Chirkov_A_Yu_Lektsii_po_TD (Лекции)
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.»2007–2008.«»,«.»-.,,,,.-,.,..[3],..[5].[1],.[2],..[4].-,-[6]...[7],.,,,..[9, 10].1[8].-,(,),,(-)..,,–.,,..,,-.,,()..,.-, –.,-...,.,.,,,–-.-2.1,,,,, –-,.,.-,.,-.1.1.1.–-,.-.,,,,(,.,.).,,.,,,.,(-),,.1,.,«,»,,,..,-,.3-,.,,,–,,-.,-,...,,.,,.,.()(–-)..().-.(-).–().).1.2...–,.:4,,().,..,-,.,,p,,-V.N().,,–(.. 1.1).. 1.1.,1–,2–5:.-.:,,,.().),-.,,-.,,, ,.,-..2,,,(.. 1.1),.-3,-.,,2,,., .«-».,,()..,–,,.3.,().-,.«»,..[9, 10].6–...,.,-..,.-,,.,.,).,,.–,-.,..().,,.,-,.(),,-,.1.3.....7,-.,,.-,pipe .(1.1)e-i.(pi(,ep ))..-,V,p.,,–,.4,.()–Ti,.-Te.(1.2)()().:.,4,,,.8,pif1 ( p e , T e ,...) ; V if1 ( p e ,T e ,...) ; N if1 ( p e ,T e ,...) ; ...(1.3).,,,(T0 ).–5p.TiTeipp,eT,.dV idV e , dN idN e , ....,,,-().,-.,).-...,–.6,()5-,.6(1813 .).,,..,(),..()()9,.,,,..-,.,,-.,,,,..7-.,-,.81.4...().,.,-,.7-.,.8,,(),,,.,.10.-,-.,,,,,,,.((-).).,,–.().9,-...
1.2.9..,, –.11-,–((,),. 1.2)..,.,,.,,,.,-.,.,f –pf,, pdxdVfdx .LL,,–pfdxpdV ,(1.4)pe )L ,),-L,-.( pidV iLpi .-(,L.p i dV ipidV e .L.(p e dV epe , ,,),-–,L,(1.4)LkYkYk dy k ,(1.5)yk –.,12-..UdN ,N–(1.6).–,U** dN()dN ,(1.7).UUi dN i,i.(1.8)(,,)».«-–.,-,,.dUQLUQ–,, U.13(1.9)–-U(1.9),QLU.(1.10)(1.10),,,–,-..-dU0,(1.11).1.5...-–.:-(S),,dSdS,Q.T(1.12):-0.(1.13),.,,(Q 0()),T const14,-(1.14),(S),( dS ~ QT = const).,, –,.,(1.5),S,-,Q TdS ,(1.15).10.,,Q 0(-).(1.16)T const,-.,T1 T2 (.. 1.3),Q)dSdS1dS 2Q / T1 0 ()., dS1,Q / T20 (Q (1 / T2 1 / T1 ) 0 .11dS 2()-,,.10()–11.,,-.[4].,,.15. 1.3.-,)().,(,)12).,.,( ,,),,.1.6.(1.9)-dUTdSpdVi dN i,(1.17)i-12,.(S. Carnot, Réflexions sur la puissance motrice du feu et sur les machines propres adévelopper cette puissance, 1824).16.13dS1dUTpdVTiiTdN i ,(1.18)(1.17).1.7..(-),.,..2,PiZi,..., W.P{Z i } , 0 Pi1.i = 1,14,WPi 1 .(1.19)i 1ZiPi = 1,log b Pi ..Pi = 0b1/ ln b k ,k–.log b Pi,.13,,.(14.-).(()Zi, Pi = 0 –k ln Pi ,).Zi.-Pi, Pi = 1Zi.17,,-WSBMk ln PikPi ln Pi ,(1.20)i 1k = 1,381 10–23,.P1 = P2 =-W.(1.20),… = PW = 1/W,SBk ln W .(1.21)W,-.-SBS1BS 2B .(1.22)(1.22),Pi,PijSBkPij ln PijijPi Pj .Pii(1.23)Pj ln PjPjjjPj ln PjjPi ln Pii(1.19)18Pj.(1.23).Pi ln PiiS1BS 2B ,(1.24),,-.,.S,.-.(),-..-15(),(Pi = 1),S = 0.«» (Pi~ 1/W),.((1.21)),...,,S,P( S )Z expS,k(1.25)15HPi log b Pi ,,,..Pk = 1, Pi = 0,b = 2,i kH.,Pi = 1/W,(W = 2)-,.1= log2W..,,,-.(.
[9, 10]),.,19-Z–,.(1.25),.,.,-,-1.8.)...1.5.,dS(1 / T ) 1 / T2 1 / T1-1T2Q1T1(1 / T ) Q 0 ,(1.26)0.,,( p1p2 ),,.p1dV .p2 dV .L ( p1p 2 )dV .,dSpp2( p1TdS( p1p2 )TdV,p 2 )dVpTdV-0,0,(1.27)p1 0 .Xk,xk20(dS ) iYkdykTdSk0.(1.28),(-(dS ) i .),,,(dS ) edUQTpdVi dN i(1.29)T.dS(1.28)( dS ) e(1.29),( dS ) i ,(1.30),-U, VTNiTi, pdS1dUTpi ,iiidS(dS )ipdVTiT–dN i ,(1.31).0.(1.26)–(1.28),,T, p-;(1/T), (–p)/T, …, Yk/T,.(1.32),,,)21.-().,,(dS )idVdtP0.(dS ) idt(1.33)dV0.(1.34)T (dS )idVdt0(1.35)VT.-,Pmin .(1.36),..,.,,,,..(1.36)dP / dtP-0,,,0.(1.28),,22dYk dy kTdxk dfdtk0,(1.37)xk –Yk, dVdx k df –,, df –-x k.(1.37)Jkdy kdfdt(1.38)y k,Ykx k.dYk / dxk..1TXk –k Jk,(1.39)k, Jk –.k Jk,(1.40)k.,-()...,23JkLkjj,(1.41)jLkj –.(1.41),0 (.(1.41)-–),.1.9...,,.,,,.,.,.,.-,...-–.16..,-16–.,.-,.24S0T0.(1.42).,.-0.(1.43),S0T,,.,.S,W=1,k ln W,0..)(TS,00.,S0T,0.,,(1.43)..,-,.,,-,.171.10.:,,17-.25.1),.2),(),,.3)(),-,.4),,,(.),.5),-,.6);().7).8),,-()..,().26-2..2.1..,,-,p, T,i(i*)V, S, Ni., i S.p, T, VNi (-).,,-(,,)..= NVM, S = NSM,VM,V.-SM –M.(p, T, )-.(),.:..,,,p, T, , V, S, Np, T, V.N.F (T , p,V , N ) 027(2.1),V,,-V (T , p, N ) .(2.2)-N.(2.2)(2.1).,-.,(2.2)VTdVVpdTpdp .(2.3)T,,().pTV = const,VTVpTVVpVppTVT,(2.3).(2.4)1.(2.5)Tp(2.4),-,.:1VVp,T28(2.6)m /V –1VVT1ppT,m–(2.4)1,Tp(2.7)p,(2.8)V.,,p/ .(2.9)(2.3)()dVVdTdp .18(2.10),, , .,(2.6)–(2.8),,1/ p ,1/ T ..,,(2.10)pVTpVconst .19,NRT (R –),1/ T .1/ p ,18(2.5).19,,.29-2.2...–.0 ),( dN i.(dUTdS-.
(1.17))pdV .(2.11)(2.11),SV,-p, V, T, S-V.S.20,.TS V,V, T p.S,,.)–,((HUp,-),pV ,-(2.12)F UTS ,(2.13)GTS .(2.14)H(2.11)dH20.[4].,TdS,TVdp ,p;(2.15)-.30dFSdTpdV ,(2.16)dGSdTVdp .(2.17)U ( S ,V ) , H ( S , p ) , F (T ,V )dUUSdSVG (T , p )UVTdHHSFTdSpGTdp ,(2.19)dV ,(2.20)dp ,(2.21)SHpSVFVdTVSdG(2.18)pTdFdV .TpGpdTpTVS,(2.11), (2.15)–(2.17).(2.18)–(2.21)TVTppSSSVS31.-(2.22)V,p(2.23)SVSpTpTTVT,(2.24).(2.25)Vp.,,,.(2.13)FT(2.21), S(2.20)GTV.p(2.14),UFHFTTGTG T,(2.26)V.(2.27)p(2.26)(UVHpTFVTGp(2.20)S/ VTTTTSp32-,(2.28).(2.29)TTF/ V Tp(2.24) (2.25),p/ T V , S / p T(2.21)TSV(2.27))G/ pV.-TV/ TpUVHppTp TTVVTTT,(2.30),(2.31)Vp,.212.3...,p, T, VN,-,–()p, T, V, N.-,.,()-().21(2.30)UNU M ( S / N ,V / N ) ,(2.32)HNH M ( S / N , p ) ,(2.33)FNFM (T ,V / N ) ,(2.34)GNGM (T , p ) ,(2.35)(2.31).33,N-.(N = const)dUdHUTUVdTVHTHpdTpdV ,(2.36)dp .(2.37)TT( U / T )V ,( H / T ) p , ( U / V )T( H / p )T.(2.30)(2.31).-UTV(2.38).(2.39)VHTCp,p,(,).-QdT(2.40).T2T1Q1 2,T2 T134(2.41)T1.22T2 –; Q1–2 –-Q1–2-Q,1–2,-121T2T1T2T1CdT .(2.42)12-(T1, p1, V1, …T2, p2, V2, …).(2.40) (2.41),,,,(2.42).,,,,.V = const dU VQ p C p dT p ,(2.11) (2.15),p = const dH p (TdS ) p(2.38) (2.39),(TdS )VQVCV dTV ,-(V = const)(p = const)CV Cp.,,.-dUV dTpTTp dVV dT( T.1(2.43)V22,1) pdV ,3, 1,1 ..35,dHp dTVTVTdpp dT(1T )Vdp .(2.44)p.(,-)(2.43)(2.44).()-.,(2.30),23( U / V )T 0 .CV const .24U CV T const .(2.36)HC pTconst ..,.,CV Cpp = constUT(2.43)TVpUTCpppVT.(2.44)pTVVTppTH,VTpUpV,(2.45)pp.VVT(2.46).(2.47)p,23--,.24.36,.2.3(.
2.2( Ni)-const ).,-,,.,,(1.18),,(1)dSTV).VTdTpTpdVTVVTdTdp .(2.48)p(2.48)T p(-,. 1)():, , ;CVCp.2). 3). 4). 5)-.,,,.,,-,,.37,.,.2.4..–.,(1.17),dUTdSpdVi dN idHTdS Vdpi dN idFSdTdGpdVSdT Vdp,(2.50),(2.51)i dN i,(2.52)i dN i.(2.53)i()-iUNiHNiS ,V , N jj iFNiS , p, N jj iT ,V , N jj iGNiT , p, N jj i,(UNS ,VHN= U, H, F, G; X. (2.54)S, pFNT ,VY–GNT, pN),(2.55)X ,Y38(X,Y).U,HH ( S , p ) , F F (T ,V ) , G G (T , p ) .(2.55),U ( S ,V ) ,(2.32)–(2.35),-(T,p,1N).NNX ,YM X ,YNMM.N(2.56)X ,YN,(2.56),, ,-(T , p ) GM (T , p ) .(2.35)(2.57)G(2.57)-N i GMidGNii dN ii.Ni di(2.53),Ni diSdT Vdp .(2.58).,,(ii-).(2.17)diSdTNiVdp ,NiNi(2.59)(2.58).,39--(T, p,i).,,-Ni d0,i(2.60).,1B12...B2B1 , B 2 , … –(B112B2();1,2...
,(2.61)); B1 , B 2 , … –,…1 , 2 , …–..,–.0.i Bi(2.62)i,dN11-dN 2...dN i2... d ,(2.63)i.25,(2.51)–(2.53)25,,.40,i dN iAd ,i idi(2.64)iA(2.65)i ii.nr,(2.63)nrnri dN iir i d rr 1 ii;rr,(2.66)r 1–irAr diAr –rr-.2.5..,,–-26T, p,i.f.-fC–CP2,(2.67),P–R.-,R,26,,,i–.T.41p,-fCPR2.(2.68)-,.T,p,CNi27..,P,CP + 2.-,1k2kPk ....(2.69)(2.69)C ( P 1) CP C .,,-NkNi .(2.70)C.-P,2 ( P C,,) 2.:,,-.,.,(Ni = 0)..(2.69),,27T,T,p.42p.-.,,,–.PNi .(2.70) (C).P,CP.f 2 (P(2.67).2,f)0,P 2 C.2.6.,,-.-.,.,.,)-.-dS0(d 2S0 (),(2.71)).(2.72),( dS,0 , d 2S0 , d 3S0 , …).28.,28,.43,-....1,dSdS1–dS 21dU1T12.p11 dNdV11T1T11p2dV2dU 2T2T22T2dN 2-0 .
(2.73),dU 2dSdS1dS 2dU1 , dV21T1dV1 , dN 2p1T11dU 1T2dN1 .(2.74)p2dV1T212T1T2dN10 , (2.75),T1 T2 ,(2.76)p1p2 ,(2.77)12.(2.78)1),,44((2.76)–(2.78),-.,-*.(2.78),12-–..(2.66),nrdSAr dr,(2.79)r 1,-.(2.79),-A 0.(2.80).,(,).,,,).,d 2SU1d 2 S11T1d 2S2U21T2U11(dU1 ) 2T11(dU1 ) 2T12U2T1U11451(dU 2 ) 2T21T22T2(dU1 ) 2U2CV 1T12 (dU1 ) 2CV 2T22 CV 1T12. (2.81),.,,-,.2d S1(2.81)V1T12 (dU1 ) 2(dU1 ) 2V2T22 CV 1T12CV 1T 2(2.72),.(2.82),–,CV0.(2.83),1 p1(dV1 ) 2T V1d 2S1 p2(dV2 ) 2T V211V1(dV1 ) 21T2V2(dV1 ) 2, (2.84)V1T0.2d S1 1(dN1 ) 2T N11 2(dN 2 ) 2T N2(2.85)(dN1 ) 2,2N T(2.86)-N0.(2.87)T, p(2.79)46-A0.(2.88)T, p,(2.83), (2.85), (2.87)(2.88).,,.2.7.:,,-,()().–T,i.,(i29ii.ii,,–S,V.Ni .,,.p,T,-,,,,.,,:CVp)-, ,Cp.-(29).,* =(eNA –,– eNA ,NA –,e).47-,,, , , CV Cp..,,.-.,,.,-,.1), , .p/ ,.-2)3).CVCp.,.4).5)6),.-.7).,..:pTdU MVVMpVM dTTTTVMpT481;pp dVM ,V-VMdH M( U M / T )V ,pM dTpMVM( p / T )V / pVMTT( HM / T ) p ,dp ,p( V / T )V / V .:dUTdSpdVVMdS Mi dN ipTdTTdUTdSdVMpdVTpMdS MTV1Ti dN iVMTdT,HMUMU:pVM , FMNU M , HSUMTS M , GMNH M , FNS M , VNFM , GNVM ,HMTS M ;NGM ;GM .:T1 T2...
, p1p2... ,1... , A 0 ,2, A1, 2, … –i i.:CV0,1VVp0,TN490,T, pA0.T, p;dp .p:dUQLL;pdV ;Q TdS»UQ CdT .,(Xk1 dYkT dxk):dYk;dxkXkdy k;dfdtJkJkLkjj,jLkjL jk –;k Jk1T0kPk Jk0;kmin .dVV,.,,-.().,,,.–50,,.,-..,,-.,,-.3.3.1.,,-,()30pVV–,; R = 8,31NRT ,(3.1);p–/()–-.(3.1)pVM~RRT ,(3.2)pv~RT ,(3.3)p~RT ,(3.4)R/M –,M–.30–,,,.-,.51(V–p ().-. 3.1)..,-.,,.,–,,.-,-,,.. 3.1.,-,1,p1,T1.T(3.5)(2.30)52(2.31)UVHp0,T0,(3.6)T.31,.(3.6)CV,N-Cp.TUMVM(T )dTU0TVM T (T0T0 ) U M 0 ,(3.7)TpM T (T0T0 )(3.8)T0THMpM(T )dTH0T0U M 0 U M (T0 )H M 0 H M (T0 ) –T0 = 298,16 (0 C), U M 0HM 0 ,;0, HM00.(2.47)C pMVM–VMR.(3.9)3 ,R2VM5R2VM3R ()..31,,.53-,.32.,.UM(TVMHMpM (TT0 ) U M 0 ,(3.10)T0 )(3.11)HM0.,,VMdS MT(2.48)RdVVdTpMTdT-Rdp .p(3.12)(3.12)TVMS M (T ,VM )T0TdTR lnVMVM 0TpMS M (T , p )T0TdTR lnpp0S 0 (T0 ,VM 0 )(3.13)S 0 (T0 , p0 ) .(3.14): T0 = 298,16, p0 = 105(1).VM0= 22,4 .32.54(3.13)S M (T ,VM )VMS M (T , p)lnpMTT0lnR lnTT0(3.14)VMVM 0S0 ,(3.15)pp0S0 .(3.16)R ln,-TFMUMTS MVM(T )dTU 0 (T0 )T0TVMTTT0dTRT lnVMVM 0TS 0 (T0 ,VM 0 ) , (3.17)TGMHMTS MpM(T )dTH 0 (T0 )T0TpMTT0FMUMGMTS MHMTS MVM(TTdTRT lnpp0T0 ) U 0 (T0 )VTRT ln MVM T lnVM 0T0pM (TH 0 (T0 )pTRT lnpM T lnp0T0TS 0 (T0 , p0 ) .
(3.18)TS 0 (T0 ,VM 0 ) , (3.19)T0 )55TS0 (T0 , p0 ) . (3.20)3.2.,.()-,pVp –NRT .(3.21),,,-; V –;N–, T –,.,.-,33..,Vi,34pi ,.–p,–V,,pV–,.TiT, N,Ni .,-(3.22)i33–,,-,.34«.«.56.»,»–,piVN i RT , ppi ;(3.23)Vi .(3.24)ipViN i RT , Vi,xiNi / N ,(3.25)riVi / V ,(3.26)gi, mmi –ri1,gimi / m ,(3.27)mi –xi 1 ,;1.(ri-),xi .,giM–xi M i / M ,(3.28).pixi p .(3.29),,-xiU Mi (T ,VMi ) , H M (T , p )U M (T ,VM )ixi H Mi (T , pi ) , …; (3.30)i57xi S Mi (T ,VMi ) , S M (T , p )S M (T ,VM )xi S Mi (T , pi ) ;i(3.31)ixi CVMi , C pMCVMxi C pMi ;i(3.32)ixi M i .M(3.33)i,,,-.3.3..,(. 3.2).21().-,Tp.,..,.p/2.x =1/2....(3.13)S( S )iS1S2(3.31),R ln12R ln,122 R ln 2 .(3.34),,.,58SR ln 2 .,-R ln 2 ..,..-(-,.)..
3.2.. 3.3.(.. 3.3),,,,.-,.,59,-,.2RT ln 2 .,– LS( S )e.Q /TQL2RT ln 2 ,-L2RT ln 2 .-2 R ln 2 .,,-,.,,,-.,,.3.4..(C = const).CV-Cp.,TdSdU.Q CdT .CdTpdV , dU(CCV )CV dT , pdTTNR60NRT / V .dV,V-(3.35)(3.36)NRV2 C CVT2T11V1,(3.37)2.CV(3.37)NRp,p1V1nn–-p 2V2n ,C(3.37)Cp(3.38)C CV.12, ,(3.36)(3.37),:-pV nconst ,(3.39)( constp1V1n )-,.,pT ( n1) / nQ1const2C (T2TV nT1 ) .611const .-(3.40)(3.41)V22L1pdV21p1V1nVnV1L1L12dVp1V11n 1p1V1 ln2Q12V2V1U1V2V1n 1n 1,n 1.2(3.42)(3.43)(3.44),U1(2CV (T2T1 ) .,(Q = 0)(3.45)),(CV =-const, Cp = const)...621.2.2000.3......,.:.:, 1983....-..,.:, 2006.4.1986.5...,., 2003.6..;.7./....,..:..:-,, 1991..-...(2002.8..:..).:..,::-//., 2004.9..1995. .
165, 8. . 967–973.10... 173, 11. . 1221–1240.//63. 2003..