3aMe-
reHa C nOMOll{blO 3JIeKTpOH3MepHTeJIbHbiX npM60pOB. TeMnepaTYPbl
B pa3HbIX TOqKaX nOBepXHOCTM B 061l{eM CJIyqae MorYT 6bITb pa3-
.'mqHbI If MX 3aMep5J1OT C nOMow,blO Cepl1lf TepMonap H 3aTeM 6ePYT
Cpe.l(Hee 3HaqeHHe TeMnepaTypbl nOBepXHOCTH


u


6


A


7


6



"r. 111. nplinUHnHaJlbH:
H cxeMa OnblTHOii YCTaHoBKH .nJlH H3YlJeHHH TenJlOOTJ1a'lH
B YCJIOBHHX eCTccTBCHHOH KOHBeKUHH (no cTaulioHapHoMY neplioJ1Y):
. J - 06UlHH xonOllHblH TepMocnaii C 3KpaHO'M npOTHB pallH3UHH; 2- ..rop.Hlme" cnaH llmpcpepeHUHanhHhl.x
TepMonap; 3 - raJlbB3HOMeTp; 4 - 9J1eKTpnlJeCKHH HarpeB8Tenb; 5 - HcnblTblBaeMblH 06"bCKr; 6 - BOJ1LT-
MeTp H a
mepMeTp; 7 - peocTaT.


npOH3Bo,gHTb
TenJIOOT,ga qH
H TPY.l(OeMKH,


Heo6xo,!{HMble 113MepeHH5I. 003TOMY OnblTbl no l!3yqeHHIO
MeTo,gOM CTaUHOHapHoro pe)KHMa BeCbMa ,gJIHTeJIbHbl
TaK KaK CTaUHOHapHblti pe)KHM HacTynaeT Me,gJIeHHO.


n
t s = *
 tSI'
i=]


EJ


3


3,geCb qepe3 Il 0603HaqeHO' qHCJIO MOHTIfpOBaHHblX Ha nOBepXHOCTH S
TerMonap.
TaKIfM 06pa30M, K03cpcpHUHeIlT TenJIOOT,gaqH, HaH,geHHbIll no cpopMYJle
(II. I), TaK)Ke 51BJI5JeTC5I ocpe,gHeHHbIM.
LIJI5I Toro qTo6bI CH5ITb no VKa3aHHOMV 3JH:'Ch MPTOflV
:'IRH('nMO(,T""
hUoI'lx!J;lUHeHra le1lJIUOrA341i or TeMnepaTYP t
 11 U, CJIe,gyeT, MeH5IH


ct>IiL 112. 3JIeKTpoKa.lOpHMeTp M. n. CTaueHKo .nJlH onpeJ1eJleHIIH K03:pct>lIlllieHTa TenJIO-
OTJ1alJli llIapa no cTaUHoHapHoMY MeTo.ny:
1- CnHpaJlb H3 HHXpOMOBOI! npOBOJlOKH; 2 - <j>ap<j>opoBhle rpy60'lKH; 3 - repMonapa


HanpHMep, Jl,JI5I Tpy6bl ,'{IWMeTpOM B 30 MM cTaUHoHapHblH pe)KHM
naCTynaeT B YCJIOBH5JX eCTecTBeHHoll KOHBeKUHH Qepe3 1,5-2 Qac:'I.
LIJI5I Toro QT06bl CHHTb 3aBHCHMOCTb K03cpcpHUHeHTa TenJIOOT,gaQH 3TOll
Trynhl OT TPMl1pr:'lTyr,..,I R TfI-fTPrR:'I.IJP TPMI1PP:'ITYP 20-C)()O° C, nOTpp-
6yeTCH HeCI\OJIbKO AHell. KpoMe TOro, Tpe6yeTc5I nOWOTaBJIHBaTb Ka)K-




OnpeaeAeHue KOacpcpU/{UeHTOB TenAOOTaa'lU. A AbcpaKaAOpUMeTpbl


203


202


H3MepeHUJl U npu60pbl



blH pa3 CneUlIaJIbHblH 06pa3eU (MOHTa:>K HarpeBaTeJIH), qTO TPY
HO
BbInOJIHIITb
JIH 06'beKTOB He60JIbllllIX pa3MepOB.
OplI IICCJIe
OBaHIIHX BbIHY:>K
eHHOH KOHBeKUlI1I B CJIyqaHX IIHTeHCIIB-
HOro TenJIo06MeHa TeJIa co cpe
OH, a TaK:>Ke nplI 1I3MepeHlIlI K03qxplI-
UlIeHTa TenJIOOT
aqlI B CJIyqaHX KlIneHIIH :>K1I
KOCTII, KOH
eHcaUHII napOB
MeTO
 CTaulIOHapHoro pe:>KIIMa HBJIHeTCH nOKa He3aMeHIIMbIM. OplIHUlIn
onpe
eJIeHIIH K03cpcplIUlIeHTa TenJIOOT
aqlI B 3TOM CJIyqae TOT :>Ke, TOJIbKO
MeTO
bl 1I3MepeHlIH pacxo
a TenJIa 3a e
IIHIIUY BpeMeHII !:L= P MorYT
't
6blTb IIHblMII II onpe
eJIHlOTCH KOHKpeTHOH 3a
aqeH. 3TH MeTO
bl cpaB-
HIITeJIbHO XOpOlllO pa3pa60TaHbi II 1I3JIO:>KeHbl B CneUHaJIbHOH JIIITe-
paType [2 I, [171.


a 3aTeM HaXO
HT IICKOMoe ex no cpopMYJIe (4. 20), KOTOpylO MO:>KHO
3anlIcaTb B cJIe
YK>lUeM BII
e:
ex=A ;'K H, (11.2)


r
e A - 1I3BecTHblH K03cpcplIulIeHT TenJIOnpOBO
HOCTH Belll.eCTBa TeJIa;
V, SIlK - 06'beM. TenJIOOT
alOlUaH nOBepXHOCTb II K03CPCP!1U lIeHT
cpOpMbl TeJIa, TaK:>Ke 1I3BeCTHble; H - 0606lUeHHblH KplITeplI1I OliO,
KOTOpblH onpe
eJIHeTCH 1I3 Ta6JI. 2, CqlITaH, qTO BeJIlIqlIHa


K
M=m-
a


(11. 3)


1I3BeCTfIa .
O-i-clO,lta BbiTeKaeT, qTO B03MO:>KHO onpe
eJIIITb K03qxplIUlIeHT TenJIO-
OT
aqlI
JIH 06'beKTOB KaK npoCToH, TaK II CJIO:>KHOH cpOPMbl.
PaCqeTHaH cpopMYJIa (11. 2) ynpolUaeTCH, eCJIII npe
nOJIO:>KIITb, qTO
BO Bee BpeMH OnbITa pacnpe
eJIeHlIe TeMnepaTYP B TeJIe paBHOMepHoe,
T. e. 11' = I II, CJIe
OBaTeJIbHO, M = H. Tor
a CPOPMYJIY (11. 2) MO:>KHO
npe06pa30BaTb K cJIe,ltylOlUeMY BII
Y:
C
a=nl s '



 3. Onpe
eJleHHe KoaljJljJHuHeHTa TenJIOOT
aqH no MeTo
y perYJlSlpHoro
TenJlOBOrO pe}\{HMa


ex BbITeKaeT Henocpe
cTBeHHo lI3
CJI e
y lOlUeM.
1-13 MaTeplIaJIa l TepMlIqe-
CKlIe K03cpcplIUlIeHTbi KOToporo
lI3BeCTHbl, 1I3rOTOBJIHeTCH TeJIO
C HaPY:>KHOH nOBepxHocTblO,
KonlIPYlOlUeH nOBepxHocTb
06'beKTa, TenJIOOT
aqy KOTO-
poro Tpe6yeTcH onpe
eJIIITb.
BHYTPb 3Toro TeJIa 3aKJIa,ltbl-
BalOT
lIcpcpepeHUlIaJIbHYlO Tep-
Monapy no cxeMe cplIL 113:
O
IIH cnaii N
HcpcpepeHUlIaJIb-
1I0i'1 TepMonapbl BbIBe,lteH Ha-
PY:>KY,
PyroH M YKpenJIeH B
KaKoH-HH6v
b TOqKe TeJIa.
TaKaH KOM6lIHaUlIH - TeJIO
IlJIlOC raJIbBaHOMeTp nJIlOC Tep-
Monapa -COCTaBJIHeT nplI60p,
KOTOPOMY MO:>KHO nplICBolITb
Ha3BaHlIe aJIbcpaKaJIOplIMeTpa,
TaK KaK nOCpe,ltCTBOM Hero
onpe
eJIHeTCH ex (aJII4>a). OplI
onpe
eJIeHIIH K03cpcpHUHeHTa
TenJIOOT
aqH TenJIOqYBCTBH-
TeJIbHYIO qaCTb npH60pa no-
rpY:>KalOT B cpe,lty. nplIqeM B MOMeHT norpY:>KeHHH 3Ta qaCTb, HMeeT
TeMnepaTYPY, OTJIHqalOlUYIOCH OT TeMnepaTypbl e cpe
b1; Ha6JIlO
aH
113MeHeHHe nOKa3aHlIH raJIhBaHOMeTpa C TE'qeHIIPM RPPMPHI-I, OnpelIeJlHlOT
T
Mn HarpeBaHlIH lIJIH o
JIa:>K.AeHHH, l\aK onJ-icaj-Io B1>lllle B
 4 rJI.
,


H
eH MeTO
HKH onpe
eJIeHIIH
CPOPMYJIbl (4.20) H 3aKJIlOqaeTCH B
,-----------
7
I


2


'---- ----_ ___J


<PilL 113. npliHUUnHaJIbHaH cxeMa OnblTHOii
YCTaHoBKH l\JlH onpeJ1eJIeHHH KO
HUH
HTa
TenJlOOTJ1alJli no MeTOJ1Y perYJlHpHOrO pe>KilMa
B YCJlOBilHX eCTecTBeHHoii KOHBeKUlfil:
1- aJlb<»aKaJlOpIlMeTp; 1- (M) .rap""HH. TepMocnal!
B Tene 3J1bq.w.tia.'JOpHMeTpa; 3 - llIapHK H3 B8TbI. OKpy-
)f{aIOlUHH .XO.1l011HbIH" en3.. f..: OT c
'IYl.J.aAHblx BO
llYIllHbIX
nOTOKOB; 4
 3JUOMHHHe03.n q:.onbra K3K 9KpaH npOTHB
pallHaUHH; [} - raJibBaHOMeTp; fi - llH<»<l>epeHUHaJlbHa"
TepMonapa; 7 - KaMepa cnoKOHHoro B03llyxa.


(11. 4)


r,lte C - nOJIHaH TenJIOeMKOCTb TeJIa.
PeaJIbHO OCYlUeCTBIITb YCJIOBHe paBHOMepHOCTH TeMnepaTypHOrO
nOJIH B TeJIe MO:>KHO, H3rOTOBJIHH 06'beKT lI3 MeTaJIJIa. B 3TOM CJIyqae

a:>Ke nplI K03cpcpnUlIeHTaX TenJIOOT
aqH nOpH
Ka COTeH TeXHlIqeCKHX
e
IIHIIU BeJIlIqHH3 qr 6JIlI3Ka K 1. .
MCTO,lt perYJIHpHOrO pe:>KIIMa MO:>KeT 6bITb nplIMeHeH
JIH onpe-
'
eJIeHIIH K03cpcpHUHeHTa TenJIOOT
aq<j npH C06JIlO
eHHH cJIe
YlOlUlIx
'YCJIOBHi.L u u u
I. TeJIo
OJI:>KHO BOIITII B perYJIHpHbllf TenJIOBOH pe)KIIM.
ECJIII TeJIO IIMeeT TaKYlO reOMeTplIqecK)'lO CPOPMY, qTO O
HII qaCTII
TeJIa conpHKacalOTcH C
PyrIIMH no He60JIblllOH nJIOlUa
lI... TO TaKoe TeJIO
B ueJIOM OqeHb
OJIro He 6y
eT BxOAHTb B perYJIHpHbllf pe:>KHM, XOTH
nplI 3TOM 6y
eT Ha6JIlO
aTbCH perYJIHpHblH pe:>KIIM B OT
eJIbHbIX qaCTHX
TeJIa, CBH3aHHbiX Me:>K
Y C060H He60JIbllllIMlI MOCTlIKaMII. OplIMepaMII
TaKIIX reOMeTplIqeCKIIX cpOpM MorYT CJIY:>KIITb TlInbl raHTeJIII (
Ba mapa
coe
IIHetlbl TOHKIIM U.IIJIIIH
pOM), TPy6a C nJIaCTIIHqaTblMII
IICKaMII (TlIn
pa

!3TOpa) II
PYrIIe no
06Hble TeJIa - cplIL 114. B paccMaTplIBaeMblx
CJIyqaHX O
HO lI3 TeJI HaqlIHaeT BeCTII ce6H B TenJIOBOM OTHomeHlI1I Ka

CIICTeMa nOqTII caMOCTOHTeJIbHblX TeJI. TaK KaK TPY
HO
aTb 061l1.1I1I
nplIeM oueHKII nOBe,lteHIIH TaKIIX qpe3MepHo CJIO:>KHbIX B reoMeTplIqeCKOM
OTHomeHHII TeJI - Be
YT JIll OHII ce6H KaK OT
eJIbHble TeJIa IIJIII KaK
O
HO u.eJIoe TeJIO, - TO 6y
eT npaBIIJIbHee He nplIMeHHTb MeT.o
a pery-
JIHpHOrO pe:>KIIMa
JIH onpe
eJIeHlIH K03qxplIUlIeHTa TenJIOOT
aqlI TaKIIX
06'beKToB.
2. Opll O'T£'lIh nOJIlJIlIIIx 3na'IelllfHX
 MeTn,\ ero nnre,\p!IPHJH! nn
perYJIHpHoMY pe:>KlI MY MaJIO nplIrO,l\eH.




204


H3MepeHll!l u nPIIOOpbl


OnpeoeAeHUe KOacpcpul{UeHTOB TenAOOToa'lU. AAbcpaKaAOpUMeTpbl


205


<DHL 1.14. npliMepbI TeJl H cHcTeM, pery.
JlHpHblli pe}KIIM KOTOpblX npaKTHlJecKH neJ10-
CTH>KIiM; HX OTJ1eJIbHble 4aCTH oXJla>KJ1<1IOTCH
nOlJTH He3aBliCliMO OJ1Ha OT J1pyroiL


LI = L 2 = 3,15.10- 2 M;


vl3JIO>KeHHblii B 3TOM naparpacpe MeTo,[t onpe
eJIeHlHI K03cpcplJLU-1eHTa
TenJIOOT
aqlJ, HecMoTpH ea CBOlO YHlJBepCaJIbHOCTb, B O
HOM OTHOllle-
HlJlJ HBJIHeTCH OrpaHlJqeHHbIM:. lJM He yqHTbIBaeTCH 3aBHClJMOCTb c: OT
pa3HOCTH TeMnepaTYP nOBepXHOCTlJ TeJIa lJ cpe
w, TaK KaK O
HOlJ lJ3
OCHOBHblX npe
nOCblJIOK TeOpHlJ perYJIHpHOrO TenJIOBOrO pe>KlJMa
HBJIHeTCH 3aKOH HblOTOHa, T. e. nOCTOHHCTBa 0:.



 4. MeTO.ll. onpe.ll.eJIeHlJSI 3aBHcHMoCTH KoaljJljJHQHeHTa TenJlOOT.lI.alJH
OT reMriep
lTypbl, oCHoBaHHblH Ha 3aKoHoMepHocTSIX HecTaQHoHapHoro
pe)l{MMa
ECJIlI npe
nOJIO>KeHIie 0 He3aBIiCIiMOCTM K03cpcpIiILIieHTa TenJlOOT
aqIi
OT TeMnepaTypbI
JlH
aHHoH KOHKpeTHoH 06cTaHoBKIi OnblTa onpaB
bl-
BaeTCH, TO npH 06pa60TKe KpIiBOH OX- a)
JIa>K
eHIiH TeJIa B nOJlYJIOrapIicpMlJqeCKIiX tn

KOOp
IiHaTax I


In (u - 8) = t ('t)


(11,5)


3TOT BbIBO
 HBJlHeTCH CJIe
CTBlJeM aCIiMnTOTIiqeCKOrO xapaKTepa
3aBIiCIiMOCTIi m = f (0:) (CM.
 5 fJI. 4): npIi 60JIblllIiX 3HaqeHIiHX K03cp-
cplJILIieHTa TenJlOOT
aqIi .lI.aJIbHeHlllee ero YBeJIlJqeHIie npaKTIiqeCKlJ He
BJIlJHeT Ha onpe
eJIHeMYlO Ii3 OnblTa BeJllJqlJHY TeMna OXJIa>K
eHIiH m.
OCTaeTCH pelilIiTb Bonpoc, KaKIie 3HaqeHIiH K03qxpIil.J:IieHTa TenJIO-
OT
aqIi CJIe
yeT CqIiTaTb «60JIblllIiMlJ». OTBeT Ha 3TOT Bonpoc
aeT 3aBIi-
CIiMOCTb (4. 23) Me>K
Y KpIiTeplJHMlJ M Ii H. 1'13 Ta6JI. 2 BIi
HO, qTO ,[to
3HaqeHIiI1 H nopH
Ka 10-]5 KpIiTepHH M elll.e 3aMeTHO YBeJllJqIiBaeTCH.
OTclO
a npIi H < I 0 MeTO
 pe-
e rYJIHpHOrO pe>KIiM'a ewe MO>KHO
\\\\\\\. \,\\\,,\\\) npIiMeHHTb
JIH onpe
eJIeHIiH
K03cpcpHILIieHTa TenJlOOT
aqIi. Pac-
KpblBaH 3HaqeHIie KplJTeplJH H,
nOJlyqaeM, qTO 3HaqeHIiH K03cpcpIi-
UIieHTa TenJIOOT
aqIi
IOAV
cx<J(S


MO>KHO CqIiTaTb ewe He qpe3-
MepHO 60JIbllllJMIi ,[tJIH paCCMaT-
pIiBaeMOH 3a
aqH.
npu.Mep 27. Onpe
eJIHeTCH
IW3qxpIiUIieHT TenJlOOT
aqIi npH-
MoyrOJlbHOrO napaJIJIeJIenIine
a
co CTOpOHaMlJ


nOJIyqaeTCH npHMaH JIIiHHH, TaHreHC yrJIa
HaKJIOHa KOTOpof! qlJCJIeHHO paBeH TeM-
ny OXJla>K
eHIiH TeJIa (CM.
 4 rJI. 4).
OpIi OXJIa>K
eHIiIi (IiJIIi HarpeBaHIiIi)
TeJI B YCJIOBIiH x eCTecTBeHHoH KOHBeKUIilJ
K03clxP Ii UIieHT TenJIOOT
aqH
OBOJlbHO 3a-
MeTHO 3aBlJCIiT OT TeMnepaTypbI. B 3TOM
cJIyqae rpacpIiK 3aBIiCIiMOCTIi (I ]. 5) He
6y
eT npe
CTaBJlHTb npHMOH JIIi HlJ Ii
JcpIir. 115, a). O
HaKo lJ 3
eCb MO}KHO
. .npIiMeHIiTb paCqeTHbIe 1jJ0PMYJIbI TeopIiIi
perYJIHpHOrO TenJIOBOrO pe>KHMa.
B caMOM
eJIe, eCJIIi Ha KpIiBOH
IjJIif. I ]5, a 6paTb He60JIbUIIie IiHTepBaJIbI
BpeMeHIi 6. 't, TO OTpe3KlJ KpIiBOH MO>KHO
3aMeHIiTb OTpe3KaMH npHMblX JIIiHIiH,
T. e. B 3TOM IiHTepBaJIe TeMnepaTYP OXJI3}K-
,[teHIie CIiCTeMbI MO>KHO CqliTaTb npaKTlJ-
qeCKIi npOTeKalOWIiM no 3KcnOHeH-
UIiaJI bHOMY 3aKOHY. ECJIIi 06blqHO TeMn
OXJIa>K
eHIiH paCCqIiTblBaeTCH no cpOPMY-
JIe (8. ] 4), T. e.
In 3, - In 3 2
m= .
't 2 -'tl


L3 = 12,2. 10- 2 .lit.


LJ:JIH 3TQro TeJIa 3H3 l IeHHe KOMnJlel{Ca
KS = ] 39. ] 0 -2
v' M.


PaCCMOTpIiM Tenepb CJIe.ll.YlOll!He CJIyqaIi.
l. TeJlo Ii3rOTOBJleHO lJ3 JlaTYHIi, A = 73,5 KIWAIM- I lfac- 1 i'paa- l .
Tor
a MeTO,[t perYJlHpHOrO pe>KHMa MO}KHO npIiMeHHTb
o 3HaqeHIiH
a nopH
Ka


10.73,5 _. 3 '
0: -< 1,39.10-"
5, . IO
 KKaA M- 2 Ifac- 1 epaa- l .


2. To >Ke TeJlO H3rOTOB.1eHO lJ3 360HIiTa C A = 0, ]8. B 3TOM CJIVlJae
MeTO
 perYJlHpHOrO pe>KHMa MO}KHO nplJMeHHTb
o 3HaqeHHH a nOp5l,[tKa
\0.0,18
ex < 1,39.\0-2 = 130.


h..

"
----- '---0....
---
In. --,


6} -T
.-;1 I
t


I
-T

)
m
I
--II
zJ
a
t


<DHr. 115. npHMep 06pa6OTKH
pe3YJIbTaTOB onbITOB, npoH3Be.neH-
HblX no MeTOJ1Y perYJlHpHoro pe-
}KliMa, IiMelOll.lliX UeJIblO onpeJ1e-
1IlITb 3aBliCHMOCTb KO
HlllieHTa
TenJIOOTJ1a41i 01' pa3HOCTH TeMne-
paTYP nOBepXHOCTIi TeJla H cpeAbl.


paBeHCTBO:


113 paCCMOTpeHHblX npHMepOB BH
HO, qTO BbIrO
Hee BCerO Ii3rOTOBJlHTb
:J T1hrp:JJ<:J.T)npHMPTpf-,J In M'PT
!I!I
 C On'lhlllllM K03cppIIIUleilTOM TenJIO-
IIpOBO.ll.HOCTIi; B03MO>KHOCTIi TaKIiX npIi60pOB 60Jlee lllIipOKHe.


TO
JlH npe,[teJlbHOrO CJIyqaH cnpaBe
JIHBO cJle
YlOwee
1 ,
 In 1\ _ d In 1\
Tn = 1m -.;::- - - d , .
j\,
O L> .


lil. G)




206


H3MepeHUR u npu6op



1'13 BbIllieCKa3aHHoro CTaHOBIiTCH HCHbIM Ii MeTO,l\ 06pa60TKIi OnbITHbIX
,l\aHHbIX ,l\JIH onpe,l\eJIeHIiH K03cpcpIiIJ.IieHTa TenJIOOT,l\a<IIi B 3aBIiCIiMOCTIi
OT TeMnepaTypbI.
OOJIYJIOrapIicpMIi<IecKYlO KPIiBYlO (cpIir. 115, a) CJIe,l\yeT rpacpIi<I
CKIi
npo,l\Ii(fCP
peHIJ.IipoBaTb no BpeMeHIi Ii nOJIY<IIiTb 3aBIiCIiMoCTb, Ii306pa-
>KeHHYlO Ha «pIir. 115, 6, T. e.


m= m('t'),
Ii 3aTeM nepeBeCTIi, nOJIb3YHCb rpacpIiKoM (<<pIir. 115, a) OCb BpeMeH
B OCb TeMnepaTYP, T. e. nepeHTli K 3aBIicIiMoCTIi, !i306pa>KeHHOH
Ha cpIir. 115, 6:


r J1 A B A 12
i\n1KPOKAJIOPI1METP 11 EI1KAJ10PI1METP, OCHOBAHHblE
HA TEOPI1I1 PErYJ1SlPHOrO PE)I(I1MA nEPBOrO PO,lJ,A


m=m(&).


YCTaHOBIiB 3TY 3aBIiCIiMoCTb, HeTpY,l\HO HaHTIi BJIIiHHIie TeMnepaTYP-
HOH pa3HocTIi & Ha K03cpqmUIieHT TenJIOOT,l\a<IlJ. LIJIH 3Toro He06xo,l\HMO
COrJIaCHO «popMYJIe (II. 4) BeJIIi<IIiHY m (&) nOMHO>KIiTb Ha K03cpcpHUIieHT
CIS; nOJIY<IaeM KPIiBYlO «pIir. 115, 2.
CJle,l\YeT OTMeTIiTb, <ITO npIi rpacpH<IeCKOM ,l\H4><PepeHUIipOBaHIiIi KPIi-
BOH «pIir. 115, a HeT CMbICJIa npIi6eraTb K TO<IHbIM MeTO,l\aM, a ,l\OCTaTO<IHO
pa36IiTb KPIiBYlO Ha HeCKOJIbKO oTpe3KoB Ii onpe,l\eJIIiTb ,l\JIH Ka>K,l\OrO
/--,3 HIiX TeMn OXJIa>K,l\eHIiH m no «popMYJIe (8. 14), OTHeCH nOJIY<IeHHOe ero
3Ha<IeHIie K Cepe,l\IiHe oTpe3Iw. B pe3YJIbTaTe nOJIY<IIiM HeCKOJIbKO TO<IeK,
no KOTOpbIM JIerKO nOCTpoHTb KPIiBYlO, Ii306pa>KeHHYlO Ha «pIir. 115, 6.
OnIicaHHbIM 3,l\eCb cnoc0601\1 MO>KHO 6bICTpO Ii rOpa3,l\0 TO<IHee, <IeM
npIi nOJIb30BaHIiIi MeTO,l\OM cTauIioHapHoro pe>KIiMa, onpe,l\eJIIiTb B YCJJO-
BIiHX eCTecTBeHHoH KOHBeKuIiIi 3aBHCIiMOCTb K03cpcpIiUIieHTa TenJJOOT-
,l\a<IIi OT pa3HocTIi TeMnepaTyp & = u - 8.
mOT MeTO,l\ TaK>Ke npIirO,l\eH ,l\JJH onpe,l\eJJeHIiH IiCCJJe,l\yeMoi-i 3aBIiCIi-
MOCTIi B BbIHY>K,l\eHHOCTIi nOTOKa ra3a IiJJH >KlJ,l\KOCTH, eCJJIi TOJIbKO
npouecc OXJIa>K,l\eHIiH npOTeKaeT C TaKOH CKOpOCTblO, <ITO B03MO>KHO
,l\OBOJIbHO TO<IHO CHHTb 3aBIiCIiMOCTb & = f ('t).
LIJIH paC<IeTa BeJI Ii <Iii HbI CIS aJIbcpaKaJJOpIiMeTpa CJJe,l\yeT 3HaTb
Y,l\eJIbHYlO TenJJOeMKOCTb Tex MaTep, IiaJIOB Ii3 KOTOpbIX Ii3rOTOBJIeH
3TOT npIi60p. 06bI
HO aJI b«paKaJIOp IiMeTpbI Ii3roTOBJJHlOT Ii3 MeTaJIJJa,
3Ha<IeHIiH Y,l\eJIbHOIi TenJIOeMKOCTH KOTOpbIX npIiBe,l\eHbI B
 6 T. I.
OpIi IiCnbITaHIiIi MaTepnaJIOB Ha TenJIOnpOBO,l\HOCTb no MeTO,l\Y
JIaM6,l\aKaJJOpIiMeTpa (rJI. 10) B paC<IeTHbIe CPOPMYJJbI DO,l\CTaBJIHlOT 3Ha-
<IeHIiH K034><PIiUIieHToB TenJI OOT,l\a <Iii , nOJIY'IeHHbIe Ii3 onbITOB C aJIbcpa-
KaJIopIiMeTpaMIi. OpIi 3TOM He06xo,l\IiMO nOJIb30BaTbCH 3Ha<IeHIiHMIi
K03qxpIiUIieHTa TenJIOOT,l\a'lIi, HaH,l\eHHbIMIi ,l\JIH TOro >Ke TeMnepaTypHoro
IiHTepBaJIa, npIi KOTOpOM onpe,l\eJIHJICH TeMn OXJIa>K,l\eHIiH JIaM6,l\aKaJIO-
pIiMeTpa. 3TOT BbIBO,l\ HBJIm!TCH CJIe,l\CTBIieM 3aBIiCIiMOCTH Q: = ex (&).



 I. UIinlJH,l\pIiqeCKIiH MIiKpoKanopIiMeTp
AKaJIOpHMeTp n03BOJIHeT onpe,l\eJJIiTb TOJIbKO TeMnepaTyponpOBO,l\-
HOCTb a MaTepIiaJJa. ]lJJH HaXO>K,l\eHIiH ero TenJJOnpOBO,l\HOCTlJ A He06-
XO,l\HMO onpe,l\eJIlJTb ero 06'beMHbIH Bec i, '1TO He npe,l\CTaBJIHeT TPY,l\HO-
CTIi, Ii HaHn! ero Y,l\eJIbHYlO TenJIOeMKOCTb C. 00 «popMYJIe (8.2) onpe-
,l\eJJHeTCH A.
MlJKpOKaJIOpHMeTp Ii npe,l\Ha3Ha<IeH ,l\JJH onpe,l\eJIeHIiH c. Ope,l\no-
JIaraeTCH, '1TO MaTepHaJi H3MeJIb'leH lJ npIiBe,l\eH B COCTOHHIie O,l\HOpO,l\-
Horo nopOlllKa, pa3MepbI 3epHa KOToporo He 60JJbWe I .il'tM.
B03bMeM MaJIYlO nOpUlJlO 3Toro nopolliKa H HanOJIHHM HM He60JIb-
mOH UIiJIIiH,l\plJ'IeCKIiH COC Y,l\ , BblCOTa KOToporo B 3-4 pa3a 60JJ bIDe
,l\IiaMeTpa OCHOBaHHH. B03bMeM BTOpOH KaJIOp
MeTp. no BHelllHlJM pa3-
MepaM O,l\IiHaKOBbIH C nepBbIM, Ii3rOTOBJJeHHbIH Ii3 BemeCTBa lIJill He-
CKOJIbKIiX BemeCTB, TennoeMKOCTb KOTOpbIX H3BeCTHa, a n03TOMY Ii3-
BeCTHa Ii nOJIHaH TenJJOeMKOCTb C N 3Toro «HOpMaJJbHoro» KaJJOpIiMeTpa.
. . Ope,l\nOJIO>KIiM, '1TO TenJIOeMKOCTb nepBoro UlIJIH
,l\plIKa, HanOJJHHel\lOrO
. lIcnbITyeMblM MaTepIiaJIOM, Ii3BeCTHa Ii paBHa C. COBoKynHocTb 3TIiX
UIiJIIiH,l\pIiKOB Ii COCTaBJJHeT MlJKpOKaJIOplJMeTp.
OpIiMeHHH K aHaJIIi3Y perYJIHpHOrO OXJIa>K,l\eHIiH OCHOBHbIe KplJTe-
plJIi lJ BOcnOJJb30BaBlllIiCb CBH3blO Me>K,l\Y HIiMIi, npIiXO,l\IiM K 3aKnlO'Ie-
HIilQ. '1TO npli ManbiX pa3Mepax UIiJJIiH,l\pIiKOB Iiu MaJibIX ex, T. e. npIi
OXJIa>K,l\eHIilJ 'B cnOKOHHOM B03,l\yxe, MO>KHO HaIiTlJ nOJIHYlO TenJIOeM-
KOCTb C HaBeCKIi P MaTepIiaJIa npOCTblM cpaBHeHIieM TeMnOB OXJIa>K,l\e-
HIiH mx Ii m - UIiJIlJH,l\pIiKa, HanOJJHeHHoro HOpMaJIbHbIM BellI.eCTBOM,
Ii UHJIIiH,l\pIiKa C IiCnbITbIBaeMbiM MaTepIiaJJOM, a HMeHHO:
C=cP = ( mN .C.._C' ) '1". (12.1)
m ..


3,l\eCb '1" O'leHb 6JIIi3KO K I Ii BbI'IIiCJIHeTCH no cpopMYJJe
R2 m
'1"=1--,-,
8 a nop


( 12. 2)


rJ\f' R - BH)'Trf'HHl-df r
p
liyr IH-ITIHH
pl-iK:'I C napOII/KOM;
a - TeMnepaTyponpOBO,l\HOCTb nopowKa.
nop




208


l1alolepeHUR U npU60pbl


JIJl5I OnpeAeJleHl.J5I Qnop MO)KHO npHMeHHTb MaJleHbKl-d:j CTeKJI51 HHblii
aKaJlOpHMeTp B BHAe wapoBoii KOJl60lJKH, HMelOllLel'I AHaMeTp 30-35..iI'tJIL
R
1l
LIJl5I wapa K =
, rAeR ",-paAHYC wapa.
7t
3m cpOPMYJlbl BepHbl, nOKa R MaJlO. Pac-
lJeTbl npHBeJIH K CJleAYlOllLlIM pa3MepaM:
BblCOTa UllmIH.:J.pllKOB . 50-75 M.M,
!lliaMeTp 20-25 MM.


Ha cpHr. 116 nOKa3aHbl MeAHble H CTe-
K.'l5lHllble MHKpOKaJlOpHMeTpbl, C ycnexoM
npHMeH5IBWHeC5I AJiH onpeAeJleHH5I c nJlo-
XHX npoBoAHHKOB TenJia.
OnblTbl npOH3BOAHJlHCb B KOMHaTe.
KaJlOpHMeTpbl, nOABeweHHble K wTaTHBY,
cToHBweMY Ha CTOJle, 6blJlH 3alll.Hlll.eHbl 3Kpa-
\':::. HOM, oKpY)KaBWHM HX co Bcex CTOpOH.
:". ". B KalJeCTBe HOpMaJlbHOrO BellLeCTBa B
;:

:<: OnblTaX cpHrYPHpOBaJiH Me){"b H BOAa.

 2. llJapoBoH 6HKaJlOpHMeTp AJISI HcnblTa-
HHH Ha TenJlOnpOBOAHOCTb 3epHHcTblX H
BOJlOKHHCTbIX, TenJlOH30JlSlU,I-IOHHbIX MaTe-
pl-laJIOB


..
.
..
.,
" '.
'.
.'
'. ;
;



N )(
<!JHL 116. CxeMa IlIiJIIiHJ1Pll'
lJeCKOrO MIiKpOKaJlOpliMeTpa
perYJIHpHoro oXJIa}K.neHlIH:


N - 8J1b<j>8K8J10pHMeTp H3 HOpM8.%.
HorQ (HJlM .9T8.110HHoro") MaTepHaJla;
X -KanopHMeTp. HSnO.1lHeHHblH HC-
cnellyeMblM Me
'JKOH3Me.1lbl.J.eHHhlM
MaTepHanOM


J.1mKeHepy TenJlOH30Jl5lTapllLHKY B npaK-
THlJeCKOH Ae5lTeJlbHOCTH HepeAKo npHXOAHTC5I
CTaJlKHBaTbC5I C He06xOAHMOCTblO 6b1CTpO,
B TelJeHHe 2- 3 lJac" onpeAeJlI:JTb TenJlOnpo-
BOAHOCTb ). KaKOrO-JlH60 MaTepHaJia Ha He60Jlbwoi-i ero np06e HJlH
Ha HeCKOJlbKHX npo6ax. EOJlbWOH TOlJHOCTH npH 3TOM lJaCTO He Tpe6yeTC5I;
HY)KeH npOCTOH, ,lteweBblH H AocTynllblii B yc.nOBH5IX npOH3BOACTBa
npH60p (npeAnOJIaraeTCH, lJTO BOCnOJlb30BaTbCSI CneLl.HaJlbHol'I TenJlO-
BOH Jla60paTopHeH npOH3BOAcTBeHHHK He MO)KeT, lJTO OH npeAOCTaBJleH
c06CTBeHHbiM CHJlaM).
JIJl5I YAOBJleTBopeHH5I TaKHX Tpe60BaHHH H npeAHa3HalJeH wapOBOH
npH60p. J.1Ae51 MeTOAa 3aKJllOlJaeTC5I B CJleAYKJlIJ.eM.
OYCTb perYJl5lpHO OXJla>KAalOlIJ.a5lC5I CHCTeMa npeACTaBJl5IeT C060H
c.nO)KHOe TeJlO, COCTOSllIJ.ee H3 wapoBoro MeTaJlJlHlJeCKoro SlApa 1 (cpHr. 117)
H oKpY>KalOlIJ.era era co Bcex CTOpOH KOHLl.eHTpHlJeCKOrO C HHM wapoBoro
CJl051 2 HcnblTyeMoro TenJlOH30Jl5lTOpa.
TaKHM 06pa30M, TenJlOH30JlSlTOp 3allLHllLaeT 5IAPO OT TenJlOBOrO B03-
AeHcTBH5I BHPWHeii cpe,'{bl E. nYCTb 3TO B03,lteHcTBHe HaCTOJlbKO HHTeH-
CHBHO, lJTO npaKTHlJeCKH K03cpcpHLl.HeHT TenJlOOTAalJH ex MO>KHO ClJHTaTb
paBHblM oeCKOHPlJHOCTH - VC',TJORJ-IP, KnTnpnp pP;:1 'lJ-l1YPTCH nplf OXJlaH<-
AeUHH CHCTeMbl, HarrpHMep, B nepeMewHBaeMoll >KHAI<O<;TH.


JWUKpOKaAopUMeTp U 6uKaAopuMeTp


209


m


5ICHO lJTO TeMn perYJl5lpHoro OXJlaH<AeHH5I m TaKoH CHCTeMbl, KOTO-
PYlO Ha;oBeM 6HKaJlOpHMeTpoM (bi - ABa)KAbl), 6YAeT 3aBHceTb, npH
npOlJHX paBHblx YC.nOBH5IX, OT TenJlOnpOBOAHOCTH ). TepMOH30Jl5lTOpa:
lJeM OHa 60JlbWe, TeM 60JlbWe m. Ec.nH YAacTc5I CB5I3aTb 3TH ABe BeJlHlJHHbl
npOCTblM B MaTeMaTHlJeCKOM CMblc.ne COOTHoweHHeM, TO, 3Ha51 H3 OnblTa m,
HaHAeM H ).. TaKOBa HAe51 MeTOAa.
JIJl5I ee npeTBOpeHH5I B )KH3Hb nOHaA06HJlOC
 npOBeCTH OAHO H3 Teo-
peTHlJeCKi1X Hcc.ne,ltOBaHHH, 0 KOTOpOM rOBOpHJlOCb B
 8 rJl. 4. BBe-
AeHHeM 'HOBbIX KpHTepHaJlbHblX BeJlHlJHH 5 H )K 6blJlO OXBalJ
HO Bce
MHoroo6pa3He perYJl SlpHblX pe-
)KHMOB BceB03MO)KHbIX wapoBblx =- - _ 8
6i:IKaJlOpHMeTpoB OAHOll 06llLell =- ---=- ---=--- -=- ----=- -=
3aBHCHMOCTblO


6 = f ()K, l).


(12.3)


3Ta 3aBHCHMOCTb Ta6YJlHpo-
BaHa H nOKa3aHa rpacpHlJeCKH Ha
cpHr. 55. Ha Hell 6YKBOll! 060-
3HalJeHa npaBHJlbHa51 ,ltpOOb


D'
I=D'


(12.4)


---
---
-----
- -- -


rAe D' :- AHaMeTp SlApa;
D - HapY}KHbIH AHaMeT[J
TepMOH30Jl51 Ll.H OH Horo
c.noo. 0
KpHTeplfH 5 Jle>KHT MeR{AY 0 HI, KpiITepHH )K MeH5IeTC5I OT AO
6eCKOHelJHOcTH.
JIJl5I 3HalJeHHH )K :;;;.. 2 cpOPMYJlY (12. 3) C AOCTaTOlJHOH u JJ.Jl5I npaKTH-
lJeCKHX Ll.eJleH TOlJHOCTblO MOR<HO 3aMeHHTb npH6J1H)KeHHOH:
3)1{
5
 3* + l


ct>lIL 117. CxeMa llIapoBoro 6HKaJIOpIiMeTpa:


1 - MeT8J1J1' 2 - TenJlOH30Jl.ITOP; 6HK8J10pHMeTp
norpY>KeH
 nJlomylO cpeAY E p8BHOMepHOH TeM-
nepaTypbl, 6 = const. TalC I.J.TO a -+-00.


02.5)


KpHTepHH )K AaH


cpOPMYJlOH [eM. (4. 27)]
T
)K=C'


(12. 6)


rAe


T =
 (1 + I +
) C'.
B cpopMYJlaX (12. 6) H (12. 7) C' 0603HatJaeT nOJIHYIO TenJlOeMKOCTb
5IApa; C - nOJIHYlO TenJlOeMKOCTb TepMOH30Jl5lTOpa.
KpHTepHH E n03BOJl5leT HaHTH HCKOMoe COOTHoweHHe Me)KAY TenJlO-
npoBoAHOCTblO ). H m; OHO HMeeT BH,n
A=
 m. (12.8)


(12. 7)


14 l{oHAp8TbeB 2763




210


1f3MepeHUJI U npU60pbl


3,l\eCb A BbltIHCJ1S1eTCSI no llJopMYJIe
A=
 (
-
 ) C"
2'fl: D' D


(12.9)


1'13 BblllIeH3J10>KeHHOro CTaHOBHTCSI SlceH H cnoc06 paCqeTa A.
npe,l\nOJlO>KHM, qTO Bbl6paH MeTaJlJla, H3 KOToporo H3rOTOBJleHo SI,l\pO,
Hero ,l\HaMeTp D'. nYCTb H3rOTOBJleHa llIapOBaSl MeTaJlJlH'-IeCKaSl 060Jloq-
Ka, KOHueHTpHqHaSl C SI,Z\pOM H >KeCTKO C HHM CKpenJleHHaSl; CJJe,Z\OBaTeJIb-
HO, H3BeCTeH ee BHYTpeHHHH ,Z\HaMeTp D, H3BeCTHO /; n03ToMY MO>KHO
C'-IHTaTb H3BeCTHblMH ,l\Be BeJlH'-IHHbl A H T - «nOCTOSlHHble npH6opa»
(4)OPMYJlbl (12. 7) H (12. 9), H60 C' 6y,Z\eT nOJlY'-IeHO H3 B3BellIHBaHHSI
SI,l\pa, yqHTbIBaSl, '-ITO TenJIOeMKOCTb c' MeTaJlJla H3BeCTHa (HanpHMep,
0,0917 ,l\JISI Me,l\H H t. ,Z\.).
HanOJlHHB 6HKaJlOpHMeTp HcnbITyeMblM MarepHaJlOM, HarpeeM ero
H, Ha6JJ10,l\aSl ero OXJla>K,Z\eHHe B TepMocTaTe, 06blqHblM npHeMoM BblqHC

JlHM m.
nYCTb H3BeCTHa TenJIOeMKOCTb C np06bl MaTepH
Jla. 3HaSl T, Bbl-
qHCJJSleM >K H no 4>opMYJle (12. 3) HaXO,l\HM 5; Tor,Z\a, nOCKOJlbKY A
H3BeCTHO, 4-'OpMYJIa (12. 8) n.03BOJlSleT BblqHCJJHTb A.
OTclO,l\a BH,Z\HO, qTO ,Z\JlSI onpe,l\eJleHHSI ). Tpe6yeTcSI npe,Z\BapHTeJIbHO
3HaTb c. O,l\HaKO 3TY nOCJJe,Z\HIOIO BeJlH'-IHHY HeT Ha,Z\06HOCTH 3HaTb
C 60JlbiliOH TO'IHOCTblO, H60 3aBHCHMOCTb 5 OT )K (a )K 06paTHo nponop-
UHOHaJlbHa C) TaKOBa, qTO 60J1 blllaSl 0llIH6Ka B onpe,Z\eJleHHH C HJlH C -
nopSl,l\Ka 20-30% - Bbl3bIBaeT B Bbl'-lHCJJeHHH 5 He3HaqHTeJlbl:lYIO
OIlIH6KY, nopSl,l\Ka 2-3 %. n03TOMY BnOJlHe ,l\OCTaTO'-lHO oueHHTb C
rpy60. OpHeHTHpOBO'-lHO MO>KHO CqHTaTb C
 0,2 KKaflKZ- 1 zpaa- 1 ,l\JISI
HeopraHH'-IeCKHX BeIlleCTB H C
 0,4 KKQJl KZ-1zpaa- 1 ,Z\JlSI CYXHX opra-
HHtIeCKHX MaTepHaJlOB.
TaK KaK MaCCHBHoe MeTaJIJlHqeCKOe SI,l\pO 06J1a,Z\aeT 3Ha'-lHTeJlbHO
60JlbilieH TennoeMKOCTblO, '-IeM TepMOH30JlSlUHOHHble MaTepHaJlbl, TO
KpHTepHH )K 6y,Z\eT Bblpa>KaTbCSI 60JlbllIHMH '-IHCJJaMH, BCJJe,Z\CTBHe qero
KpHTepHH E 6y,Z\eT 6J1H30K K 1 (nopSl,l\Ka 0,95-1,00). JI.JlSI BblcoK03llJcpeK-
THBHblX MaTepHaJIOB, HMelOlllHX MaJlblH 06'beMHbIH Bec, 5.:::::: 1.
YqHTbIBaJII CKa3aHHoe, npHxo,Z\HM K npocTOH npH6JIH>KeHHOll $)pMYJIe
A
 Am. (12. 10)


TeMn oxJia>K,l\eHHSI npH6J1H3HTeJlbHO nponopUHOHaJleH )..
KOHcTaHTY A HY>KHO onpe,lteJIHTb C 60JI blliOH TO'-lHOCTblO, TaK KaK
OT 3Toro 3aBHCHT, B nepBYIO.O'-lepe,l\b, TO'-lHOCTb onpe,lteJIem!SI )..
KOHcTaHTa T, OqeBH,Z\HO, HrpaeT MeHbllIYIO pOJlb; 'laCTO eIO MO>KHO
npeHe6peqb.
5I'z\po llIapOBoro 6HKaJlOpHMeTpa CJJe,l\yeT H3rOTOBJlSlTb 113 MeTaJIJla,
Y,l\eJlbHaSl TenJlOeMKOCTb KOToporo XOpOIliO 113yqeHa - 113 Me,Z\II, >KeJI€38
H T. n., a HapY>KHYIO 060JloqKY - H3 Hep>KaBelOIllero MeTaJlJla.
Ha 4>Hr. 118 H306pa>KeH 611KaJIOpHMeTp co CJJa60 pa3BHTblM SI,Z\pOM,
Hd 4>HI'. llY - C CHJlbHO pa3BH I"bIM H).WOM. Y I1epBOro LJ' = 2U ---;-- 25 MM,
D = 45 -+- 48 . MM; Y BTOpOro D' = 20 ---;-- 45 MM, D = 50 -+- 70 MM.


lWUKPOKQAOPUMBTp U 6UKQAOpUMeTp


211


ECJJI1 orpaHlI'-IHTbCSI TOqHOCTblO H3MepeHHSI A nopSl,Z\Ka 5u- 1O %, TO
MO>KHO npliMelHITb CTeKJISlHHbllJ 6HKaJlOpliMeTp, COCTOSlllI.HH 113 ,l\BYX
,Z\JII1HHOrOpJIbIX llIapOBblX KOJI60{leK, pa3Mepbl llIapOB H ropJl KOTOpb
X
nO,lt06paHbl TaK, '-ITO MeHbillaSl MOIKeT OblTb BCTaBJleHa BHYTPb 60JlbllIe:;
ueHTplipOBam!e np01I3BO,l\lITCSI Ha rJIa3 no HaHeceHHblM npe.lwapHTeJlb 0


6


If


3


4


<!JIlL 119. lllapoBoii 6liKaJIOpliMeTp
CpCJI,HIIX pa3Mepoa C CHJlbHO pa3BlITbIM
H.npOM:
1 _ BBO.n.H8.n 9f)OHHTOB8.n". TeKCTonHTOBaSi HJ1H
KepaMH4ecKaH Tpy6Ka; 2 - HanonHHTenb (BoAa.
MeT8J1J1H4eCKHH Cn.1l8B. MaCAO H T. n.); 3 - Me-
TannH4eCKoe II.llPO; 4 - HcnblTye
n:.lH Te
JlOH30-
JUITOP; 5 - MeTiiJl.1lH'.J.ecK8.n npo6Ka.


<!Jm. 118. lllapoBoii 6I1KaJlO'
pHMeTp MaJIblX pa3MepoB co
C1la60 pa3BlITbIM HJ1POM:
1 - <jJap<jJopOBaH :lByxKaHanbHaH
Tpy604Ka AnH TepMonapbl; 2 --BBOA-
HaS! 96oHHTOB8H HJlH TeKCTOJlHTOB3.H
Tpy6K3. coe.n.HHeU1I3.H C MeTanJlW.J.e.:
CKHM .H.D.pOM 3; -1 - HcnblTyeMbUt
TennOH30n.HTOp; 5 - Me-r3.'1J1W.J.eCK3.H
np06Ka; 6 - naAKa.
· JITpliXaM Ha rOpJIaX KOJI6. JI.lIaMeTpbI (npH6JI1I31ITeJlbHO) D' = 20 -+-
-+- 25 .MJI't, D = 45 -;.- 50 Jl'tM.
B MaJlYIO KOJI60'-lKY HaJlHBalOT KaKYIO-JIH60 >KH,l\KOCTb, He OqeHb
nJIOXO npOBO,l\SlIllYIO Tem1O, TenJlOeMKOCTb KOTOpOH TOqHO H3BeCTHa,
Hanpl1Mep BO)].Y HJIH PTYTb.
JI.JlSI H3MepeHlISI U, 8 H {)- = U - 8 B HeKoTopblX cJlyqa
x HapSl,l\Y
C ,l\lIcpcpepeHUHaJIbHO
i TepMonapoH MOIKHO npliMeulITb PTYTHbIll CTeKJISlH-
Hbili TepMoMeTp.
B 1955 r. M. M. rOJlSlH,ltOM 3TOT MeTO)]. 6bIJI npHMeHeH K on'pe,l\eJleHHIO
TenJIonpoBo,ltHOCTli TenJI01I30J1HUlIOHHbIX MaTeplIaJlOB np" HH3KHX TeM-
nepaTypax - BIJJIOTb )].0 _200 0 C.


.


14* 2763


*


1




212


H3MepeHUJI U npuf50pbl


MeTo,'!. «wap B wape»
OBOJIbHO llmpOKO npIiMeH5IeTCfI
.TJfI onpe
eJIe-
HIifI TenJIOnpOBO.l(HOCTIi )KIi
KOCTeH; TaK, r. H. LIaHIiJIOBa B 1948-49 rr.
npIiMeHIiJIa ero K IiCCJIe
OBaBIiIO TenJIOnpOBO
HOCTIi OTelJeCTBelU-IbIX
cppeoHoB .l(JIfI TeMnepaTypbI .l(0 _30 0 no
 .l(aBJIeHIieM
o 8 anza. KpaTKIie
CBe
eHIifI 06 9TOM MeTo
e MO)KHO HaHTIi B CTaTbe [20].



 3. nJlOCKIiH 6IiKaJlOpl-lMeTp


OnIicaHBbIH BbIwe wapoBoH 61IKaJIOpIiMeTp npIiro
eH
JIfI IiCnbITaHIiH
Ha6IiBHbIX Ii HaCbIllHbIX TepMOIi30JIfIUIiOHHbIX MaTepIiaJIOB, a TaK)Ke
HCXO
HbIX cbIpbeBbIx MaTepIiaJIOB 11, KOHelJHO, He npIiro
eH .l(JIfI IicnbI-
TaBIiH TepMOIi30JIfIUIiOHHbIX Ii3.l(eJIlIH, BeCbMa MHorIie Ii3 IWTOPbIX Ii3ro-
TOBJIfIlOTCH B cpopMe nJIIiT Ii JIIiCTOB (O
HO- lIJIIi MHOroCJIOHHbIX); TaKOBbI,
HanpIiMep, .l(peBeCHO-BOJIKOHIiCTbIe, TOpcpfIHbIe, npo6KOBbIe nJIIiTbI, Kap-
TOH, cpaHepa.
Me)f(
y TeM CKOpOCTHbIe IiCnbITaHIifI Ha. TenJIOnpOBO.l(HOCTb MaTepIiaJIOB
9Toro pO.l(a, KaK MeTO
 CIiCTeMaTHlJeCKOrO KOHTpOJIfI BbIllYCKaeMOH npo-

YKUIiIi, lJpe3BbIlJaHHO Ba)KHbI
JI5I 3aBO.l(OB - Ii3rOTOBIiTeJIeii Ii30JIfIUIiIi.
OCTpO OIll,YIll,aeTCfI nOTpe6HOCTb B MeTO.l(aX Ii npIi60pax
JIfI Ii CnbITaHIi H,
KOTopble 6bIJIIi 6bI npOCTbI Ii .l(ocTynHbl TeXHIiKaM Ii IiH)KeHepaM, He 06JIa-

alOlUIiM 60JIbWl1MIi 3HaHIifIMIi B 06JIaCTIi TenJIOBbIX Ii3MepeHllIl.
,lJ,JIfI Y.l(oBJIeTBOpeHIiH 9T01I nOTpe6HocTIi Ii 6bIJI c03
aH HOBbIH MeTO.l(
Ii nOCTpoeH A. cI>. 5erYHKoBoH
eHcTBYlOlUIiH no 9TOMY MeTO.l(Y npIi60p,
Ha3BaHHbIH
JIfI KpaTKocTIi nJIOCKIiM 6IiKaJIOpIiMeTpoM.
l"l.l(efl MeTo
a BnOJIHe aHaJIOrIilJHa Ii
ee, JIe)KalUeH B OCHOBe wapoBoro
6IiKaJIOpIiMeTpa. Pa3JIIilJIie 3aKJIIOlJaeTCH JIIiWb:
I) B cpopMe MeTaJIJIIilJeCKOrO fI
pa, KOTOPOMY B nJIOCKOM 6IiKaJIOpl1-
MeTpe npIi
aHa cpopMa nJIOCKOrO
IiCKa IiJIH KBa
paTHoi1 nJIaCTIiHKIi C
TOJIlU.IiHOH, KOTopafI B 10-12 pa3 MeHbwe CTOpOHbI IiJIIi .l(IiaMeTpa;
2) B paClJeTHbIX cpopMYJIax:
3) B cnoc06e no
rOTOBKIi o6pa3ua K Ii cn bITaHIi 10.
OCHoBHaSl paClJeTHafI cpopMYJIa HMeeT COBepweHBO TOT )Ke BIi.l(, lJTO
Ii
JIH wapoBoro 6IiKaJIOpIiMeTpa:
).=
m
E '


HO nOCTOfIHH3fI .A - 3
eCb HHafI, a IiMeH.HO:
A=t£ ·
s' ,


(12. II)


r.l(e t - TOJIlUHHa 06KJIa.l(OK Ii3 IiCnbITyeMoro TepMOIi30JIfITOpa, OXBa-
TbIBalOIll,IiX ueHTpaJIbHYIO nJIaCTHHKY, KaK 9TO nOKa3aHO Ha cxeMe 6IiKa-
JIOpIiMeTpa (cpIir. 120); S' Ii C' - HapY)KHafI nOBepxHocTb Ii TenJIoeM-
t;OCTb fI
pa.
BeJIJ.fIIHHa R - rpVHI<IHH! f1T )J(. Kf1Tnpml nn MPrp Rn1r
H'TaHHH >v
.'1.0 6eCKOHelJBOCTIi cTpeMIiTcH K 1 Ii C .l(OCTaTOlJHbIM npH6JIIi)KeHIieM MO)KeT



UKpOKaAopUMeTp U 6uKaAopuMeTp


· 213


6HTb BHlJIiCJIeHa no cpopMYJIe


3)1{
5
 3)1{ + 1


5YKBa )I( 0603Ha
IaeT
Ii TepMOH30JIHTopa C:
c'
>K=c'


OTHOWeHI:le TenJIOeMKOCTeH Macc MeTaJIJIa C'
Medb


(12. 12)


.c


QJ
::s:


MCiJb


,lJ,JIfI y
06cTBa BbIlJIiCJIeBIiH MO)KBO
. nOJI b30BaTbCfI npIi6JIIi>KeHHOH CPOPMY-
JIOH 13]:


KOHcmaHmaH,


A
 (A + BC) m,


(12. 13)


B KOTOpOH 6YKBOH B 0603HalJeHa BTO-
paH nOCTOfIHHafI 6IiKaJIOpIiMeTpa. .
BeJIHlJIiHa B BbIlJIiCJIfIeTCH no
cpopMYJIe


2


5


...
'l::>
cu






B = 35' .


(12. 14)


.


BeJIIilJIiHa C HaXO.l(IiTCfI YMHO>Ke-
HIieM Beca P IiCnbITyeMoro MaTepIiaJIa
Ha ero y
eJIbHYIO TenJIOeMKOCTb C, a
IiMeHHO: C = Pc; BeJIlJlJIiHY C MO)KHO
oueHIiTb npIi6JIIi>KeHHo. KaK YKa3aHo
Ha CTp. '212. LlJIfI HblHe npIiMeHfIeMblx
9cpq;eKTIiBHbIX TepMOIi30JIfITOpOB lJJIeH
BC B paClJeTHOH <topMYJIe (12. 13)
COCTa BJ1 fIeT OT A 3-5 % , H Toro Me- <f>HL 120. CXeMa nJIOCKoro 6HKaJIO
Hee. n03ToMY B nepBoM npIi6.TJIi)KeHIiIi pHMeTpa (cHMMeTpHlJHblH THn):
MO)KHO ClJHTaTb A ::::::; Am, T. e. Ii 1- MeTannH4eCKHR cepne4HHK; 2 - nHCKH
H3 HcnblTyeMoro Ten.1l0H3o.'1f1TOpa; 3 - Ten
3
eCb HMeeTCfI TO )Ke, lJTO B CJIYlJae nOH30nSITOp.
WapOBoro 6IiKaJ10pl'lMeTpa.
I1l1alJe 06ClOHT
eJIO C nO
rOTOB!WH 06pa3ua. 06pa3eu IiCCJIe
yeMoro
MaTepHaJ1a B nJ10CKOM npIi60pe IiMeeT CPOPMY
IiCKa 3apaHee 3a.l(aHHOH
TOJIlUIiHbI (y HaC 8,5 .il'tM); n09ToMY
J1fI Ii3rOTOBJIeHIiH 06pa3ua TepMo-
H30J1fIUIiOHHYIO nJIHTY He06xo
HMO paCm!J1HBaTb B Ha!1paBJIeHIiIi, napaJI-
JIeJI bHOM ee CTopoHaM, T. e. nepneH.l(IiKYJIfIpHO K 1:), TaK KaK nJIIiTbI
06JIa.l(a1OT 06blKHOBeHHO TOJILUIiHOH OKOJIO 3-5 CM. Talwe paCnIiJIIiBa-
HIie rOTOBoro H3
eJIIifI
J1fI 3aBo
a, 06JIa
alOLUero MeXaHIilJeCKIiMIi npIi-
cnoco6J1eu Ii fIMIi, TpYJlHOCTeH He npe
CTaBJIfIeT.
B03MO>KeH, KOHetIHO, Ii IiUOH BbIXO.l( Ii3 n0J10)KeUHfI: MO)KHO Ii3ro-
TOBIITb lIeCKOJII,KO 6UKaJIOpIlI\1£'TpOD C palIIj,[1\111 t, paBHblMH TOJIUUlUe
pa3JIHlJUbiX H3)1.eJIHH 3aBO)l.a.


<c


N




214


A1u
po
aAopUMeTp u 6U
aAOpUMeTp


215


H3MepeHUR U npu6op



$lir. 121. CxeMa nJlOCKOrO 6IiKaJIO-
pliMeTpa (HccliMMeTplilJHblii Tlin»)\JIH
OTHOCHTeJIbHbiX 1i3MepeHliit


B p5l
e CJlyqaeB Ha npaKTHKe npHXO
HTC5I HMeTb
eJIo co CJ10)KHbIMH
Ma1'epHaJIaMH Heo!lHopO}lHoro cTpOeHH5I, npe
CTaBJI5IlOllLHMH qepe
OBa-
HHe CJ10eB C pa3HblMH )., C rOcppHpOBaHHblMH H3!leJIHSIMH H T. n. B 9THX
CJ1Y'Ia5lx
JI5I oqeHKH TepM01l30JI5IUHOHHOro 3cpcpeKTa MaTepH8JIa nOJI b-
3YIOTC5I TenJIOBblM conpOTlIBJIeHlIeM




Q)
::i!:
<::>
'"
to
"'"
-0


I '"




o
p=

"YCA


HanpllMep, HaH
51 a H C nocpe
CTBOM aKaJIopHMeTpa H MHKpOKaJIOpH-
MeTpa, MO)KHO BblllHCJ1HTb ). no cpopMYJIe A =ac vol = aq H conOCTaBHTb
nOJIyqe!fHYIO UHcpPY C TOH, KOTOpa51 nOJIYllaeTc5I nocpe
cTBoM 6HKaJIO-
pHMeTpa. 9TH npH60pbl
OJI)KHbl 6bITb nOJIe3Hbl
JI5I KOHTpOJl51 KalleCTBa
npO
YKUHH TenJIOH30JI5IUHOHHbIX 3aBO
OB,
OJI)KHbl nOMO'Ib YCTaHOBHTb
BJIH5IHHe Ha TenJIonpOBO
HOCTb TeXHOJIOrHH npOH3BO
CTBa, HanpHMep
nponHTKH aHTHnHp9HaMH H rH
pOH30JI5ITOpaMH, ynJIOTHeHH5I CTPYK'
Typbl, H3MeHeHH5I BJIa)KHOCTH.


I
=
H,--
i
C;j

H
:\


H K09cpcpHUlIeHT TenJIOnpOBO
HOCTH
npno6peTaeT YCJ10BHbIH CMblCJ1.
OJIOCKHll: 6IiKaJIOpHMeTp OlleHb
y
06eH
JI5I onpe
eJIeHH5I P. PaC'IeT-
Ha51 cpopMYJIa B TaKHX CJ1Ylla5lX JJ.JI5I
6HKaJIOpHMeTpa A. cI>. EerYHKOBOH
HeCHMMeTpHllHoro THna, T. e. C 06-
KJIa
KaMH H3 pa31-1blX TenJIOH30JISITO-
pOB pa3HO
! TOJIllI.HH,bl (cpHr. 121),
HMeeT BH
 (eCJ1H CllHTaTb 5 ;:;;:; 1):
C' I I
2S'm
p;- + 1>;' (12.15)


OlleBH
HO, 'ITO TaKa51 TpaKToBKa
aeT
B03MO>KHOCTb eIll,e 60JIee ulHpoKoro
npHMeHeHH5I nJIOCKOrO 6HKa
opH-
MeTpa.
ECJ1H 06KJIa
KH H3rOTOBJIeHbl H3
O.'lHOro MaTepHaJIa, HO TOJIllLHHbl HX
pa3JIHllHbl H paBHbl 0 1 H 0 2, TO JJ.JI5I Bbl-
'lHCJ1eHH5I CJ1e
yeT nOJIb30BaTbC5I cpop-
MYJIOH


C' 0.02
A;:;;:; 2-. m. ( 12.16 )
S' 0] + 02


OJIOCKHH 6HKaJIOpHMeTp npHMeH5IeTC5I JJ.JISJ onpe
eJIeHH5I K03cp-
cpHUHeHToB TenJIOnpoBo!lHOCTH pa3Ho06pa3HeHulHx MaTepHaJIOB -
6YMarH, KapTOHa, neHOnJIaCTOB H
PYrHX C 06'beMHbIM BeCOM
to - 2000 K2,'h/- a .


'" '"
*


KOMnJIeKC npH6opoB, onHcaHHblX B
 I, 2, 3 3TOH rJIaBbl, eCJ1H ellLe
npHcoe
HHHTb K HHM aKaJIOpHMeTp, n03BOJI5IeT onpe
eJIHTb He TOJIbKO
KaKYIO-.IJHnO n
HY. "I-JTPrp(:ylO"
YIO nrnn
Rn'{(,TRPHHHKa, TenlJOBYIO
xapaKTepHCTHKY M3TepHaJIa, HO H BblTIOJIHHTb KOHTpOJIbHble H3MepeHH5I.




PeZYAJfpHbltJ. pe
UM BTOPOZO U TpeTbeZO poiJa


217


nepaTypa 8 Ii3MeHSleTCSI no 3aKOHY (13. 1); Ii3MepIiM pa3HocTb TeMne-
paTYP tJ. Me)j{
Y KaKOH-JIIi60 TOliKOH, HaXO
SlIlI.eHCSI B paccToSlHIiIi x OT
ueIITpa IiJIIi nJIOCKOCTIi, IiJIIi OCIi CIiMMeTpIfIi 06pa3u a , Ii TeMnepaTypoH 8
cpe
bl (CM. (5. 3) I, KaK nOKa3aHO Ha 4mr. 122; Tor
a Ii3 ypaBHeHIiH (5. 9)
Mbl HaH
eM TeMnepaTyponpoBo
HOCTb MaTepIiaJIa 06p a3 u a a no qJOpMYJIe
.
a = - 2:1t} (V - x 2 ), (13. 3)
"


B IWTOpOH 6YKBa L 0603HaliaeT onpe
eJISlIOIlI.IiH pa3Mep, T. e. nOJIOBIiHY
TOJIIlI.IiHbi nJIaCTIiHKIi HJIIi pa
IiYc, a lJIiCJ10
r = 1 B cJIyqae nJIaCTIiHKIi
r = 2 .. UIiJIIiH
pa
f = 3 " lllapa
B OTJIIilJIie OT nepBoro Ii3 MeTO
OB, OCHOBaH-
HblX Ha TeopIiIi perYJISlpHoro pe)KIiMa nepBoro
po
a, B KOTOpOM MeCTO pacnOJIO)KeHIiH cnaSl TepMo-
na'pbI BHYTPIi 06pa3ua He IirpaeT pOJIIi (CM. rJI. 9),
3
eCb, B CJ1YlJae perYJISlpHoro pe)KIiMa BToporo
pO)I.a, 3HaHIie KOop
IiHaTbI TOliKIi M, r
e Ii3Me-
pSleTcSI TeMnepaTypa, Y)Ke He06xo)I.IiMO; olllIi6Ka
B oueHKe x OTpa)KaeTCH Ha TOlJHOCTIi Ii3Mepe-
HIiSl a. B uemtx CHIi)KeHHH 3ToH OlllIi6KIi BbIrO
HO
TOliKY M COBMeCTI1Tb C UeHTpOM, T. e. nOMeCTIiTb
repMonpIieMHIiK Ii3Mepn-reJISI TeMnepaTypbI U B
ueHTpaJIbHYIO 30HY 06pa3u a 0 (4mr. 122).
I1TaK. eCJ1Ii C06JIIO
eHbi YCJ10BIiSl (13. 1) Ii (A)
Ii Ii3MepeHa pa3HocTb Tel\mepaTYP Me)K
Y UeHTpOM
n cpe
oH - T. e. {}" (r
e x = 0), TO )I.JISI a noJiy-
qaeM OlJeHb npoCTYIO <POPMYJIY:
b L 2
a=- 2f3'1 .


r JI A B A 13


METO.D.bl H3MEPEHlUI TEnJ10BbIX CBoflcTB MATEPHAJ10B,
OCHOBAHHblE HA TEOPHH PEfYJ151PHOfO PE)I(HMA BTOPOfO
H TPETbEfO PO.D.A



 1. j\'\eTO)l,bl HarpeBaHHH o6pa3Qa C nocToHHHOH CKOpOCTblO
(perYJlHpHbIH pe*HM BToporo pO)l,a)
9TH MeTO
bI pa3pa6aTbIBaJIIi.Cb A. B. JlbiKOBbiM Ii ero COTpY
HIiKaMH
npIiMeHIiTeJI bHO K oGpa3ua
 TenJIOIi30JISlUIiOHHbiX MaTepIiaJIOB, IiMelO-
IlI.IiM O
HY Ii3 Tpex npOCTeIilllIiX <pOpM - HeOrpaHIilJeHHOH nJIaCTIiHKH,
6eCKOHelJHO
JIIiHHorO UIiJIIiH
pa Ii lllapa. KaKIie CJIe
yeT 6paTb COOTHO-
llleHIiSl M:)K
Y TOJIIlI.IiHOH nJIaCTIiHKIi Ii ee 06BO
OM Ii Me>K
Y
IiaMeTpOM
H BbiCOTOH UIiJIIiH
pa, lJT06bI MO>KHO 6bIJIO ClJIiTaTb peaJIbHbIe nJIaCTIiHKIi
Ii UIiJIHH
pbI npaKTlJlJeCKIi HeOrpaHIilJeHHbIMIi (B
BYX Ii O
HOM HanpaB-
JIeHHSlX),
O KOHua eIll.e He BbISlCHeHO: 3
eCb HP06,{OJlHMbI
OnOJIHHTeJIbHbIe
TeOpeTIilJeCKIie Ii 3KcnepIiMeHTaJIbHbIe IiCCJ1e
OBaHIiR.
AHaJIOrIilJHO MeTo
aM, OCHOBaHHblM Ha TeopIiIi perYJISlpHOrO pe>KIiMa
nepBoro po
a, B paCCMaTplJBaeMblX MeTo
ax HarpeBaHIiSl 06pa3ua
C nOCTOSlHHOIi CKOpOCTblO onbiT Be
eTCSI JIIi60 B YCJ10BIiSlX a KOHelJHOrO.
JIIi60 B YCJ10BIiSlX a
 00. .
n e p B bi H MeT O
. 06pa3eu HarpeBaeTcSI, npIilJeM TeMnepaTypa
cpe
bI, B KOTOPYIO OH norpY)KeH, B03pacTaeT CO CKOpOCTblO .
dB
lh=b= const, (13.1)


x


x(r)


ct>IiL 122. K TeopHIi
MeTO]J.OB, OCHOBaHHblX
Ha perYJIHpHOM peJKIIMe
BToporo po.na: Heorpa-
HHlJeHHblii UHJIIIHJ1p.


(13. 4)


B TOp 0 fi MeT 0.11.. 06pa3eu HarpeBaeTCSI B YCJ10BIiSlX IX KOHeq-
HOro. ..QJISI TeMnepaTypbl B JI1060i-i TOlJKe ero IiMeeM <POPMYJIbI (5. 7) Ii
(5. 8); 06'be
IiHHSI HX B O)I.HY, MO)KHO HanIicaTb:


r
e r = 1, 2, 3 B 3aBIiCHMOCTH OT <pOpMbi 06pa3u a - CM. BbIllle.
113MepIiM pa3HOCTb TeMnepaTYP U 1 H U2 B
BYX KaKIiX-JIH60 TOlJKaX
06pa3u a M 1 Ii M 2 (<pIir. 122), Koop)I.IiHaTbi KOTOpbIX CYTb Xl Ii X2; npn-
MeHSISI npe
bl
YIlI.ee paBeHCTBO K 3THM
BYM TOlJKaM Ii BblljIiTaH Ii3 nepBoro
nOJIYlIeHHoro ypaBHeHIiSl BTopoe, IiMeeM [B CIiJIY (5. 3)]:
n b ( 2 2 )
tl t -It.=n t --A-'= 2ra .X1-X
.


a Ha HapY>KHOH nOBepxHoCTIi S 06pa3ua nOJU].ep)KIiBaeTCSI TeMnepaTypa,
npaKTIilJeCKIi paBHaSl TeMnepaType cpe
bI
U 18= 8. (13.2)
KaK YKa3aHo B
 I rJI. 4, YCJ10BIie (13. 2) Ii YCJ10BIie


-3-=
(V-X2) -
.L
2fa fah '


a
oo


(*)


paBHOClJJIbHbI.
npe
nOJIO>KHM, liTO YCJ10BIie (*) OCYIll.eCTBJIeHO B npouecce onbITa;
9TO ..l1.0CTIiraeTCSI TaK )Ke, KaK B MeTO
lJKe perYJISlpHOrO pe>KHMa nepBoro
pO.l1.a, - nYTl'M norpY>Kl'IIIHI 06p33Ila IICCJIl'
Yl'MOrO M('T('pIl3JIa B >K1I.l1.-
KOCTb, nO
BepraeMYIO 3HeprnliHOMY nepeMeWHBaHIiIO. nYCTb ee TeM



(13. 5)


(13.6)




218


HSMepeHUJI U npU60pbl


PeZYAJfpHbltl Pe3fCUM BTOPOZO U TpeTbeeO poaa


219


n03TOMY
OCTaTOqHO, npHHUHnHa
bHO rOBOpH, H3MepHTb pa3HOCTb
TeMnepaTYP B
BYX KaKHX-
H60 TOqKaX 06pa3ua, T. c. U 1 - U2, H TOr
a
H3 ypaBHeHHH (13. 6) MbI no
yqHM TeMnepaTyponpoBO
HOCTb MaTepHa
a
06pa3ua. PauHoHa
bHo 3a O
HY H3 3THX TOqeK B3HTb ueHTp 06pa3ua,
a 3a
PyrylO - KaKYIO-
H60 TOqKY ero nOBepxHocTH; Tor
a no
yqHM
b L 2 3
U nOB - U"eHmp = 2fa ' . (1 . 7)
I1cK
lOqHTe
bHaH npocToTa paCqeTHbIX cpOPMY
 npe
CTaB
HeT 60
 b-
IlIoe npeHMYllJ,eCTBo 3TH X l\IeTO
OB, oc06eHHO fCJIH 06pa3CU HMeeT cpOPMY


<f>lIr. 123. BapliaHT YCTaHOBKII lI
H BblBo
a 3TOH q)OPMY
bI 3aMeTHM,
.nJlH 1I3MepeHlIH TeMnepaTyponpo- B
B0J1HOCTliTenJI01l30JlHUIIOHHblX Ha- LITO (H3 13. 5) c
e
yeT &noB = - Tah ' L;
CblnHblX MaTepllaJIOB ("(:;;;;. 1000 A
KZM-3) no MeTo.ny perYJlHpHOrO 3aMeHHH 3
eCb a qepe3 - H h qepe3
pe}KIIMa BToporo po.na (06pa3ell Ma- C"[
TepllaJla lIMee-r mapoBYIO qJOPMY). T' no
yqHM (13.8).
3HaH C vo1 ' HaH
eM UA = ac vo1 ' npHMeHHH

H onpe
e
eHHH TeMne-
paTyponpOBo
HOCTH a nepBbIH H
H BTOpOH H3 BbIIlIeonHcaHHbIX MeTO
OB.
J-:la
Hr. 123 npe
CTaB
eH O
HH H3 OqeHb npocTbIX BapHaHTOB npH-
60pOB J{
H onpe
e
eHHH TeMnepaTyponpoBo
HOC:rH, OCHOBaHHbIX Ha
TeopHH perY
HpHoro pe:>KHMa BToporo po
a B npHMeHeHHH K llIapy.
B llIapoBYIO Ko
6y 1
HaMeTpoM
8 CM HaCbmaH nopollIKo06pa3HbIH
MaTepHa
 2 (06'beMHbIi1 era Bec He MeHee 1000 KG .M- B ), H B ueHTpe llIapa
nOMellJ,eH pe3epByap CTaH
apTHoro Ka
oplfMeTpHLIecKoro TepMoMeTpa 7
THna EeKMaHa. Ko
6a HaXO
HTCH B BO
HHOH BaHHe 3, cHa6:>KeHHOH MOllJ,-
HOH MellIa
KOH 6 re
HI{(m
a
bHoro THna, KOTopaH 3aKmOLIeHa B OTKpbI-
TYIO cBepxy H CHH3Y Tpy6y 5. E
aro
apH HHTeHcHBHoMY nepeMellIHBa-
HHIO BO
bI 4 MO:>KHO CqHT3.Tb c06
IO
eHHbIM yc.TJOBHe ex
 00. ECJIH
TeMnepaTypa nOMellJ,eHHH
a60paTopHH OqeHb Me

eHHO nOBblllIaeTCH,
TO TaK :>Ke Me

eHHO 6y
eT nOBbIllIaTbCH TeMnepaTypa BaHHbI 3, npHqeM
HeKoTopylO pO
b 3
eCb CbIrpaeT H Ten
o, BbI
e
HeMoe 6
aro
apH TpeHHIO
Rn'{f-,I n .!J0m1CTlf '\I[eIIla
Kn. Me'Vlenllhlc 113Ml'IICIIIIH MOH<JIO cqlfTaTL npOHc-
XOAHllJ,HMH BO BpeMeHH no JIHHeHHOMY 3aKQHY. n03TOMY qepe3 Hel<OTopoe


-:J 1 Z

/
/


10
9
B-
7


BpeMH H Ko
6a BCTynHT B perY
HpHblH pe:>KHM, qTO Mbl 06HapY}KHM,
Ha6
IO
aH TeMnepaTYPY B BaHHbI no BTOPOMY EeKMaHOBCKOMY TepMO-
MeTpy.8. Kor
a pa3HOCTb nOKa3aHHH TepMoMeTpa 8 H TepMoMeTpa 7,
O TO-
pbIH nOKa3bIBaeT TeMnepaTYPY u q B ueHTpe llIapa, T: e. pa3HocTb q-
= U - B CTaHeT nocToHHHOH, 3TO H 6y
eT CBH.'J.eTe
bCTBOBaTb 0 HacTY-
n
eH
H perY
HpHoro pe}l{IfMa. Tor
a no (13. 4), r
e r = 3, L = R =
= pa
HYcy llIapa, 3HaH -It/{' onpe
e
HM a. u
BaHHa HMeeT 06'beM npH6
H3HTe
bHo 45-50 A, UHmlH
pHqeCKOH

OpMbI, BbICOTa HeCKO
bKO 60

llIe
HaMeTpa OCHo
aHHH, cHa6:>KeHa
3
eKTpOHarpeBaTe
bHOll 06MOTKOH 9 H Ten
OH30
HUHeH lq. HarpeBaHHe
perY
HpyeTcH TaK, qTO B Me

eHHO B03paCTaeT no
HHeHHOMY 3aKOHY.

 2. CpaBHHTeJlbHblH MeTO
, oCHoBaHHblH Ha TeopHH perYJlSlpHoro
pe*HMa BToporo po
a
ByxcocTaBHwx TeJl (6HKaJlOpHMeTpw)
PaccMoTpHM MeTOJ{ perY
HpHoro pe:>KHMa BToporo po
a, aHa
OrHq-
Hblll TOMY MeTo
y perY
HpHoro pe:>KHMa nepBoro po
a, r
e npHMeHHIOTcH
6HKa
opHMeTpbI (CM. 3TOT TepMHH B
 8 r
aBbI 4). B 3TOM CJIyqae
MO:>KHO oCB060
HTbCH OT He06xo
HMOCTH H3MepHTb K03
qmUH
HT Ten
OOT-

aqH. nO
06HbIH MeTO
 6bI
 npe

O:>KeH E. n. WYPblrHHOH H COCTOHT
B CJIe
YIOllJ,eM. 113 3Ta
OHHoro MaTepHa
a 'H3ro-
TOB
HIOT HapY:>KHoe Te
o N, co Bcex CTOpOH
OKpY:>KalOllJ,ee HCCJIe
yeMbIH 06pa3eu X (<p
r. 124).
I13MepHIOT pa3HocTH TeMnepaTYP B - U Me:>K
Y
BHellIHeH cpe
oH H nOBepx
ocTblO pa3
e
a SS

06pa3ua H «3Ta
OHa» H It - u" Me:>K
Y 3TOif
1l0BepXHocTbIO H UeHTpOM 06pa3ua.
K03<P<PHUHeHT TeMnepaTyponpoBo
HOCTH onpe-

e
HeTCH no npocTOH cpopMy
e


J
I)
5
6


llIapa; B 3TOM CJIyqae TeopHH MeTo
a
cOBepllIeHHo cTpora.
T peT H H MeT O
. Onpe
e
eHHe
C vo1 ' npe
nO
O:>KHM, LITO OnblT npOH3BO-

HTCH B YCJIOBlIHX ex KOHeqHOrO; H3Me-
pHM, Bo-nepBbIX, pa3HOCTb TeMnepaTYP
Me:>K
Y nOBepXHOCTblO 06pa3ua (r
e x=L)
H cpe
OH, T. e. B - UnOB = - &nOB' H,
BO-BTOPbIX, K03<p<pIfUHeHT Ten
OOT
aqH ex;
TOr
a 06'beMHaH Ten
OeMKOCTb C vo1 = CI
BbIqHCJIHTCH no <popMy
e
a (6 --- u noB ) r
C V01 = cr = bi . (13.8)


bL2
a = (u' - u,,) 2f '


(13. 9)


e


s S 5' S
l2=

'

<f>1Ir. 124. K Teopllll
cpaBHlITeJJbHOrO MeTo.na
onpe;\eJleHlIH TenJIOnpo-
BOJ1HOCTII H TeMnepary-
ponpoBoAHOCTII TenJIO-
L 1I30JIHTOpOB,o
HoBaHHo-
fL' (6 - u') - bL.'2f ( - L ' ) ro Ha Teopllll perYJIHp-
A (13. 1 m Horo pe}KIIMa BToporo
1..= 8 ( L ) p0J13: AByxCOCTaBHbI

2r (u' - u,,) aF 77 TeJla (cHMMeTpHlJHble).
EYKBaMH f H F 0603HaqeHbi <PYHKUHH (6e3pa3MepHble Be
HqHHbl) OT
6e3pa3MepHoro reOMeTpHqeCKoro napaMeTpa L/ L'; B CJIY'lae Hoorpa-


r
e r = 1, 2, 3 - CMOTpH no <popMe Te
a.
npH 3TOM 3KcnepHMeHT Be
eTCH TaK, qTO?bI
MO:>KHO 6bI
0 CqHTaTb c06
IO
eHHbIM YCJIOBHe (").
K03<P<P H UHeHT Ten
onpoBo
HOCTH A BbIqHC-

HeTCH no
OBO
bHO CJIO>KHbIM <popMy
aM L
TaKOH 06llJ,eH CTpYKTYPOH: 1


1 J.1H}\eKC «
» OTHOCIiTCH K
Ta,JIOHY.




220


H3MepeHUR U npu6op



HlPleHHoro U:HJ1HH]l.pa I1MeeM:
( L ) ( L ,2 L
f T' = T') - 21n L' ;


F ( f, ) = In Z, .


(13.11)


<DOPMYJ1bI ]l.J151 lllapa H nJ1aCTI1HKI1 CM. (8).
OpH nOCTpoeHlUl KOH]l.YKTI1MeTpOB, npe]l.IIa3HaqeHHblX ]l.Jl51 peaJlI1-
3aLl.I1H MeTO]l.OB, KOTopbIe OCHOBaHbI Ha TeOpl1H perYJl5lpHOro TenJ10BorO
pe)!<HMa BToporo pO]l.a, TPY]l.HO ocy
eCTBI1Tb xopolllee 113MeHeHHe TeM-
nepaTypbI cpe]l.bI co BpeMeHeM no J1IfHeilHoMY 3aKoHY, T. e. (13. 1), B
llll1pOKOM HHTepB3J1e TeMnepaTYp. KpoMe Toro; npl1 3KCnepl1MeHTaX B
YCJlOBI151X ex. - KOHeqHOe ql1CJlO, eCJlI1 06pa3L1.bI 60Jl blllHX pa3MepoB, CI1-
CTeMa He CKOpO BCTynaeT B perYJ151pHbIH pe)!{I1M.
HeCOMHeHHoe npeI-lMy
ecTBo MeTO;'\l1KH - B03MO)!{HOCTb YCTaHOBI1Tb
B npou:ecce onbITa 3aBI1CI1MOCTb TenJlOBblX CBoilcTB a 11). OT TeMnepa-
TYpbl, He MeH5I5I Cpe]l.bI.
MI1HYCOM nOCJle]l.Hero - CpaBHI1TeJlbHOro MeTO]l.a, KaK, BnpOqeM.
H Bcex ]l.pyrl1x CpaBHI1TeJ1bHbIX MeTO]l.OB, 5IBJ151eTC5I HaKOnJ1eHl1e norpelll-
HOCTell, 06YCJlOBJleHHOe HeI136e)!{HOH HeTOqHOCTblO 3HaHI151 TepMl1qeCKI1X
. K03cpcpl1L1.l1eHTQB a 9 11 ).. «3TaJlOHHoro» Be
eCTBa 11 I1X HeCOBepllleHHOH
cTa6HJlbHOCTblO. Hal160Jlee CTa611J1bHOH 5IBJ151eTC5I y]l.eJ1bHa51 TenJ10eM-
KOCTb HeKOTO
bIX 'II1CTbIX MeTaJ1J10B 11 cnJ1aBOB 11 HeKOTopblX XI1Ml1qeCKI1
qHCTbIX ]l.113J1eKTpI1KOB.

 3. OnpeJl.eJ1eHUe TeMnepaTyponpOBOJl.HOCTU no MetoJl.Y
TeMnepaTypHblX BOJ1H
B OCHOBY 3Toro MeTO]l.a n0J10)!{eHO 5IBJleHHe pacnpocTpaHeHI151 TenJ1a
B nOllynpoCTpaHcTBe (11J111 TOJlCTOH CTeHKe, 11J111 CTep)!{H5I 6eCKOHeqHOii
]l.J1I1HbI), KOTopoe 6bIJ10 nO]l.p06HO paccMoTpeHo B
 3 rJ1. 5 11 11J1J11O-
CTpl1pOBaHO cpl1r. 59, 60, 61 11 62.
Ope]l.n0J10)!{I1M, QTO Ha O]l.HOH cTopoHe 06pa3u:a, HMelO
ero cpOPMY
BblT5IHYToro U:I1JlI1H]l.pa 11J111 napaJ1J1eJlenl1ne]l.a, TeMnepaTypa 113MeH5IeTC5I
co BpeMeHeM no 3aKOHY rapMOHI1QeCKOrO K0J1e6aHI151.
3aJ10)!{I1M cnaH TepMonap B]l.OJ1b OCH 06pa3u:a B ]l.BYX TOQKaX . M'
H M", KOOp]l.l1HaTbl KOTOpblX nycTb 113BeCTHbI 11 paBHbI x' 11 x". 060-
3HaQl1M cpa3Y TeMnepaTypHoro K0J1e6aHI151 B KaKOii-J11160 TOQKe M
C KOOp]l.HHaTOH X. 6YKBOii
, B TOQKaX M' H. M" - 6YKBaMH W H W';
B CH
y onpe]l.eJ1eHH5I

=xv a
 ; W=x'V a; I
r (13.12)
Q" - " 1 ---;-
t-'-X -
. aT

YpaBHeHHe ]l.J151 K0J1e6aHH5I TeMnepaTypbI U B TOQKe M OK0J10 CBoero
cpen.Hero 3HaQeHH5I U m B CI1JlY (5. 16) B Hallll1X 0603HaQeHH5IX npl1-
MeT BH]I.:


{-J- = tl- {X, or) = tl- m cas (2'1t-f- -
), .


(16.1.1)


PeZY.llRpHbli1 pe
CUM BTOPOZO U TpeTbezo poiJa


221


r]l.e fi rn 0603HaQaeT aMnJ1I1TY]l.y K0J1e6aHH5I, T. e. Hal1BblClllee OTKJ10He-
Hl1e TeMnepaTypbl U OT urn; OHO paBHO
fin! = Ae-
. (13. 14)
OTHe051 3TO ypaBHeHl1e K TOQKaM M' 11 M", B KOTOpbIX Ha6J11O-
JI.alOTC5I 3HaQeHI151 fi m , r aBHble {}
 11 fi;;', nOJ1Y'II1M ]l.Ba ypaBHeHH5I:
{}
 = Ae- W = Ae- x ' V aTtT ,
fi
 = Ae-[i" = Ae -X" Y aTtT;


no n.eJ1eHlUl O]l.HOrO H3 HHX Ha ]l.pyroe, nOJ1YQI1M


, Y Tt
!I (x"-x')-
m aT'
----,,- = e
!1 m


a OTClO]l.a


a-..!:- [ x"-x' ] 2.
- T in \ :: )
AHaJ10rHQHbIM nYTeM nOJ1YQaeM H3 (13. 12)
'It ( x" - x' ) 2
a=y W'-W .


(13. 15)


(13. 16



I


Op e n.n0J10)!{I1M, QTO H3MepeHbI Hal1BblCllll1e K0J1e6aHI151 TeMnepaTypbI
OK0J10 Cpe]l.HeH Um' I1MeHHO tl-
 H &
, KOTopbIe ]l.OCTl1ralOTC5I B TOQ
Kax M' H M", 11 H3MepeHbI x' 11 x", a TaK)!{e 113MepeHbI <pa30BbIe CMe
e-
HI151 W H
" TeMnepaTypHoll BOJ1Hbl; Torn.a no O]l.HOH 113 q;OPMYJ1 (13. 15)
HJ1H (13. 16) 6Y]l.eT Hall]l.eHa HCKOMa51 TeMnep:1TyponpoBO]l.HOCTb MaTe-
pl1aJla.
OpH npaKTHQeCKOM ocy
eCTBJ1eHHI1 3Toro, OQeHb npoCToro no l1]1.ee
MeTO]l.a, BnepBbIe npl1MeHeHHoro OHrCTpeMoM (1861 r.) K MeTaJ1J1aM, Ha
O]l.HOM KOHLl.e 11J111 cTopoHe 06pa3L1.a nOMe
alOT 3J1eKTpI1QeCKI1H Harpe-
BaTeJIb, HarpY3Ka KOToporo MeH5IeTC5I cTporo no 3aKoHY rapMOHI1QeCKorO
K0J1e6aHI151, QTO n03BOJl5leT peaJ1H30BaTb H rpaHI1QHoe YCJlOBl1e.
LLJl51 HCKJ1lOQeHI151 TenJ10006MeHa Me)!{]l.y 60KOBOH nOBepxHocTblO
06pa3L1.a 11 oKpy)!{alOlll.eH cpen.oH onbIT np0113Bo]l.5IT B BaKYYMe, a 60KOBYlO
nOBepxHocTb nOKpbIBalOT OTpa)!{alO
I1M J1YQHCTYlO 3HeprHlO CJlOeM 11J111
nOJ1l1pYlOT; HHor]l.a npHMeH5IlOT H TenJ10BOe 1130J1l1pOBaHl1e, nOJi b3Y5lCb
BbICoK03cp<peKTI1BHbIM MaTepHaJ10M. HecMoTp51 Ha MO]l.epH113aU:111O pa3-
J1HQHbIX Bapl1aHTOB MeTO]l.a TeMnepaTypHbIx BOJ1H, ero]l.O cero BpeMeHH
HeJ1 b351 CQHTaTb OKOHQaTeJ1 bHO pa3pa60TaHHbIM 3KCnep11MeHTaJ1 bHO 11
]l.OBe]l.eHHbIM ]1.0 npocTOro H y]l.06HOrO o<p0pMJleHI151 B np1160pHO.M BH]l.e;
OCTaeTC5I no]l. COMHeHl1eM, B KaKOH Mepe BJlI151lOT Ha TOQHOCTb H3Mepe-
HHH OTKJ10HeHI151 YCJlOBHH 3KcnepHMeHTa OT Tex l1]1.eaJ1bHbIX YCJ10BHH,
np" KOTOphlX RhIBel1eHhI paCQeTHbIe <pOpMVJ1bI MeTO]l.a.




r JI A B A 14
METO
bl OnPE.LJ.EJ1EHI151 TEnJ10BbIX CBoflcTB MATEPI1AJ10B,
OCHOBAHHblE HA AnEPI10
114ECKI1 113MEH5IIOll.{EMC5I
TEnJ10BOM nOTOKE B HEOfPAHI14EHHOM npOCTPAHCTBE



 t. 30H)J.OBbIe MeTO)J.bI
fpynna 30H)J.OBbIX MeTo
oB pa3pa6aTbIBaJlaCb, rJlaBHblM 06pa30M,
B CCCP A. <D. 4Y}].HOBCKI1M 11 ero COTpY}].HHKaMH [9 J.
l1}].eH, 06
aH }].JlH Bcex MeTO]J.OB, 3aKJlIOqaeTCH B CJle}].YlO
eM. Hcnbl-
TyeMblH 06pa3eLl. yno}].o6J151IOT HeOrpaHl1qeHHOH cpe}].e,' T. e. npe}].noJla-
ralOT, qTO l!M 3anOJlHeHO Bce npoCTpaHcTBo. BHYTPb npocTpaHcTBa
BBO}].HT HCTOqHI1I{ TenJla, I1MelO
HiI (POPMY HJlII I1eOrpaHwleHHoH TOHKOH
nJlOCKOH nJiaCTHHKH, pa3.'l.eJlHIO
ei1: npoCTpaHcTBo Ha }].Ba nOJlynpoCTpaH-
CTBa, HJlH wapa, I1J1H Ll.HJlHHl1.pa (6ecKOHeqHO l1.JlI1HHblii). 3TO H eCTb
«30H}].». BBe}].H ero B 06pa3eLl. - cpe}].y, nOCTynalOT pa3J1HQHo: HJlI1
H3MepHIOT TeMnepaTYPY B KaKoH-HH6Y}].b TOQKe M, y}].aJleHHoH OT 30H}].a,
HJlH H3MepHIOT KOJlHQeCTBO TenJla, cJlY)j{a
ero }].JlH nOCTOHHHoro ero
nHTaHHH. HanHcaB ypaBHeHHe, Bblpa)j{alO
ee TeMnepaTypHoe nOJle
npocTpaHcTBa H BBO.'l.H, eCJlI1 HY)j{HO, MO
HOCTb HCTOQHHKa TenJla, Haxo-
l1.HT H3 HHX TenJlOBbIe K03cpcpHLl.HeHTbI Cpe.'l.bI.
OpH 3TOM }].eJlaeTCH pH)]. }].ony
eHI1H, KOTopble C HeKOTopbIM npH6J1H-
)j{eHHeM }].OJl)j{Hbl 6blTb C06J11O}].eHbI npH 3KcnepHMeHTaJi bHOH pa3pa60TKe
MeTo}].a, a HMeHHO:
I) nOJle TeMnepaTYP npe}].nOJIaraeTCH nOBClO}].Y O}].HOMepHbIM: U =
= u (x, T) HJlH U = U (r, T);
2) I1CTOQHHKH TenJia HMelOT 6eCKOHe1.JHO MaJlb!i-'I onpe}].eJlHIO
HH pa3-
Mep (TOJl
I1HY HJlH pa}].HYc);,
3) B HaQaJlbHbIH MOMeHT BpeMeHH npOCTpaHcTBo HMen BO Bcex TOQ-
Kax o}].HHaKoBYlO TeMnepaTYPY, 3a I1CKJl101.JeHHeM TeX ero MeCT, Ky}].a
BBe}].eH 30H}]..
113 Bceil rpynnbI MeTo}].oB, npHHa}].Jle)j{a
Hx K 3TOH KaTeropHH, MbI
OCTaHOBHMCH Ha CJle}].YlO
eM. OYCTb HCT01.JHHK HMeeT cpOPMY nJiaCTHHKH,
KOTOpOi'I co06
eH 3a 6eCKOHeQHO KopoTKoe BpeMH TenJlOBOil HMnYJlbC,
pacnpOCTpaHHIO
HilcH B HanpaBJleHHH OCH X-OB no BceMY npOCTpaHcTBY
«(jmr. 125). TeopHH nOKa3bIBaeT, 1.JTO eCJlH BeJ1HQHH3 TenJlOBOrO HMnYJlbCa
pa{:\H<1 Qo' TO


I ) QII
U \X,T -- UHO' = V -' e
2 'It.a...


x'
4a<
,


\11.1)


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 '. ,j


AnepuoiJU'IeCKU U3MeHJlIOU{udclI TenAOBod nOTOIC


223


113MeHeHHe C Te1.JeHHeM BpeMeHH TeMnepaTypbl U B cpHKcHpoBaHHoH
T01.JKe M, T. e. B TO'IKe C cpHKCHpOBaHHOH a6CLl.HCCOH x, nOKa3aHO Ha
cpHr. 126: B Ha1.JaJlbHblH MOMeHT BpeMeHH TeMnepaTypa U I <=Ii = uNa.. =
= const; 3aTeM, Kor}].a HMnYJlbC npoHHKaeT B cpe}].y, OHa nOCTcneHHO
nOBblwaeTCH; B HeKOTopblll MOMeHT BpeMeHI1 Tm }].OXO}].HT}].O MaKCHMYMa
U H 3aTeM HaQHHaeT cna}].aTb, CTpeMHCb K U Ha .. npH T -+ 00, TaK KaK
cpe}].a -6eCKOHeQHOe TeJlO H norJlO
eHHe HM KOHeQHOrO TenJia (c e}].HHHLl.bl
nJlo
a}].H nJiaCTHHKH) He MO)j{eT Bbl3BaTb KOHe1.JHOrO nOBblweHHH TeM-


B


II


o


M


r


Tin


x


B'


<I>Hr. 125. K TeapRR 30HJ10BbIX
MeT0J10B:


<I>Rr. 126. 113MeHcHRe C Te'lCHHCM BpeMeH H
TeMncpaTypbI U = U (x, 1:) B TOlJKC M C
3aJ\aHHb1M paccToHHHeM x OT nJIaCTHHKH
BB'. KOrJ11J OJIaCTHHKe C0061l.lCH MrHOBeH-
HblH TenJIOBOH HMOYJlbC.


BB' -HeorpaHlI4eHH8H BeCbM3 TOH

K3D nnaCTHHI<8. norpY>KeHH3S1 B He-
orpaHH
eHHYW O
HOpO

Yw cpe
y
(npocTpaHcTBo); TennOBOH nOTOK q
nOl<838H C O.ll.HOH ee CTOpOHbI.


1


nepaTypbl. 113 cpOPMYJlbl (14. 1), npHpaBHHB HYJllO 1.JaCTHYlO npOH

O}].-
HYlO no T, nOJlY1.JHM cpopI\1YJlY, cBH3bIBalO
YlO x C. Tm' ol K y}].a HaH}].eM


x 2
a= 21: m '


(14. 2)


CJJe}].OBaTeJlbHO, 3aMeTHB TOT MOMeHT BpeMeHH Tm' B KOTOpbIi'I TeM-
nepaTypa U }].OCTHraeT CBOero MaKCHMYMa, no cpopMYJle (14. 2) BbI1.JHCJlHM
H TeMnepaTyponpoBo}].HOCTb a cpe}].bl, B KOTOpylO norpY)j{eH 30H}]..
OpH 3TOM HeT He06xo}].HMOCTH H3MepHTb 3TY TeMl1epaTYPY: nOJlb3YHCb
KaKHM-JlH60 HH}].HKaTopoM TeMnepaTypbl, CJle}].yeT TOJI bKO CJle}].HTb 3a
ero nOKa3aHHHMH H OTMeTIITb TOT MOMeHT, Kor}].a nOKa3aHl1e }].OCTHrHeT
MaKcHMYMa. He Tpe6yeTcH TaK>Ke BeCTH HenpepbIBHo Ha6J1IO}].eHHe, }].o-
cTaTOQHO 3aMeTHTb HaQaJlbHblH MOMeHT BpeMeHH - TOT, Kor}].a 30H}].
norpY)j{eH B cpe}].y, H OTMeTHTb pH}]. MOMeHTOB B6J1H3H Tm - }].O II 110CJle
Hero. 0
OpH npaKTHQeCKOM ocy
eCTBJleHHH MeTo}].a HcnblTyeMbIH MaTepHaJl
nOMe
alOT B H
HK HaCTOJ1bKO 60JlbWHX pa3MepOB, 1.JTo6b1 MO)j{HO 6bIJlO
CQHTaTb }].onYCTHMblM K era cpe}].HeH 1.JaCTH npHMeHHTb ypaBHeHHe (14. 1).
PW
MPrh' YCT3HaB.TIl1R310TCH 3KcnepHMeHTaJlbHO - [9], paBHo KaK H pa3-
Mepbl nJIaCTHHbl-HCT01.JHHKa, KOTOpylO qeJleCOOOpa3HO H3rUlOlUU'b e HH)J.t:




224


H3MepeHuR u npu6op



AnepUOaU'leCKU U3AIeHJIIOU{UUCR TenAOBOU nOTOK


225


TOHKoro JlHCTa TOJIllumOH 0,5-2 MM H3 MeTaJlJla, HanplfMep JlaTYHH;
pa3MepbI ee npH6J1lf3lfTeJlbHO 15 X 10 CM 2 .
OnbIT Be}J.eTC5I TaKHM o6pa30M, 'ITO HarpeTa5I nJiaCTHHa 6bICTpO, B Te-
'IeHHe OT 0,5}J.o 2 ceK., norpY}KaeTC5I B lfCnbITyeMYlOcpe}J.Y. 4YBCTBHTeJIb-
HblH opraH TepMOMeTpa nOMem.alOT Ha np5IMOH, nepneH}J.HKYJl5IpHOH K CTO-
pOHaM nJl3CTlfHKH II npoXO}J.5IWgH 'Iepe3 ee UeHTP, TaK KaK TOJI bKO B6J1lf3lf
:JTOH JlHHHII TenJlOBOH nOTOK He HCKa>KeH (He pacXO}J.5I
I1HC5I) H, XOTH
H C HeKOTopbIM npIl6J1H}KeHHeM, TeMnepaTypHoe nOJle B}J.OJlb ;=nOH JlHHHH
MO}KHO onHcaTb npOCTOH CPOPMYJlOH (14. 1).
Onpe}J.eJlIlTb npH nOMO
H 30H]J.a 3Toro THn8 K03cpqmUHeHT TenJlO-
npOBOLlHOCTH). He npe}J.CTaBJl5IeTC5I B03MO}KHbIM, nOTOMY 'ITO onpe}J.eJle-
HIIe ). CB5I3aHO Bcer}J.a C onpe}J.eJleHHeM TenJlOBorO nOTOKa, a }J.Jl5I 3Toro
Heo6xo}J.HMO 3HaTb q (I1J1H Q) HJlH IX. fl03TOMY }lJl5I onpe}J.eJleHH5I ). cJle-
n:yeT npI1MeHlfTb «H30TepMH'IeCKHlI 30H}J.», T. e. O'IeHb TOHKYlO nJiaCTHHKY
C 3aJlO}KeHHbIM BHYTPH Hee 3J1eKTpOHarpeBaTeJleM, HarpY3Ka KOToporo
npH nOMOIll.H peOCTaTOB perYJlHpyeTC5I TaK, 'ITo6bI TeMnepaTypa ee OCTa-
BaJlaCb nOCT05IHHOH H paBHOH U 1 . Tor}J.a cpYHKUH5I U = U (x, 't) }J.OJl}KHa
Y}J.OBJleTBOp5ITb CJle}J.YlO
lIM YCJlOBlI5IM:
1) B nJlOCKOCTH nJiaCTHHKH - 30H}J.a, T. e. npll x = 0, }J.Jl5I m06oro
. MOMeHTa BpeMeHI1 TeMnepaTypa paBHa const = U 1 ;
2) B Ha'IaJlbHblH MOMeHT 't = ° B Jl1060H TO'IKe npoCTpaHCTBa (cpe]J.bI)
TeMnepaTypa paBHoMepHa H paBHa uno'l;
3) B 6eCKOHe'IHO }J.aJleKHX TO'IKaX npoCTpaHcTBa, T. e. npH x
 00,
TeMnepaTypa OCTaeTCH nOCT05IHHOH Bcer}J.a.
MaTeMaTH'IeCKH 3TII YCJlOBH5I 3anllwYTC5I CJle}J.YlO
HM o6pa30M:
U (x, 't) Ix=o = U (0, 't) = const = U 1 ;
U (x, 't) 1,=0 = U (x, 0) = const = Uno'l;
.
Iim [ au (x, 't) ] = au (00, 't) _ 0.
x-+-oo. ax ax
B aHaJlHTH'IeCKOlf TeopHH TenJlOnpOBOLlHOCTH LlOKa3blBaeTCH, 'ITO
o6
ee peweHHe ypaBHeHH5I <Pypbe B 3TOM cJlY'Iae MO}KeT 6bITb npe}J.-
CTaBJleHO B BH}J.e TaK Ha3bIBaeMoro rayccoBa HHTerpaJia oWH6oK <P (
),
a HMeHHO:


T a6AUlja 7


faYCCOB HHTerpaJI oUIH6oK it> (S)


E I <I> (E) II E I <I> (E) II E I <I> (E)
0.05 0,056 0,75 0.711 1,50 0.966
0,10 0,113 0,80 0,742 1.55 0,972
0.15 0.168 0,85 0,771 1,60 0,976
0.20 0,223 0,90 0,797 1,65 0,980
0,25 0.276 I 1,00 0,843 1,70 0,984
0,30 0,329 1,05 0,862 1.75 0,987
0,35 0379 1,10 0.880 1.75 0,987
--0,40 0.419 1.15 0,896 1,80 0.990
0,45 0,476 1,20 0,910 1,85 0,991
0,50 0,521 1.25 0,923 1,90 0,993
0.55 0,563 1,30 0,934 1,95 0,994
0,60 0,604 1,35 0,944 2,00 0,995
0,65 0,642 1.40 0,952 1
0.70 0.678 1,45 0,960
.


0603Ha'IliM S BeJlH'IHHY nJlO
a}J.H O}J.HOH H3 nOBepXHOCTeH nJiaCTHHKH
H 6YKBOH Q MO
HOCTb, BbI}J.eJl5IeMYlO HCTOLIHHI\OM TenJia II npOHlI3bIBalO-

YlO nOJlynpoCTpaHCTBO (npe}J.nOJlara5I, 'ITO MaTepI1aJl, 3anOJlH5IJOIJJ.HH
Bce npOCTpaHCTBO, O}J.HOpO}J.HbIH H H30TponHblH, a ri03TOMY YCJlOBliH no
06eHM CTOpOHaM nJiaCTlIHKII EE' Ha llmr. 125 - cliMMeTpH'IHbIe). Tor}J.a
BeJlH'IHHa Y}J.eJlbHorO TenJlOBoro nOTOKa, npoxo}J.5I
ero B HanpaBJle-
HHH OX, 6Y}J.eT paBHa


Q
q=-S-


(14. 6)


U] - U ex, 't) _ <P (
),
u] - U'W'I


(14.3)


;:ha BeJlH'IHHa B CHJlY caMoH H}J.eH MeTOJ{a - He nOCTOHHHaH, a eCTb
CPYHKUHH BpeMeHH q = q ('t). .lI.Jl5I nOJlY'IeHH5I ee aHaJlHTH'IeCKoro
BbIpa}KeHH5I BOCnOJlb3yeMC5I OCHOBHbIM 3aKOHOM <pYPbe H npHMeHHM
ero K CJlOlO MaTepHaJla, Henocpe}J.CTBeHHO npHJleralO
eMY (c npaBOH
CTOpOHbl Ha cpI1r. 125) K nJiaCTlIHKe BB', npe}J.nOJIarafl, '1TO npllJlera-
HHe a6COJIlOTHO nJlOTHoe. flOJlb3YHCb BbIpa}KeHH5IMli (14
 3), (14. 4)
H (l4. 5), I1MeeM

 au
oq= q.o-r=-Agrad.u o-r=-I\.(jX'o't=


npH'IeM 3}J.eCb



=


x
2Ya't


(14. 4)


Onpe}J.eJleHlIeM rayccoBa lIHTerpaJia 5IBJlHeTCH paBeHcTBo


-
<P (E) = : it S e- 2 'dz.
u


(14. 5)


OH Ta6YJlHpoBaH; KpaTKa5I Ta6J1Hua - ]J.aHa 3}J.eCb (Ta6J1. 7).


d

 0
=A
.-(1Il-lIntl..)O-r [B CH.TIY (14. a)) =
..
 lb.


15 [{oHJlpaTbeB 2763




226


H3MepeHUR U npU60pM


=}" :'it .e-E"

 (UI-UHa'l)'O't [B CliJIy (14.5H=
_ 2"A -EO 2 ( 0:,
-
r- e .
/- U I - UHa'l) o't [B CHJlY (14.4)] =
r 'It 2 "a'!:


-
. e -Eo (u - u ) .o:,

-
r-I HQ'l 0..
r'lta'!:


OTlIOC5I 3TO ypaBHeHHe K HaqaJlY Koop}J.HHaT, T. e. nOJlara
 X = 0
H yqHTbIBa5l, qTO (e:-E')x=o = 1, nOJlyqHM:
"A
oq =
r- (u I - uHa'l)' o't ,
r'lta'!:


a OTClO}J.a, HHTerpHpY51 nOCJle}J.Hee paBeHcTBo Me>K}J.y npe}J.eJlaMH 'r = Tl
H T = 'r2 H BOCnOJlb30BaBllHlCb paBeHcTBoM (14.6), nOJlyqaeM }J.Jl5I pacxo}J.a
:JHeprHH, 3aTpaqeHHOrO B TeqeHHe BpeMeHH 'r2 - 'rl Ha nO}JJI.ep>KaHHe
nOCT05lHCTBa TeMnepaTypbl nJlaCTHHKH Ha 3a}J.aHHOM ypoBHe Ul, cJle-
}J.YlOljJ,ee BbIpa>KeHHe:
Q


: = :'it S. (u I - UHQ'l)' b. ev 't 2 -
/ T l ). (14.7)
"A .
3}J.ecb Mbl 3aMeHHJlH Va qepe3 TenJlOBYlO aKTHBHOCTb MaTepHaJla b =
= lr ACvol Ha OCHOBaHHH onpe}J.eJl.eHH5I - CM. (7. 1).
BeJlliqHHa, CT05l
a51 B JleBoi'r qaCTH ypaBHeHH5I (14. 7), onpe}J.eJl5leTC5I
H3 3KcnepHMeHTaJlbHoi'r KPHBOi'r, H306pa>KalO
eH H3MeHeHHe C TeqeHHeM
BpeMeHH MO
HOCTH Q, Bbl}J.eJl5leMoi'r 3J1eKTpOHarpeBaTeJleM; npOMe>KYTKH
BpeMeHH T2 H 'rl, npoTeKalO
He C MOMeHTa npHBe}J.eHH5I 30H}J.a B }J.eH-
CTBHe, TaK}!(e HaXO}J.51TC5I no 3ToH KpIlBOi'r; Ul - uHa'i H S - H3BeCTHbIe
BeJlIlqHHbl; n03ToMY H3 ypaBHeHII5I (14. 7) MO>KHO Hai'rTH H BeJlHqHHY b.
3Ha51 ee II H3MepHB a C nOMO
blO 30H}J.a MrHOBeHHoro }J.eHcTBII5I, MO>KeM
onpe}J.eJlHTb II A, I160 A = aC vol H b = 1/ Acvol ' OTClO}J.a cJle}J.YeT,
'ITO A = bVu.
B KaqeCTBe TaKoro 30H}J.a MO>KHO npHMeHHTb TOT }!(e «H30TepMHqeCKHii
30H}J.»I, }J.aB eMY HarpY3KY Ha OqeHb KopOTKoe BpeM5I H BblKJllOqliB nocJle
3Toro 3J1eKTpOHarpeBaTeJlb.
Ho MO>KHO nocTynHTb HHaqe, a IIMeHHO, nO}JJI.ep>KHBa51 TeMnepa-
TYPY Ul nOCT05lHHOi'r, perHCTpIlpOBaTb TeMnepaTYPY U (x, T) B TOqKe M,
I13MeHHlO
YIOCH CO BpeMeHeM, H nOCTpOHTb }J.JlH 3TOH TOqKH 3KcnepIiMeH-
TaJl bHYlO KPHBYlO U = U (T)x-3anaHHoe. 00 3THM }J.aHHbIM CTpOHM
rpaqmqecKH JlCBYlO qaCTb ypaBHeHH5I (14. 3) KaK <PYHKUHlO BpeMeHI1,
nocJle qero no Ta6J1. 7 HaXO}J.HM cooTBeTcTBYlO
Iie 3HaqeHIi5I
 11 no (14. 4)
BblqHCJlHeM IiCKUMoe a.


1 ::hOT TCpMl1II lIem,]R npltll1ftTb YJ\a'lllblM, nOTOMY '1TO OH lie OrpBH<BeT lIJ\eH MeTo.na;
npaBIiJlbHCH 6b1J10 6b1 CKa3aTb CTepMocTaTHpYeMbIH».


AnepuoiJU'lectf,U U3MeHJlfOU{Uu.CR TenAoBoi1 nOTOtf,


227


Ha I}JHr. 127, 128, 129 .u.aHbI cxeMbi nnOCKIiX 30H}J.OB Ii 9J1eKTpHQeCKOH
annapaTypbl K HHM [9].





2


i '
1
.



 .


.'. .".-.'. ..".. . . -." -. ...
-
 r


3


I


IS> 127. CxeMa YCT8110BKH .nJlH onpeJJ,e.leH HH K03qxt m ll.lleliTa TeMnepaTyponP.OBO;.lHOCTit
Hr. no MeTOA)' nnOCKoro 30HJJ,a C MrHOBeHHblM TenJlOBblM HMnYJIbCOM.
. _ 1- n"aCTHH"a _ SOHA' 2 _ TepMonapa; 3 - ranbBaHOMeTPj.6 - 4 - TepMoMeTp; 5 -Hcn"T"Bae"..fI
06pa3eu - .HeorpaHH'IeHHali cpena , 6 - IIUJ.HK.


HJl.eSl 3aJlO>KeHHa51 B OCHOBY YCTpOHCTBa Ll.HnHH}J.pHqeCKOrO II mapo-
BOrO 30H
a, - Ta >Ke, qTO }J.n51 nJlOCKOrO 30H}J.a, HO ypaBHeHIiSl, cJly}!(aw. ne
3tfoHum


Jl epe
o
MemaM


J


c1>Hr. 129. 3neKTpli'lecKaH cxeMa YHHBep-
C8JIbHOro nnOCKoro cH30TepMII'IeCKoro»
30a.na


c1>Hr. 128. CxeMa nnOCKoro
SOH.na MrHOBeHHoro JIeHCTBHH
C 9J1eKTpH'IeCKOH annapaTypoH
K HeMY.
,JI;nSl onIicaHIiH TeMnepaTypHoro nOJl5l, ropa3}J.0 cnO>KHee Ii Be}J.YT K rpo-
MU3 J!. KHM BLlltJla}J.KaM O}J.lIaKO, ecnll IIMPTb B BH.ny RP \{OVInJleKCHOe onpe-
,
 a CTaBHTb 3a}J.aQeIi TOJlbKO
}J.eneHHe repMIiqeCKIiX K03qxlmUHeHToB 1\ H a,
t5.




228


/13MepeHUJI U npU60pbl


onpeJ{eJ1eHHe nOCJ1eJ{HerO H3 HHX, J{J1H 1.Iero BnOJ1He nplHOJ{Hbl 30HJ{b1
MrHOBeHHOrO J{eHCTBUH, TO pacqeTHbIe CPOPMYJ1bl nOJ1yqalOTCH OfleHb
npOCTbIMH, - TOrO )!{e nma KaK (14. 2), a HMeHHO: 1
r 2
a = _ 4 n.J1H U HJ1HH n.pHqeCKOrO 30HJ{a (CM. [9]);
't m


r 2
a = _ 6 )l.J1H wapOBoro 30HJ{a.
'm


B npaKTHqeCKOM OTHoweHHH HaH60J1bWerO BHHMaHHH 3aCJ1Y)!{HBaeT
UHJ1HHJ{pH1.IeCKHH 30Hn.



 2. CpaBHHTeJ1bHble MeToJ{b1, OCHOBaHHble Ha npHMeHeHHH
«HeorpaHH1.IeHHOrO 9TanOHa»
3TH MeTOJ{bI, pa3BIIBaeMbIe no HJ{eHM A. B. .nblKoBa ero COTPYJ{HH-
KaMH, OCHOBaHbI Ha ypaBHeHHHx, cny)!{alll.HX J{J1H onHcaHHH TeMnepaTYP-
HblX noneH nJ10THO conpHKaCalOlll.HXCH Me)!{J{Y C060H TeJ1, OJ{HH H3 KOTO-
pbIX HBJ1HIOTCH HeOrpaHHqeHHbIMH nJ1aCTHHKaMH KOHeqHOH TOJ1Ill.HHbI,
a J{pyme - nOJ1ynpoCTpaHcTBaMH HJ1H HeOrpaHHqeHHbIMH CTep)!{HHMI1
(6e3 60KOBOH TenJ100TJ{aqH) B TOM CMbICJ1e, KaK 3TO 6bIno pa3'bHCHeHO B
 3
r.T!. 5. OJ{HoBpeMeHHo npeJ{nOJ1araeTCH HaJ1HqHe HCT01.lHHKOB TenJ1a,
HanoJ{06l1e Toro, KaK 3TO CJ{eJ1aHO B 30HJ{OEbIX MeTOJ{ax. D,J1H Onl1CaHHH
sm"leHHH paUHOHaJ1bHO npH6erHYTb K BBeJ{eHHIO 6e3pa3MepHoH BenH-
qHHbI - TaK Ha3bIBaeMoro KpHTepHH <1?YPbe, onpeJ{eJ1HeMOrO paBeHCTBOM


Q,
Fo = T2'


(14.8)


rJ{e L - onpeJ{eJ1HIOIll.HH pa3Mep OJ{HOH 113 qaCTeH CHCTeMbI; B paCCMa-
TpHBaeMbIX MeTOJ{ax ::no 6y J{eT n0J10Bv.Ha TOnlll.l1HbI nJ1aCTHHbl, 3aJ10)!{eH-
HOH Me)!{J{y J{BYMH HeOrpaHHqeHHbIMH CTep)!{HHMH. KpaHHe CnO)!{HbIe
MaTeMaTHqeCKl1e Bblpa)!(eHHH, nOJ1yqeHHbIe A. B. .nbIKOBbIM J{a)!{e npH
npeJ{nonO)!{eHHH OJ{HOMCpHOCTH TeMnep<JTypHbIX nOJ1en conpHKacalO-
Ill.I1XCH TeJ1 [9], 3HaQHTe.'lbHO ynpOlll.alOTcH, ecnH OrpaHHQHTbCH cTapWHMI1
Q.T!eHaMH pHJ{OB, QTO .nonYCTHMO npH MaJ1bIX 3HaQeHIfHX KpHTepHH Fo.
npeJ{n0J10)!{eHl1e, I:JTO Fo MaJ1, HBnHeTCH OCHOBOl1 3TOH rpynnbI MeTOJ{OB;
.npyme J{onYlll.eHHH - le )!{e, QTO CPOPMYJ1HpOBaHHbIe paHee B
 I J{J1H
30HJ{OBbIX MeTO):{OB.-
B KaQeCTBe npHMepa npHBe.neM MeTOJ{ M. B. KYJ13KOBa [9]. B ero
OOHOBe J1e)!{HT peweHHe 3aJ{aQH 06 oxna)!{J{emIH 06pa3ua B cpopMe Heorpa-
HHQeHHOH nnaCTHHKH B HeOrpaHHQeHHOH cpeJ{e npl1 HaJ1I1QHI1 MrHOBeH-
Horo nnOCKoro I1CTOQHHKa Tenna, HaXOJ{Hlll.erOCH B cepeJ{HHe nnaCTI1HKI1.
YCJ10BHH no 06eHM CTOpOH3M nJ1aCTHHKH - cHMMeTpI1QHbIe; oKpy)!{aIO-
Ill.He ee «cTep)!{HH» - I If IIHa cpHr. 130 - 11 HBJ1HIOTCH «HeorpaHHQeH-
HbIMH 3TaJIOHaMI1»; CJ1e.L\oBaTeJ1bHO, H3BeCTHbi Bce TenJ10BbIe CBoHcTBa


1 CM. CTp. 210 [9].


AnepuOaU'teCKU U8MeHJlIOU{U/1cJl TenAoBou nOTOK


229


Belll.eCTB3 3THX CTep)!{HeH, a I1MeHHO as' "As, c s ' 1s (CMblcn 0603HaQeHI1H
nOHHTeH). ·
ECJ111 J{aTb MrHOBeHHYIO HarpY3KY 3J1eKTpOHarpeBaTeJ1lO, nOMelll.eH-
HOMY B ueHTpaJ1bHOH nJ10CKOCTH CHMMe'rpHH CI1CTeMbl cpHr. 130, 11 H3Me-
. pHTb TeMnepaTYPy U (x, T) B KaKOH-J1H60 TOQKe OJ{Horo H3 3TaJ10HOB,
paccToHHHe KOTOpOH x OT OJ{HOH 113 CTOpOH nJ1aCTHHKH H3BeCTHO, TO
H3MeHeHI1e 3TOH TeMnepaTypbI C TeQeHHeM BpeMeHH T 6YJ{eT aHaJ10mQHO
onl1caHHOMY B
 I 3TOH rJ1a- I(
anb6aH0lr1emp!J I1cnblmyeMble
BbI (cpHr. 125). B HeKOTO- 06paaIJ.bl
pblH MOMeHT 'BpeMeHI1 Tm
TeMnepaTypa U J{OCTHrHeT
MaKcHMYMa, a nOTOM HaQ-
HeT cnaJ{aTb (BpeMH OTCQI1-
TbIBaeTCH OT MOMeHT3 co06-
lll.eHHH MrHOBeHHoro Ten-
nOBoro HMnynbc3 HarpeBa-
TeJ1 10).
IhaK, 3J{eCb cpHrYPH-
PYIOT J{Be nJ1aCTHHKH, H3ro-
TOBJ1eHHbIe 113 HCnbITyeMoro
MaTepI13J13, COBepweHHO
OJ{HHaKOBbIe: BeCbMa OJ{HO-
pOJ{HbIH MaTepHaJ1, OJ{HHa-
KOBbIe pa3Mepbl.
nYCTb Tm H3BeCTHO, x-
TO)!{e. 3aTeM H3BeCTHO HaH-
60J1b
ee 3HaQeHHe {}.m pa3HOCTH TeMnepaTYP U - U Ha ', = -&, T. e.
{t I - = {}. . TorJ{a H3 BbIweynoMHHYTblX CPOPMYJ1 A. B. .nbIKOBa Bbl-
't-'t m m'
BO.ll.HTCH CJ1eJ{YIOIll.He paCQeTHbIe CPOPMYJ1bI J{J1H "A H a HcnbITyeMoro
MaTepH3J13:


<1>Hr. 130. CxeMa YCTaHoBKH M. B. KYJIaKOB8 .nnH
onpeAeJleHHH TeMnepaTyponI1oBo.nHOCTH H TenJIO'
npoBo.nHOCTH nJIOXO npOBOAHIl.lHX Ten1l0 MaTepHa-
1I0B no Mero.ny «HeorpaHH'IeHHOrO 3TaJIOH8»; I H
II - 6J10KH H3 «3TaJIOHHoro» MaTepHaJIa. KOHAYK-
THMeTp cHMMeTpH'IHOrO THna. llepHbIMH TO'lKaMH
nOMelJeHbI MeCTa pacnOJlO}KeHHH cnaeB TepMonap.


rJ{e 6YKBQH


L2.a s
a=
(Y2a s 't m - x + L)2
"A = 2 - A s yk-1I
II '
k 0603HaQeHa J{p06b
k = ..!!- ,
as


(14. II)


(14. 9)


(14.10)


3 6YKBOH n - BbIpa)!{eHHe
II _ 2
",S Y 1C.ea"m
- Qa
3J{eCb e - OCHOBaHHe HaTypaJ1bHbIX J10rapHcpMOB; u
Q - HarpY3Ka, C0061ll.eHH3H HarpeBaTeJ1lO, - TennOBOH HM-
nYJ1bC;
S - n:nOlll.aJ{b COnpHKOCHOBeHHH HarpeBaTeJ1H C 06pa3UOM
HCl1blTbIBaeMOro Ma rep113n3.


(14. 12)


,




230


W3MepeHUR u npu6op



YpaBHeHHe (14. 9) n03BOJlHeT HaHTH HCKOMoe a, nocJle lIero. H3Me-
pHB Q H 3HaH {)om H Tm' BbIlIHCJ1HeM BcnOMOraTeJlbHYIO BeJlHlIHHY n
H3 (14. 12); HaKOHeu, no (14. 10) BbllJHCJlHeM A.
Ha (!mr. 130 u 131, 3aHMCTBOBaHHbIX H3 MOHorpacpm1 A. <1>. JIbiKoBa,
npe
CTaBJleHa cxeMa TOJlbKO LITO onHcaHHoro MeTo
a U eMY pO
CTBeH-


3


f JI A B A 15


3AI<.J1104I1TEJ1bHbIE 3AME4AHI151 I<. rJ1ABAM 6-14



 1. l<.o9!JJ!JJHLl.HeHTbl A, a, c vo1 KaK TeXHI1'JeCKHe xapaKTepHcTHKH
MaTepHaJlOB


<1>Hr. 131. CXeMa OJ1HOm H3 BapHaHToB MeTo.na «Heorpa.
HHlJeHHOrO 3TaJIOHa»:
1- 9TaJlOHHbl.. KaJlOpHMeTp - .HeorpaHH4eHtJaD" cpeJla; 2 - JlH<)J<)JepeH
UHaJlbHBD TepMonBpa; 3 - rBJlbBBlloMeTp. 06p83eu 1I0pOUIKOofipB3Horo
M3TepH3n3 HaCbmaeTCIl B BbleMKY BHYTP" 9TanOHHoro Tena.


Cnoc06HOCTb JlI060ro BellJgcTBa nponYCKaTb TenJlO lJUCJleHHO xapaK-
TepH3yeTcH KO:J(pcpHuueHTOM TenJlOnpOBO
Hocrn A; ero cnoc06HoCTb
aKKYMYJlUpOBaTb TenJlO - 06'beMfIOH TenJlOeMKOCTblO c vol ' MHorue Eer.u;e-
CTBa, C KOTOpbIMH UMeeT
eJlo cpu3uKa, npe
CTaBJl5IIOT C060H TBep
bIe
TeJla (HenpepbIBHYIO cpe
y), H K HHM C
OCTaTOlJHOH CTporocTblO MO)j{eT
6bITb npHMeHeH saKOH <1>YPbe, CJlY)j{aIIJ;HH
JlH MaTeMaTHlJeCKOrO onu-
caHHH nepe
alJH TenJla B HHX. Ho OlJeHb MHorHe TeXHHlJeCKHe MaTepHaJlbl,
B lJaCTHOCTH TeXHHlJeCKUe TenJlOH30JlHTOpbl, orpoMHoe 60JlbllJHHCTBO
cTpOHTeJlbHbIX MaTepHaJlOB, a TaK)j{e nopollJKo06pa3HbIe H BOJlOKHHCTbIe
MaTepHaJlbI, rPYHTbI, nOlJBbI 1 H T.
., OTHIO
b He HBJlHIOTCH TBep
bIMH
TeJlaMI-I B TOM CMbICJle, KOTOpblH npH
alOT 3TOMY CJlOBY B TeopUH TenJlO-
06MeHa H B cpH3HKe, a npe
CTaBJlHIOT C060H CUCTeMbI 113 OlJeHb 60JlbllJOrO
lJHCJla TBep
bIx lJaCTHU, OT
eJleHHbIX
Pyr OT
Pyra nopaMH pa3J1UlJHOH
cpOpMbI 1-1 pa3MepoB, 3anOJlHeHHbIMH ra30M (lJar.u;e Bcero B03
YXOM) UJIU
)j{U
KOCTblO HJlH CMeCblO HX 060HX. Ha cpHr. 132 npe
CTaBJleHbI cxeMaTU-
lJeCKH p33J1HlJHbIe THnbl MaTepua.TJOB :noro pOlla. nepe
alJa TenJlOBOH
3HeprHu B HUX CJlaraeTCH U3 nepe
alJu TenJla TenJlOnpOBO
HOCTblO lJepe3
TBep
bIiI nopo06pa3YIOIIJ;HH CKeJleT, TenJlOnpOBO
HOCTblO H KOIIBeKUHeiI
lJepe3 nopbI H H3J1YlJe
llfeM Me)j{
Y CTeHKaMH nop. Ka)j{
oe U3 KOJlUlJeCTB
TenJlOBOH 3HeprHH, nepe
alOIIJ;eecH JlI06b1M U3 3THX cnoc060B, MO)j{HO
npU6J1H)j{eHHo ClJUTaTb nponopu.uoHaJlbHbIM pa3HoCTH TeMnepaTYP
u - u'
ByX npUJle)j{ar.u;Hx u30TepMHlJeCKHX nOBepxHocTeH (ecJlu TOJlbKO
nopbI He lJpe3MepHO BeJlHKH). n03TOMY npUHHMaIOT, lJTO MaTeMaTHlJeCKH
CYMMapHbllf npou.ecc Ten.;IOnepe
alJH U B TaKUX MaTepUaJlax npOHCXO
UT
cor
aCHO 3aKOHY (I. 3) <1>ypbe, HO no
 A CJle
yeT Y)j{e nOHUMaTb YCJlOB-
HblH K03CPCPuUHeHT, KOTOpblH lJHCJleHHO xapaKTepu3yeT cBoikTBO Ma-
TepUaJla nepe
aBaTb TenJlOBYIO 3HepruIO o
HoBpeMeHHo BceMil YKa3aH-
HbIMH cnoc06aMH. Yno
06J1eHHe TeXHHlJeCKOrO MaTepUaJla cpH3HlJecKOMY
TeJlY, T. e. HenpepbIBHoH cpe
e, 6y
eT TeM 6J1u)j{e K J.1CTaHe, lJeM M,Hbllle
KpynHHKH UJIH B.OJlOKHa MaTepHaJla no cpaBHeHHIO C pa3MepaMH Te.'la,
1 «llHcnepCHble Te.
a» HJIH «AHcnepcHble cpeAbI» no TepMHHOJIOrHH A. <1>. 4YAHOB'
CKoro (9).


Horo [9]. ll.Hcppbl jKa3bIB31OT pa3MepbI OT
eJlbHbIX 3J1eMeHTOB YCTaHoBKH
B MUJlJlHMeTpax. MrHoBeHHbIll: UCTOlJHUK TenJla - TOHKaH MeTaJlJll1lJe-
CKaH nJlaCTHHKa, HarpeBaeMaH 3J1eKTpHlJeCKUM TOKOM B TelJeHHe KOPOT-
Koro BpeMeHH (0,5-2,5 celc), BBO
HTCH B nJlOCKOCTb CUMMeTpUH nJla-
CTHHKU, 06pa30BaHHOH
BYMH nJlaCTHHKaMH HCnblTbIBaeMOro MaTepUaJla.
3,AeCb HeT He06xo
HMOCTH BBO
HTb cnau TepMonap B HCCJle
yeMbIH
MaTepUaJl, O
HaKO He06xOAUMO HX BBeCTU B 3TaJlOHHble napaJlJleJlemme
b1
(CM. TOlJKU Ha cpur. 130).




232


/13MepeHUJI U npU60pb!


HSrOTOBJleHHOrO HS ,noro MaTepHaJla; TaK, HanpHMep, CJlOH neCKa TOJl-
IllHHOH 30 M.M npH pasMepax neCqHHOK npHGJlHSHTeJlbHO 0,3-0,5 .M.M
H TaKHX }Ke HJlH MeHblllHX pasMepax nop npaKTHqeCKH Be.n.eT ceGSI KaK
CnJlOlliHOe -TeJlO.
TOqHO TaK }Ke YCJlOBHbIH CMbICJI npHoGpeTaeT H K03(pqmLl.HeHT TeMne-
paryponpOBO]l.HOCTH H BH]l.HMaSl nJlOTHOCTb HJlH oG'beMHbIH Bec; qTO }Ke


5'
.' _ c, /2
o} 6} 6}
L 1)
\
t: L
:
z) o}


<1>Hr. 132. CXeMbI CTPYKTypbl pa3JIH'IHbIX TenJIOH30JIHUHOHHbIX CTpOHTeJIbHblX MaTepHaJIOB:
a - nopHcThll! MaTepllaJi C COOOl1l.alOl1I.lIMIICQ nopaMII: 1 - T8epJlhlM cKeneT; 2 - nopbl; 6 - nopHcThifi
MaTepHaJi C 3aMKH}'ThlMH nopaMII: 1 - T8epJlbIM KOMnOHeHT; 2- ra3 (B03J1YX '1al1l.e Bcero); B - 3epHIICThiM
M8TepH8n: / - 3epHa; 2 - nopbl, 38nOJIHeHHble ra30N. >KH.lI.KOCTblO HJlM CMeCblO >KHAKOCTH H raJOB:
a -BOJlOKHHCTblH M8TepH8n c ynopSl.ll.Ol.J.eHHblM, npaBHJlbHblM pacnOJlO>KeHHeM BOJlOKOH; d"- BOJlOKHRCTblA
M8TepH8n C HeynopSl.ll.o1..leHHblM pacnOJlO>KeHHeM BOROKOR.


KacaeTCSI Y]l.eJlbHOH HJlH oG'beMHOH TenJlOeMKOCTH MaTepHaJla, TO, 6Y]l.yqH
TenJlOeMKOCTblO e]l.HHHLl.bI BeCa HJlH MaCCbI, 3TH BeJlHqHHbI HenOCpe]l.-
CTBeHHO CBSlSaHbI C 3anaCOM TenJlOBOH ::meprHH H COXpaHSllOT qmSHqecKHH
CMbICJI.



 2. 0 BbI60pe MeTO]l.OB onpe.n.eJIeHHSI TenJIOBblX CBoifcTB MaTepHaJIOB
3]1.eCb MbI 6Y]l.eM rOBopHTb 0 TeXHHqeCKHX TBep]l.bIX MaTepHaJlaX,
npeHMYIlI.eCTBeHHO 0 ]l.H3J1eKTpI1KaX, TenJlOHSOJlSlLlHOHHbIX H CTpOHTeJlb-
HbIX MaTepHaJlax.
o MeTO]l.aX, npHrO]l.HbIX ]l.JlSI onpe]l.eJleHHSI A MeTaJlJlOB, - CM.
rn. 7.
Bonpoc 0 TeXHHqeCKHX }KH]l.KOCTSlX CTaBHTCSI ropas]l.o pe}Ke; HS MeTO-
]l.OB, oCHoBaHHbIx' Ha cTaLl.l:I0HapHOM TenJlOBOM pe}KHMe, HaH60Jlee pas- .
paGoTaHbI ]l.JlSI }KH]l.KOCTeH, Bo-nepBbIx, MeTO]l. HarpeTOH npOBOJlOKH, no
H]l.ee TO}K]l.eCTBeHHbIH C «MeTO]l.OM TPy6bI», onHcaHHbIM B
 8 rJl. 6
[13]; BO-BTOPbIX, MeTO]l. TOHKOH nJleHKH, npe]l.CTaBJlSllOIllHH C060H pas-
HOBH]l.HOCTb MeTO]l.a O]l.HOH nJlaCTHHKH [10]; HS MeTO]l.OB, OCHOBaHHbIX
lid IJCl:JaLl.ltulJdpIlUM lellJlOBUM pe}\<IIMe. onpaB]l.aJl c('6f1 MCTO;l I1wp0(Joro
OHKaJlOpHMeTpa [3] .


3aKAIO'lUTeAbHbte 3aMe'laHUJI K ZAaBaM 6-14


233


Y]l.eJlbHaSl TenJlOeMKOCTb MeTaJlJlOB SlBJlSleTCSI BeJlHqHHOH, XOpOlliO
H3yqeHHOH; qTO }Ke KacaeTcSI Y]l.eJlbHOH TenJlOeMKOCTH ]l.H3J1eKTpHKoB
H TeXHHqecKHX TenJlOHSOJlSlTOpOB, TO ]l.JlSI HHX Ll.eJlecooGpasHee Bcero
npHMeHSlTb MeTO]l.bI, ]l.OnYCKalOIllHe KOMnJleKCHOe onpe]l.eJleHHe A, a, C,
KOTOpbIM 6bIJlO Y]l.eJleHO ]l.OCTaTOqHO BHHMaHHSI B npe]l.bI]l.YIlleM HSJlO}Ke-
HHH.
B TeXHHKe BCTpeqaeTCSI orpoMHoe qHCJlO BceBOSMO}KHbIX nJloxo
npoBo]l.SlIlI.HX TenJlO MaTepHaJlOB, H HX qHCJlO HenpepbIBHo BospacTaeT;
npHMeHSllOTcSI OHH B BeCbMa paSJlHqHbIX BH]l.ax - B <POp Me TOHKHX JlH-
CTOB, nJlHT, KHp'nHqeH, nopHCTbIX neHOMacc (HanO]l.oGHe Ty<p a ) H T. ]I..
Hx CTPYKTypa H CTeneHb O]l.HOpO]l.HOCTH OqeHb pasHo06pasHbI (<p HL 132).
Z


<1>Hr. 133. CxeMa CTpYKTypbl 06pa3ua HeOJ1HOpoAHoro MaTe-
pHaJla, 3aJIO}KeHHOro B nJIOCKHH npH60p:
x - TOJll1l.lIHa 06pa3Lla: 1. 2 - JIBe pa3J1H'IHbIe KOMnOHeHThi (OJlHa 113
IIHX MO>KeT 6h1Tb ra30M).


HHOr]l.a Bce nopbI HMelOT OqeHb 6J1HSKHe ]l.Pyr K ]l.pyry pasMepbI H <POPM}
HMeHHo TaKHe renJlOHSOJlSlTOpbl H cTpeMSlTcSI cos]l.aBaTb B HacToSlIllee
BpeMSI; O]l.HaKo, H3-sa HecoBepllleHcTBa TeXHOJlOrHH HSrOTOBJleHHSI MaTe-
pHaJlOB 3TO He Bcer]l.a ]l.OCTHraeTCSI: Ha
Hr. 133 npe]l.CTaBJleHa cxeMa
CTpYWrypbI TaKoro MaTepHaJla; npHMepoM ero MO}KeT CJlY}KHTb HeOTCOp-
THpOBaHHaSl saCbtnKa H3 sepeH lllJlaKa HJlH nJloxo HsrOTOBneHHoe neHO-
CTeKJlO.
3TH CBoHcTBa MaTepHaJlOB npe}K]l.e Bcero H npHXO]l.HTCSI npHHHMaTb
BO BHHMaHHe npH pellleHHH Bonpoca 0 <popMe H pasMepax 06pasLl.a ]l.JlSI
HCnblTaHHSI Ha TenJlVnpOBO]l.HOCTb H 0 BbI60pe MeTO]l.a HcnbITaHHSI.
Cne]l.yeT yqHTbIBaTb TaK}Ke H TO oGcToSlTeJlbCTBO, qTO MHorHe MaTepHaJlbl
COCTOSIT He TOJlbKO HS O]l.HOro KaKOrO-JlHGo BeIlleCTBa 60Jlee HJlH MeHee
nopHCToro. a npe]l.CTaBJlSllOT COGOH MHorOKOMnOHeHTHbIe oGpasoBaHHSI:
HanpHMep: GeTOH, HCKYCCTBeHHbIH KaMeHb H npHpO]l.HbIH KOHrJlOMepaT,
cxeMbI KOTOpbIX ]l.aHbI Ha
HL 134, a H 134, 6.
PasMepaMH H <popMoiI sepeH KOMnOHeHTOB H creneHblO O]l.HOpO]l.HOCTH
MaTepHaJla onpe]l.eJlSleTCSI npe}K]l.e Bcero OCHOBHOH pasMep oGpasua
]l.JlSI HCnblTaHHSI: OH MO}KeT GbITb BSSlT TeM MeHbllle, qeM GOJlee O]l.HOpo]l.eIl
MaTepHaJl; TaK, HcnbITbIBaSl oGbIKHoBeHHbIH KapToH, nJloTHYlO pesHHY.
MO}KHO TnnUtHHy'onpaSItOR .'\()RPCTJ-I
n HPC'KO.TJJ,KHX MH.IIJ1HMeTpoB: Hcnbl'
Thma
 6
TOHbI. ocoGeHHo }Ke 'fe, KOTopbIe npHMeHSllOTcSI B m.ll.P0Te
HH'




234


H3MepeHUR U npu60pu


3aKAIO'tUTeAbHbte 3aMe'taHUR K i?AaBaM 6-14


235


qeCKHX cOOpY>KeHHHX, npI1Xo}J.HTCH 3Ha'IHTeJlbtlO YBeJlJlqHBaTb OCHOB-
HOH pa3Mep 06pa3Ua, }J.OBO}J.H era}J.o 30-40 CM H }J.a>Ke 60Jlee. Bo06
e
H3 CKa3aHHoro BbIwe HCHO, 'ITO qeM 60JlbWe Heo}J.HopO}J.HOCTb TeXHlJlle-
CKoro MaTepnaJla, TeM OOJlbWnX pa3MepoB npHxO}J.HTCH BbI6npaTb-
npl1 npoqnx paBHbIx YCJlOBHHX - 06pa3eu, qT06bI nOJlyqHTb ocpe}J.HeH-
HbIe UH<PPbI, xapaKTepH3YlOLU,l1e npo}J.YKUHlO B ueJlOM. .lI.a>Ke npB Y}J.o-
EJleTBOpnTeJlbHOM KaqeCTBe MaTepnaJla Ha6J11O}J.alOTcH BapnaUI1B B 06'beM-
HOM Bece KYCKOB, BbIHYTbIX H3 OT}J.eJlbIIbIX 'IaCTeH 6J10Ka l1J1n OT}J.eJlbHbIX
n3}J.eJlHH (nJlnT. Kl1pnn'IeH n T. }J..).


0)


4


TepMonapy BHYTPb 06pa3ua: }J.JlH HI1X CJle}J.yeT OCTaHOBHTbCH Ha nJlOCKOM
611KaJlOpHMeTpe A. <D. EerYHKoBoH (
 3, rJl. 12) nJlI1 Ha MeTO}J.e nJlaCTnH-
Kn. VI3}J.eJlHH, KOTOpbIM npH}J.aHa <PO pM a CKOpJlyn (<pl1r. 82), BbIrO}J.HO ucnbI-
TblBaTb no MeTo}J.Y TPy6bI BaH-PI1HcYMa, onHcaHHoMY B
 8 rJl. 6. HaH-
60Jlee YHuBepcaJlbHbIMl1, B CMbICJle OXBaTa MaTepHaJlOB, HBJlHeTCH rpynna
MeTO}J.OB, OCHOBaHHblX Ha TeopHn perYJlHpHOrO pe>KI1Ma nepBoro pO}J.a:
C HX nOMOllJ.blO 6bIJlU u3MepeHbI A 11 a OqeHb pa3J1HqHbIX MaTepHaJlOB,
HaqnHaH OT «JlerqaHWnX» neHOnJlaCTOB (I1nOpKI1) C 06'beMHbIM neCOM
nopH}J.Ka 10-15 KclM- s n KOH'IaH nJlOTHblMU ropHbIMH nopo}J.aMH U Me-
TaJlJlaMH. Pa3MepbI 06pa3uoB KOJleGaJlliCb OT IJ,fIJlnH}J.pHKoB }J.HaMeTpoM 3
11 BbICOTOH 4 CM }J.O UHJlI1H}J.pH'IeCKHX 6J10KOB n3 6eToHa }J.HaMeTpoM B 50 CM
11 BbICOTOH 100 CM.
B arpo<p113liKe H reoJlonm na>KHOe 3HaqeHHe HMeeT 3a}J.aqa 06 U3Me-
peHHH TenJlOBbIX CBOHCTB nO'IB, rpYHToB 11 ropHbIx nopo}J., KaK BbIpa-
>KaIOTCH, in situ, T. e. B YCJlOBHHX ux eCTeCTBeHHoro 3aJleraHHH, 6e3
BbIeMKI1 06pa3uoB. E}J.uHcTBeHHbIMH MeTO}J.aMH, npHro}J.HbIMH }J.JlH pewe-
HUH 3TOH 3a}J.a'II1, HBJlHlOTCH 30H}J.OBble, Onl1CaHl1e O}J.HOr? H3 KOTOpbIX
}J.aHO B
 1 rJl. 14; HaH60Jlee Y}J.06HbI UI1J1HH}J.pnqeCKl1e 30H}J.bI.
06pa3qnKn nCnbITblBaeMOro MaTepnaJla cJle}J.yeT nPul1rOTOBJlHTb, Bbl-
pe3aH HX n3 nJlI1T, KUpnUqeH U npo'Inx Bn}J.OB U3}J.eJlI1li, COCTaBJlHlO
HX
TeKYllJ.YlO npo}J.YKUl1lO 3aBO}J.a, a He nopyqaTb 3aBO}J.Y 113rOTOBJleHHe
OC06bIX 06pa3UOB, nO}J.orHaHHblX no}J. }J.aHHbIH npl160p; 3TO He }J.aCT
npaBHJlbHOrO npe}J.CTaBJleHI1H 0 KaqeCTBe npO}J.YKunn.


<1>Rr. 134. CxeMbI CTpYKTYpHoro CTpoeIlHH:
a - 6eToHa: 1 H 2 - MenKHe H Kpym-Ible 3epH8 rpam-IR; 3 - 3epHa necHa; 4 - l.leMeIlTHbIH KJleH;
6 - np"poluIOro KOHrnoMepaTa.


Pa3MepaMl1 U <pOpMOlI 06pa3Ua II MeXaHUqeCKI1MU CBOlICTBaMIJ Ma-
TepliaJla onpe}J.eJl5IeTC5I BbI60p MeTO}J.a U KOHCTPYKUUH npn60pa. nO npn-
qnHe, Y>Ke paHee OTMeqeHHOH, KpaHHero pa3Ho06pa3HH CBoifcTB li IImpo-
KliX Bapnaumi A li a MaTepl1aJlOB, HeT B03MO>KHOCTli OXBaTI1Tb Bce Ma-
TepHaJlbI KaKHM-JlIJ60 O}J.HHM MeTO}J.OM H npu60poM: CJle}J.yeT BbI6upaTb
TOT MeTO}J., KOTOpbIH HaH60Jlee COOTBeTcTByeT oc06eHHOCHIM MaTepl1aJla
n YCJlOBU5IM ero 3KCnJlyaTaUHH. HanpliMep, }J.Jl5I HaCbInHbIX MaTepliaJlOB
BpO}J.e neCKa 6Y}J.eT npnrOJJ.eH MeToJJ. wapa (
 9 rJlaBbI 6) ltJln KaKOH-JlI160
li3 MeTO}J.OB perYJlHpHOrO pe>KIIMa (
 1 rJl. 9 U 1'p) H MaJlO npuro}J.HbI
MeTO}J.bI nJlaCTUHKI1 (
 4 11 5 rJl. 6) HJlII MeTO}J. HeOrpaHI1'IeHHOrO
3TaJlOna. Ha060poT, }J.Jl5I O}J.HOpO}J.HbIX H MeJlKOnOpHCTbIX TenJlOIl30JlH-
UHOHHbIX li CTpOUTeJl bHbIX MaTepHaJlOB ueJleC006pa3Ho npHMeHHTb
MeTO}J.bI nJlaCTHHKH; OHU 6Y}J.YT npHro}J.HbI n }J.JlH onpe}J.eJleHH5I A 3TaJlOH-
HbIX M3TepnaJlOn. MeTo}J. HeOrpaHII'IeIIHOrO 3TaJlOHa U eMY nO}J.o6HbIe,
5IBJlHlOllJ.lIeCH cBepxCKopOCTHblMH MeTO}J.aMI1 (n60 O}J.Ha 113 nx rJlaBHbIX
npe}J.nOCblJlOK - MaJlOe Fo, T. e. MaJlOe or), npHrO)J.Hbl }J.Jl5I ncnbITaHU5I
nJlOTHbIX MaTepnaJlOB, HanpUMep pe3UHbI. D,JlH HCnbITaHI1H BbICOKO-
3Q:JQ:JeKTUBHbIX TenJlOH30JlHTOpOB OqeHb MaJlOH nJlOTHOCTI1 - OT 100
}J.O 10 Kc M- 3 - He npl1rO}J.HbI Te H3 MeTO}J.OB perV.THlpHOrO PP}!{J-IM
,
VlIHcdHHble 11 IJI. !:J 11 10_ KUTopbIe CBH3aHbI C He06xoJJ.HMOCTblO BBO}J.lITb



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X K03Q:JQ:J"
UeHTOB
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A, a, C npu I1CnbITaHHflX O}J.HOpO}J.HbIX MaTepUaJlOB. u
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eH cxeMe
Q:Jur. 67 - u}J.ee MeTO}J.a U cxeMe Toro H}J.eaJlH3UpOBaHHoro TenJlOBOrO
HBJleHnH, KOTOpOE} MaTeMaTHqeCKI1 onHCbIBaeTCH npn nOMOllJ.n TeopHH
MeTO}J.a li BblBe}J.eHHbIX H3 3TOH TeopHH paC'IeTHbIX <POPMYJI.
n p H Me p bI: I) B MeTO}J.e HeOrpaHl1qeHHOrO 3TaJlOHa (
 2 rJl. 14)
npe}J.nOJlaraeTCH OTCYTcTBue 60KOBbIX YTe'IeK TenJla B napaJlJleJlenune}J.e.

KonHpYlO
eM nOJlynpocTpaHcTBo; npe}J.nOJlaraeTCH, qTO Buecb TenJlOBOH
nOTQK Q OT HarpeBaTeJlH npoxo}J.HT napaJlJleJlbHO }J.JlHHHOI1 OCB 3TaJlOHa
(OCH X-OB Ha <pBr. 58); 2) TPy6Ka }J.JlH BBO}J.a BHYTPb MaTepHam TepMonapbI
B aKaJlOpllMeTpe pery Jl5IpHOrO pe>KHMa nepBoro pO}J.a (
 1-3 rJl. 9)
liCKa>KaeT ero TenJlOBOH pe>KI1M; 3) YCJloBHe a
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CTBHe nJlOTHOrO conpnKocHOBeHH5I Me>K}J.Y OT}J.eJlbHbIMH 'IaCT5IMH Cl1CTeMbI,
06pa3YlO
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(2.21) Ha rpaHHue conpHKocHoBeHHH. I
2. CTPYKTypa paCqeTHbIX <POPMYJI H oc06eHHocTH, npncY
He BXO-
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236


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TaK qTO OHa - pe3YJlbTaT 60Jlee HJlH MeHee CJlO)!{HbIX MaTeMaruqeCKHX
Onep
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3, 4, 5 rJl. 9 Ha npHMepe aKaJlOpHMeTpa perYJlHpHoro
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qeHHH BJlHHHHH cJlyqaHHblX OlllH60K H3MepeHHH He06xo}J.HMO MHorOKpaT-
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HOCTH, npHqeM BH}J. CPYHKlJ,HH F MO)!{eT 6bITb TaKHM, qTO }J.a)!{e He3Ha-
qHTeJlbHaH norpelllHOCTb B onpe}J.eJleHHH KaKOrO-JlH60 H3 napaMeTpoB A,
CH.lJbHO OTpa3HTCH Ha 3HaqeHHH X. .
B KaqeCTBe npHMepa MO)!{HO npHBeCTH onpe}J.eJleHHe A no BTOPOMY
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npH 60JlblllHX 3HaqeHHHX KpHTepHH H: H3 OnbITa HaXO}J.HM M (H60 a
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H = H (M), nOJlyqaeM HCKOMoe A, T. e. X; HO H3 Ta6J1HlJ,bI Herne HarJlH}J.-
Hee H3 rpaqmKa (cpHr. 47) cpa3Y BH}J.HO, qTO B 3THX YCJlOBHHX 3KcnepH-
MeHTa }J.a)!{e He60JlblllaH OlllH6Ka B M - }J.PyrHMH CJlOBaMH, B m - BbI30-
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Tlll.aTeJlbHOe H3yqeHHe CTPYKTYPbI CPOPMYJI H cpH3HKH HBJleHHH, Ha
KOTOpOM OHH OCHOBaHbl, n03BOJlHeT H36e)!{aTb olllH60K 3Toro pO}J.a.
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CTOJlbKO CJlO)!{Ha, qTO oueHKa norpelllHOCTH onpe}J.eJleHHH X npe}J.CTaB-
JlHeTCH 3aTPY}J.HHTeJlbHOH. OpHMepOM MorYT CJlY)!{HTb paCqeTHbIe cpop-
MYJlbI (14. 10) H np. }J.JlH onpe}J.eJleHHH A no MeTo}J.Y HeOrpaHHqeHHOrO
3TaJlOHa: 3]J.eCb n = 7 (X eCTb A, A, - CYTb: ag, As' {}.m' Tm' S, Q, a).
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cpopMYJla ropa3}J.0 npOlll.e-CM. (10. 2), (10. 3), (10. 4). B MeTO}J.e 30H}J.a
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3. I1CTOqHHKaMH OlllH6oK npHHlJ,HnHaJlbHOrO xapaKTepa HBJlHIOTCH:
B MeTO}J.ax CTalJ,HOHapHoro TenJlOBOrO nOTOKa - TPY}J.HO YJlaBJlHBaeMble
MaJlbIe OTKJlOHeHHH TenJlOBOrO pe)!{HMa KOH}J.YKTHMeTpa OT cTauHoHap-
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nepaTypHble pa3HoCTH B OT}J.eJlbHbIX qaCTHX 06pa3lJ,a MaTepHaJla, qTO
CTaBHT
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OCHOBHOH npe}J.noCbIJlKOH KOTOpbIX HBJlHeTCH He3aBHCHMOCTb A, a, c, c vol
OT TeMnepaTYP; 3TO oc06eHHo nO}J.qepKHBaJlocb B
 1 rJl. 8.
TpY}J.HOCTH TenJlOBbIX H3MepeHHH 3aCTaBJlHIOT C OC06blM BHHMaHHeM
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CHCreMaTHqeCKHe OlllH6KH }J.aHHoro npH60pa, KaK BbITeKalOlll.He H3 TOJlbKO
qTO YKa3aHHbIx 06CTOHTeJlbCTB, TaK H 06YCJlOBJleHHbIe norpelllHocTHMH
KOHTpOJlbHO-H3MepHTeJlbHOH annapaTYPbl - I I cpHr. 67 (TepMonap,
nOTemUfOM£'Tpn, rn.'II.na IIOM£'Tpn,.....) - II HenOJl3}J.KaMIl B JIll IIH II
CBH3H I I I (nepexo}J.HbIe conpOTHBJleHHH KOHTaKTOB, napa3HTHble



 4. 06 OC06blX cJIYLJaSix onpe.n.eJleHHSI A a, C HeKoTopblX TeXHHLJeCKHX
MaTepHaJIOB H u3.n.eJIHU
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MarepHaJlbl B npouecce HX 3KcnJlyaTauHH MorYT YBJla)!{HHTbCH. HaJlHqHe
}J.a)!{e He3HaqHTeJlbHbIX CJle}J.OB BJlarH, KOTopaH MO)!{eT npHCYTcTBoBaTb
B BH}J.e ra3a, )!{H}J.KOCTH HJlH HaCbIlll.eHHoro napa, - nopH}J.Ka 3-5 npo-
ueHTOB no Becy ,- y)!{e 3aMeTHO OTpa)!{aeTCH Ha TenJlOBbIX K03CPCPHuHeHTax
MaTepHaJla, YXY}J.lllaH ero TenJlOH30JlHlJ,HOHHbIe CBOHCTBa. B TaKHX )!{e
Belll.eCTBaX, KaK nOqBbI H rpYHTbI, HaJlHqHe BJlarH HBJlHeTCH HOpMaJlbHblM
HBJleHHeM. .
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MeHHTb TOJlbKO MeTO}J.bI HecTaUHoHapHoro TenJlOBOrO nOTOKa; BO-BTOPbIX,
BeCTH 3KcnepHMeHTbI TaK, qTo6bl B 06pa3ue MaTepHaJla He B03HHKaJlH
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HeH36e)!{HOM, eCJlH nOJlb30BaTbCH MeTo}J.aMH cTaUHoHapHoro T'::IlJlOBOrO
nOToKa, npoHcxo}J.HT pe3Koe nepepacnpe}J.eJleHHe BJlam B 06pa3ue;
rOpHqa-H ero CTopoHa nO}J.CYlllHBaeTCH, H BJlara nepeMelll.2eTCH K XOJl0JJ.-
HOH cTOpoHe, HHor}J.a BbI}J.eJlHHCb Ha HeH B BH}J.e KaneJlb. .D.JlH nOJlyqeHHH
)!{e npaBHJlbHOH xapaKTepHcTHKH Heo6xo}J.HMO coxpaHHTb paBHOMep-
Hoe pacnpe}J.eJleHHe BJlarH BO BceM 06"beMe 06pa3ua MaTepHaJla. ;:ho
H }J.ocTHraeTcH HeKoTopbIMH MeTo}J.aMH HeCTalJ,HOHapHoro TenJlOBoro
nOTOKa.
AHU30TponHbie MaTepHaJIbl. Orpor.moe 60JlblllHHCTBO TeXHHqeCKHX
MaTepHaJlOB - He TOJlbKO O}J.HOpO}J.HbIe, HO H H30TponHbIe, H Bce HalllH
paCCY)!{}J.eHHH HMeHHO K HHM H OTHOCHJlHCb.
MaTepHaJl MbI Ha3bIBaeM H30TponHbIM, Kor}J.a K03cpcpHuHeHT A B OCHOB-
HOH cpopMYJle 3aKOHa <I>YPbe He 3aBHCHT OT Toro, KaK H30TepMHqeCKHe
nOBepXHOCTH, B03HHKalOlll.He B TeJle, H3rOTOBJleHHOM H3 3Toro MaTepHaJla,
pacnOJlO)!{eHbl OTHOCHTeJlbHO reOMeTpHqeCKHX 3J1eMeHTOB, onpe}J.eJlffiOlll.HX
3TO Te.TIO: 3aHHMaeT JlH H30TepMHqeCKaH nOBepXHOCTb, npOXO}J.Hlll.aH
Qepe3 TOQKY ;\1 nOJlO)f{ClIlle FF' IIJlII nOJlO)KCIIIIC GG' (cpllr. 135), K03(jJ-
qmu.HeHT A OCTaeTCH 6e3 H3MeHeHUH. O
HaKo B03MO)KHbl cJlyqaH (npH-




238 .


Jf3.1>IepeHUJI II npu60pbt


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lJeHIi5J npIi paSHbIx HanpaBJ]eHIi5JX TenJ]OBoro nOTOKa Mqp' MqO Ii T. ]I..
B 3TIiX cJ]YlJa5Jx MaTepHaJ] 5JBJ]5JeTC5J, KaK rOBOp5JT, aHHsaTponHbIM.


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Il.lHX lJepe3 qJHKCHpoBaHHYIO TO'lKY M B TeJle;
Mqp H M qO - HanpaBJleHHH TenJIOBblX nOTO-
KOB B saBHCIfMOCTH OT SToro pacnOJlO}KeHHH:
Mqp..L FF'; Mqo..L GG'.


<DHr. 136. flpHMep
aHlf30TponHoro BOJIOK-
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(BOMJlOK, 1f3.neJiHH H3
MHHepaJIbHOrO BOJIOKHa
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J1epeBa; TPH xapaKTepH-
CTH'IeCKHe HanpaBJIeHHH B
J1epeBe:
1- BKCHanbHOe (>'2)' 11- pa
JlHanbHOe AT; III - TaHreH-
LlHanLHOe(A t ) .


<DHL 138. CXeMbl CTPYKTypHOro cTpoeHHH:


a - roctJPHpoB8HHoro TennOH30nRl.lHOHHQro 113.l1.eJlHR
(KapToH. BennHT H T. n.) 1- nnOCKHe nllCTbl; 2 -ro<)Jp;
3 - BO:J.lI.ywHble npocnoHKH; 6 - ac6ecToBoM HLJ.eHCTOH
6YMarH: 1 - npHneralOlllaa K 6YM8:H<HbIM JlHCT8M nno-
CK8S1 nOBcp'\HOCTb TBep.ll.OrO Tcna; 2 - Ii03.l1.}'lllHble
fll.JeHKH; 3 - DnoTHblH ac6ecT.


TnnIilJHbIli npIiMep: CJ]OHCTbIH MaTepuaJ] C npaBIiJ]bHblM napaJ]J]eJ]b-
HbIM pacnOJ]O>KeHHeM CJ]oeB (qmr. 136); S]l.eCb paSJ]IilJaIOT ]l.Ba OC06bIX
lIanpanJlclUHI: napaJI.1CJILHUC LJ]OUM II LuulUClLlUClllIu Au II lIepUCII.lI. lI -
KYJ]5JpHOe IiM - A.L..


3aKAIO'IUTeAIJHlJle 3a1>le'lUHUJI 1C 2AaBaM 6-14


239


.o.pyroH, BceM IiSBeCTHblH, npHMep - ]l.peBecIiHbI - npe]l.cTaBJ]eH
Ha qmr. 137; pasJ]HlJaIOT TPIi xapaKTepHbIx HanpaBJ]eHIi5J r, z, t Ii TPIi
SHalJeHH5J TenJ10npOBO]l.HOCTH A" At' Az. OepBble ]l.Ba ]l.OBOJ]bHO 6J]HSKIi
]l.pyr K ]l.pyry H IiX npaKTwlecKH MO>KHO npHH5JTb paBHblMIi: At
 A, = A.L.;
TpeTbe npIiMepHo B 1,5-2 pasa 6oJ]bIlle: Az = A II = (1,5-2) A.L.'
ECTeCTBeHHo, lJTO 3TO CBoikTBO MaTepIiaJ]a YCJ10>KH5JeT IiCllbITaHIie, Ha-
KJ]aJ{blBa5J OrpaHIilJeHU5J Ha cpOPMY o6paSLl.OB.
TenJ]oBble conpOTHBJleHHSI. .o.J]5J HeKoTopbIX J]IiCTOBbIX H nJ]IiTOlJHblX
TenJ]OIBOJ]5JLl.IiOHHbIX HS]l.eJ]HH, ]l.J]5J rocppHpoBaHHbIx J]HCTOB Ii T. n.
Tep5JeT CMblCJ] ]l.a>Ke TOT YCJ]OBHbIH K03cpcpIiUlIeHT TenJ]onpOBO]l.HOCTIi, 0
KOTOpOM IllJ]a pelJb B
 1 3TOii rJ]aBbI: IiX TenJ]oHsoJ]HPYIO
IiH 3cpcpeKT
npIiXO]l.HTC5J xapaKTepHsoBaTb YCJ]OBHbIM cYMMapHblM TenJ]OBblM con po-
THBJ]eHHeM P Y' .
.o.J]5J ero onpeLleJ]eHIi5J npIiroLlHbl MeTO]l.bl nJ]aCTIiHKIi
 4-7 rJ]. 6,
6HKaJ]opHMeTp A. <1>. EerYHKoBoii, MeTO]l. M. B. KYJ]aKoBa Ii T. n.;
S]l.eCb IiMeeM:


!Jt
q=-.
Py






Ha cpHr. 138, a H 138, 6 npe]l.CTaBJ]eHbI CXeMaTIilJeCKIi ]l.Ba TaKIiX MaTe-
pHaJ]a IiJ]H, TO'iHee rOBOp5J, HS]l.eJ]Ii5J.


,




OrJ1ABJlEHHE


J1I1TEPATYPA


I. TepMHHOJIOrHH TenJIOnepe]lalJH, 113J1-BO AH CCCP, KOMHTeT TeXHH'IecKOii Tep-
MHHOJlOrHH, 1951.
2. M. A. M H X e e B, OcHOBbI TenJIOnepe.nalJH, H3.n. TpeTbe, foc3HeproH3.naT,
1956.. .
3. r. M. K 0 H .n paT b e B, PerYJIHpHblH TenJIOBOH pe}KHM, fTTI1, 1954.
4. TenJI03HepreTHlJecKHe npH60pbl H perYJIHTOpbl, C60fJHHK, MawrH3, 1954.
5. A. H. fop]l 0 B H J1p. MeToJ\bI H3MepeHHH TeMnepaTYP B npOMblWJIeHHOCTH,
MeTaJIJIyprH3.naT, MocKBa, 1952.
6. M. 11. non 0 B, TepMOMeTpHH H KaJIOpHMeTpHH, 113J1-BO MocK. roc. YHHBep'
CHTeTa, 1954.
7. I1ccJIe.noBaHHH B o6JIacTH TenJIOBblX H3MepeHHii, C60pHHK TPy.nOB JII1TMO,
Bbln. 12, 1954.
8. A. B. JI bI K 0 B, TeopHH TenJIOnpOBO]lHOCTH, fTTI1, 1952.
9. A.
. Y Y .n H'O B C K H ii, TenJlo06MeH B .nHcnepCHbiX cpe]lax, fTTl1, 1954.
10. M a x J a k 0 b, Heat Transfer, Vol. 1, Ed. John Wilcy & Sons, 1950.
II. A.
. 11 0 qJ qJ e, nOJlynpOBOJ1HHKH B cOBpeMcHHoii qJH3HKe, 113.n-Bo AH
CCCP, 1954.
12. r. M. K O' H .n paT b e B, OnpeJ1eJIeHHe TepMHlJeCKHX KOHCTaHT, TpYJ\bI
JIeHHHrpa]lCKOrO HHCTHTYTa .TOlJHoii MexaHHKH H onTHKH, T. 1, Bbln. 4, 1940.
13. Handbuch der Physik, herausgegeben von H. Geiger und K. Scheel Bd. XI,
Julius Springer Verlag, 1926. '
14. CoJlected Researches of the National Physical Laboratory, 1926.
. 15. P. V ern 0 t t e, ThermocinHique, N2 224 H3 c06paHHH Publications scienti.
hques et techniques du Ministere de l'Air, 1949.
16. Mesures et controle industriel, N2 102, Nov. 1945, U N2 104 J anv. 1946.
17. E. C. neT Y X 0 B ,OnblTHoe H3YlJeHHe npOlieCCOB TenJlOnepeJ\alJH, fOC3Hepro-
H3.naT, 1952.
18. M.
. M a JI H K 0 B, OCHOBbI MeTpOJIOrHH, lJ. 1, H3.n. KOMHTeTa no .neJlaM
Mep H H3MepHT. npH6. npH COBeTe MHHHCTpOB CCCP, 1949.
19. B. H. Po M a HOB C K H H, OCHOBHble 3a.nalJH TeopHH OWH60K, focTexH3J\aT,
1947.
20. r. M. K 0 H .n paT b e B, DpHJIO}KeHHe TeopHH perYJIHpHOrO OXJIa}K]leHHH
.nBYXCOCTaBHoro llIapa - MeTO.n «wap B llIape», 113B. AH CCCP, OT.n. TeXH. HaYK, .N!! 4,
1950.


n pe.nHCJIOBHe
BBeJ1eHHe .
OCHoBHble 0603HalJeHHH


3
5
10


YACTb nEPBA51


c1>H3HKO-MATEMATH4ECKHE OCHOBbl H3MEPEHHA TEnJ10BbIX BEJ1HYHH


r JI a B a I. KpaTKoe H3JlOJKeHHe OCHOBHblX nOHHTHii H 3aKOHOB Y'IeHHH 0 TenJIo-
06MeHe .......... ........



 1. TenJIonepe.nalJa KOH.nYKUHeii (TenJIonpoBO.nHocTblO)

 2. 3aKoH
ypbe. . . . . . - . . . . . . . .

 3. TenJlo06MeH KOHBeKUHeH. KpHTepHH nO)J.06HH. .

 4. TenJIo06MeH paJ1HaUHeii . . . . . . . . . . . .

 5. 0 Bbl60pe eJ1HHHIl 113MepeHHH . . . . . . . . .

 6. 0 'IHCJIeHHbIX 3HalJeHHHX K03cpcpHUHeHToB TenJIOnpOBOJ1HOCTH,
IjJHuHeHToB TenJIOOT.na'lH H cTeneHeH lJepHoTbI.

 7. YpaBHeHHe TenJIOnpoBo.nHOCTH
ypbe. . . . . . . . . .






11
12
14
15
21
24
26
29


K03IjJ.


f JI a B a 2. YpaBHeHHe c1>YPbe lI,JlH cTaQHoHapHoro nOJlH TeMnepaTYP TeJIa
6e3 HCTOlJHHKOB TenJla . .............. 33



 I. CTauHOHapHbJii TenJIOBOii nOTOK lJepe3 nJIOcKYIO cTeHKY .

 2. CTauHollapHblii TenJlOBOH nOTOK
epe3 UHJIHHJ1pH'IecKYIO cTeHKY. 36

 3. CTaUHollapHbIH TenJIOBOii nOTOK 'Iepe3 llIapoBYIO cTeHKY. . . . 39

 4. 0606weHHe npe.nbIJ1YIl.lHX qJOPMYJI (I. 2), (2. 12), (2. 16). . . .. 40

 5. K03qJcpHUlleHT 4JoPMbI cTaUHouapHoro nOTOKa . . . . . . . . . .

 6. CTauHoHapHblii TenJIOBOii nOTOK lJepe3 CJIO}KHYIO nJIOcKYIO cTeHKY.
TenJIOBOe conpOTHBJIeHHe. . . . . _ . . . . . . . . . . . .. 42

 7. TenJIoncpe.nalJa OT olllloii CpeJ1bI K J1Pyroii 'Iepe3 nJIOcKYIO cTeHKY.. 44

 8. TenJIonepe.nalJa 'Iepe3 HenJIOcKYIO cTellKY . . . . . . . . . . .. 46
r JI a B a 3. 3J1eMellTapHaH TeOpllH TenJlOBOii HHepQHH TeJJ H CHCTeM 6e3 BHYTpeH-
HHX HCTOlJHHKOB TenJla. . . . . . . . . . . . . . . . . .. 48

 I. BblBOJ1 OCHOBHOro ypaBHeHHH . . . . - . . . . . . . . . . . .

 2. nepBblii nlllH'IlIblH CJIYlJaH n
OHBJIeHHH TenJIOBOii HHepUHH: npocToe
OXJIa}KJleHHe HJIH HarpeBaHlle. . . . . . . . . . . . . . . ., 51

 3. BTOpOH THnHlJHblH CJJYlJaH npOHBJIeHIIH TenJIol1oii HHepnH H : Harpe-
p.aHl1e llJIII OXJIa}KJ1eHHe TeJIa B cpeJ1e, TeMnepaTypa KOTOpoii H3Me.
HHeTCH BO BpeMeHH C nocToHHHOH CKOpOCTblO. . . . . . . . .. 55

 4. Har.
HllHoe ItCTOJIKOBaHHe nocToHHHOii TenJIOBOii HHepuHH. . . .

 5. TpeTHii THnH'IHblH, cJIY'Iaii npOHBJIeHH
 TenJIOBOH HHepuHH: CH-
C1:CMa - B cpeJ1e, TeMnepaTypa KOTOpOH H3MeHHeTCH co BpeMeHeM
nepltOJ1l1lJeCKH no KOCHHycolI.naJIbHoMY H1IH CHHycoH.nanbHoMY 3a-
KOHY. . . . . . . . . . . 57

 6. CneJ1CTBHH 3J1eMeHTapHoH TeopHH TenJIOBOA HHepuHH. . . . . flY
16 KOHJlpaTbeB 2763




242


OZAa8AeHue


r JI a B a 4. PerYJIHpH33QHH TenJIOBoro peJKHM3 CHCTeM 6e3 HCTOlJHHKOB TenJI3

 I. npe.nBapHTeJIbHbIe 3aMelJallHH. . . . . . . .., .......

 2. MaTeMaTHlJecKaH qJOpMy.
lIpoBKa rpaHlIlJHbIX YCJIOBlliI. . . . . .

 3. PerYJIHpHble TenJ!OBble pe}KIIMbI nepBoro, BToporo H TpeTbero pOJ1a .

 4. PerYJIHpHblil TCnJIOBOH pe}KHM nepBoro pOJ1a. . . . . . . . . .

 5. ACIIMnTOTlIlJeCKIiH 3aKOH B03paCTaHIIH TeMna OXJIa}KJ1eHIIH-cHCTeMbI m
C B03paCTaHlleM K03qJqJHl.lHeHTa TenJIOOTJ1alJH a . . . . . .

 6. PerYJIHpHbIH pe}KIIM o.nHopo.nHoro TeJIa. . . . . . . . . .

 7. PerYJIHpHbIH pe}KHM HJ1pa C paBHOMepHOH TeMnepaTypOH, OKpY}KeH-
HOro TOHKOH TenJIOH30J!HUHOHHOH 060JIOlJKOH. . . . . . . . . .

 8. PerYJIHpHbIH pe}KlfM npocTeHlllHx .nByxcocTaBHblx TeJI - llIapoBoro
H nJIOCKoro 6HKaJIOpHMeTpoB (nplI a -+ (0) .......

 9. Pe310Me npeJ1blJ1Yll.lero . . . . . . . . . . .
r JI a B a 5. PerYJIHpHble TenJIOBbie peJKHMbI BTOpOro H TpeTbero poll,3.

 I. 'OCHOBHOH 3aKOH perYJIHpHoro TenJIOBoro pe}KIIMa BTOpOro pOJ1a. .

 2. PerYJIHpHbIH PE}!{HM BToporo po.na OJ1HOpOJ1HOrO 1130TponHoro TeJIa.
npOcTeHllIHe CJIYlJaH nJIaCTHHbI, UHJIHHJ1pa, llIapa. . . . .

 3. PerYJIHpHbIii pe}KHM TpeTberO pOJ1a. npoCTeHllIHH CJIYlJaH TeMnepa-
TypHbIX BOJIH B CTep}KHe IIJIH nOJIynpoCTpaHCTBe. . . . . . . . .


YACTb BTOPA51
H3MEPEHHSI H nPH60Pbl
r JI a B a 6. H3MepeHHe K031jJljJHUHeHTOB TenJIOnpOBOll,HOCTH TeXHHlJeCKHX MaTe-
pHaJIOB

 I. POJIb TenJIOH30JIllpOBaHHH npOMbIWJIeHHbIX 061>eKTOB, 3J1aHHil liT. n.
K03qJljJIIIllfeHT TenJIoc6epe}KeHHH. . .

 2. POJIb BbICOKOKalJeCTBeHHblX TenJIOH30JIHTOpOB. . . . .

 3. 06waH cxeMa MeTOllOB H npll60pOB llJlH OnpelleJIeHHH TenJIOBbIX
CBOHCTB MaTeplfaJIOB. . . . . . . . . . . . . . . .

 4. MeToll ORHOH nJIaCTIIHKH C oxpaHHbIM KOJIbUOM. . .

 5. CTaUlfoHapHbIii MeTOll J1BYX n.13CTl1II0K C oxpaHHbIM KOJIbUOM. .

 6. MeTOJ1 n.1aCTlIHKH 6e3 oxpaHHoro KOJIblia. CpaBHIfTeJlbHbIH MeTO)l
XplfCTlfaHceHa. I1cnbITaHHe MHOmCJIOHHbIX MaTepllaJIOB. . . . .

 7. MeTOll nJIaCTIfHKH npH BblCOKHX TeMnepaTypax.

 8. MeTOJ1 Tpy6bI . . . . . . . .. .......

 9. MeTOJ1 wapa . . . . . . .

 10. MeToR HWl1Ka (Box-Method)


r JI 3 B a 7. OnpClI,eJIeHHe K031jJljJHuHeHT3 renJlOnpOBOll,HOCTH MeT3J1J10B no
MeTOll,3M cTauHoHapHoro renJlOBOrO nOTOKa.

 1. DpaKTHlJeCKOe 3HalJeHHe TenJIOnpOBOllHOCTH MeTaJIJIOB . . . . . .

 2. MeTOJ1 onpeJ1eJIeHHH K03qJqJlfUlfeHTa TenJIOnpOBOJ1HOCTII MeTaJIJIOB.
OCHOBaHHbIH Ha C03.naHIIII cTauHoHapHoro aKCHaJIbHOrO nOTOKa
B UIIJJHH.npax. . . . . . . . . . . . . . . . . . . .

 3. MeTo.n KOJIbpaywa. . . . . . . . . . . .


r 11 a B a 8. H3MepeHHH KosljJljJJoIUHeHTOB TeMnepaTyponpOBOll,HOCTH, TenJIOnpo-
BOll,HOCTH H YlI,eJIbHOii TenJlOeMKOCTH TeXHHlJecKHX TCnJlOH30JIHUHOH-
HbiX M3TepH3J10B, OCHOB3HHble H3 HecT3uHOH3pHOM TenJlOBOM peJKHMe

 I. 061l.lHe co06pa}KeHHH . " . .'. . . . . . . . . .

 2. 0 qJH3HlJeCKHX BeJIHlJHHaX A, C, a . . . . . . . . . . . . . . .

 3. Me-roJ\bI onpeJ1eJIeHHH TenJIOBbIX cBoHcTB MaTerm3J10H. OCHOH:lHHhlP
H1I perYJlllpHUM pt:}KHM
 lIepIJoro pllAa l«MeTOJI.b1 perY1IHpHoro pe-
:H\.lIMa») . . . . . . . . . . . . . . . . . . . . . . . . . . .


73


74
77
78
82
83
92
93
95
98
99
100
102


110


116
117
118
125
127
131
134
140
142


145


146
147


152


155


160


I


OZAaBAeHue


243



 4.

 5.

 6.


Onpe.neJIeHHe TeMna OXJIa}K.neHHH m. .. .......
113MepeHHe Tel'mepaTYP (nepBbIH BapHaHT) . . . . . .
113MPpeHlle TCMnepaTYP nocpellcTBoM .nllqJqJepeHUII3JIbHOH TepMonapbI
(BTOPOH B3pHaHT) . _ . -'.


r JI a B a 9. nepBblH MeTO.n perYJIHpHOrO peJKHM3 .

 I. TeOpeTII'IeCKHe OCHOBbl nepBom MeTOJ1a .

 2. nOHHTlle 06 a-6eCKOHelJHOCTII . . . . . .

 3. 3KcnepHMeHTaJIbHOe OCYll.leCTBJIeHHe YCJIOBIIH a = 00. TepMo-
CTaTbI. AKaJIOpllMeTpbI . . . . . . . . . . . . . . . .

 4. OCHoBHble 3JIeMeHTbI annapaTypbI. BeJ1eHHe OnblTa H 06pa60TKa
onbITHbIX llaHHbIX . . . . . . . . .

 5. VlCTO'lHHKII olllH60K . . . . . . . .

 6. nORroTOBKa 06pa3uoB K HcnbITaHHIO .

 7. 3aMelJaHIIH 06 aHaJIH3e pe3YJIbTaTOB HcnblTaHHH .

 8. OnpeJ1eJIeHHe TenJIOnpoBo.nHOCTH A Ha OCHOBaHHH pe3Y nbTaTOB
H3MepeHHH TeMnepaTyponpOBOJ1HOCTH.

 9. 0 HeKoTopbIX cpaBHHTeJIbHbIX IicnbITaHIiHX C nOMOll.lblO aKaJIOpli
MCTpa ..................

 10. Pa3Mepbl II qJOpM3 npocTeHwHx aKaJIOpUMeTpOB . . . . . .

 11. Onpe.neJIeHlie K03<jJIjJHUlleHTa 1jJ0pMbl K. . . . . . . . . . .
r JJ a B a 10. BTOpoH MeTO.n perYJlHpHoro peJKHM3. J13M6l1,3KaJlOpHMeTp.

 I. nCpBblii BapiiaHT MeTo.na Ii ero 3KcnepHMeHTaJIbHOe oCYll.leCTBJIeHlie .

 2. OCHoBHble 3JIeMeHTbI annapaTypbl. Be.neHlle onbITa. . . . . . . .

 3. DpmleHeHlie KpllTepHeB M Ii H BO BTOpOM MeTOlle perY1IHpHoro
pe}KHMa (06pa3UbI JII060H qJOpMbI) .

 4. POJIb 060JIO'lKII

 5. BbIBO.n npellbIllyu.lliX 4>oPMYJI


r JI a B a II. Onpe.neJIeHHe K031jJljJHUHCHTOB TenJlOOTlI,3'1H. AJIbIIJaK3J10pHMeTpbl.

 I. Kos4>ljJliUlleHTbI TenJIOOT.na'lli KOHBeKuHeii H H3JIY'IeHHeM . . . .

 2. OnpeJleJIeHlle K03cpljJHuHeHTa TenJIOOTllalJH no MeTo.ny cTaliHoHapHoro
TenJIOBOrO pe}KIfMa . . . . _ . . . _ . _ . _ . . . . _ .

 3. OnpeneJIeHHe K03ljJcpHuHeHTa TenJIOOT!lalJlI no MeTollY pery.1HpHoro
Ten.
OBoro pe}KIIMa . . . . . . . . . . . . . . . . . . . . . .

 4. MeTo.n onpe.neJIeHHH 3aBHCHMOCTH K03cpqHluHeHTa TenJIOOTJ1a'l11 OT
TeMnepaTypbI, oCHoBaHHblH Ha 3aKoHoMepHocTHX HecTauHoHapHoro
pe}KIIMa ...........................


rJIaBa


12. MHKpoK3J10pHMeTp H 6HKaJIOplfMeTp, OCHOB3HHble H3 TeopHH pery-
JIHpHOrO peJKHMa nepBoro P0ll,3 . . . . . . . . . . . . . . .
UHJIHHJ1plIlJeCKIiH MHKpOKaJIOpHMeTp. . . . . . . . . . . . . .
UlapoBOH 6HKa.
opHMeTp J1J1H HcnbITaHllii Ha TenJIOnpOBOJ1HOCTb 3ep'
IIIICTblX 11 BOJIOKHHCTblX TenJIOIf30.
HUIIOH!lbIX MaTepHaJJOB.
nJIOCKHil 6HKaJIOpHMeTp . . . . . . . . . . . . . . . . . . . .



 I.

 2.

 3.


r JI a B a 13. MeTOll,bI H3MepeHHH TenJlOBbiX cBoiicTB MeTepH3JIOB, OCHOB3HHble
H3 TeopHH perYJlHpHoro peJKHM3 BTOpOro H TpeTbero pOA3. . .

 1. Me-rO.nbI HarpeBaHHH 06pa3ua C nocToHHHOH CKOpOCTblO (perYJIHp-
Hblii pe}KHM BToporo pOlla) . . . . . . . . . . . . . . . . . .

 2. CpaBHHTeJIbHblii MeTO.n, oCHoBaHHblii Ha TeopHH perYJIHpHoro pe-
}KHMa BToporo pOJ1a .nByxcocTaBHbIx TeJI (6HKaJIOpHMeTpbr) . . .

 3. ()npe
c
ellile TeMnepa-ryponpoBOnllocTIl no MeToAY TeMnepaTypllbJ'll
BOJIH .............................


162
163
165
169


172
176
178
182
183
184


185
186
188


191
193
194
195


199


200
202


,


205


207


208
212


216


219
220