冶金热力学基础

1111212345JkJQW12UKJJU13----1U=Q+WU=Q+W1-1QWQWU212W-W´U=Q-W´31QP=U+PVQP=QPºººº····23PmPmPTHdTQC)(,,∂∂==δVmVmVTUdTQC)(,,∂∂==δ1-102CPTCPm=fT+++=2,cTbTaCmP1-13+++=−2',TcbTaCmP1-14bTaCmP+=,1-15abcc´3∫==∆21,TTmPPdTCQH1-11∫==∆21,TTmVVdTCQU1-121∫=∆21,TTmPdTCH2T3∫∫∫∫+∆++∆++∆+=−TcTTbgPTbTfblPfTfTcSPCSPTdTCHdTCHdTCHdTCHH298)()()()(2981-17reactprodTHHHΣ−Σ=∆.1-1834∫∆+∆=∆TTPTTdTCHH001-19.,.,reactPprodPPCCCΣ−Σ=∆1-20prodreactAa+Dd=qQ+RrAbqraAdDqQrRH1-18RQprodrHqHH+=Σ1-21DArezctdHaHH+=Σ1-221-20DPAPreactPdCaCC,,,+=Σ1-23RPQPprodPrCqCC,,,+=Σ1-2451600º[]12All+3/2O2=Al2O3sº2All=[Al]º31/2O2=[O]º1-22-33ºººº14S45TQdSδ=1-25TQdSirδ1-271-271-25TQdSδ≥1-28TQSδΣ≥∆1-29=1-281-290.≥isoldS0.≥∆isolS1-30dTnCQQPPr==δδdTnCQQVVr==δδ∫=∆21TTPTnCpdTS1-33∫=∆21TTVVTdTnCS1-34HelmheltzGibbs----1WPdVdUQ′++=δδ56TdSQ≤δWPdVdUTdS′++≥δ1-372TdS=DTS1-37WdUTSd′+≥δ)(WdTSUd′≥−−)(1-38U-TSAA=U-TS1-39UTSA1-391-38WdA′≥−δ1-400≥−dA1-41=3TdS=dTSPdV=dPV1-37WPVddUTSd′++≥δ)()(WTSPVUd′≥−+−δ)(1-42U+PV-TSGG=U+PV-TS=H-TS1-43UPTSHG1-431-42WdG′≥−δ1-44W´=00≥−dG0≤∆G1-45=GG=0GSTHG∆−∆=∆1-46PdVSdTdA−−=VdPSdTdG+−=1-4715aA+dD=qQ+Rr67iidnGdGΣ=1-48)()(DARQdGaGrGqGG+−+=∆=reactprodGGΣ−Σ1-491-491moleº··ºº0,0,0reactiprodiGGGΣ−Σ∆=∆(1-50)0iG∆ººººººº2)/(THTTGP∆−=⎥⎦⎤⎢⎣⎡∂∆∂----ººººººººººº78º81-19ººº·º·º·T=1000Kº·ºº2dG=-SdT+VdP1moledPPRTVdPdG==TPº)ln(00PPRTGG+=G1moleTP1-533aA+dD=qQ+RrPA´PD´PQ´PR´)()(DARQdGaGrGqGG+−+=∆=⎥⎥⎦⎤⎢⎢⎣⎡+)ln(0'0PPRTGqQQ+⎥⎥⎦⎤⎢⎢⎣⎡+)ln(0'0PPRTGrRR-⎥⎥⎦⎤⎢⎢⎣⎡+)ln(0'0PPRTGaAA-⎥⎥⎦⎤⎢⎢⎣⎡+)ln(0'0PPRTGdDD1-54⎥⎥⎦⎤⎢⎢⎣⎡+∆=∆dDaArRqQPPPPPPPPRTGG)/.()/()/.()/(ln0'0'000'0=1-55JRTGln0+∆9104RTlnQº5610.1333PaMnOMnCOT22MnO(S)+C(S)=2Mn(S)+CO2(g)(1)MnO(S)+C(S)=Mn(S)+CO(g)º·)/ln(0'0PPRTGGCO+∆=∆=]1013251333.0ln314.8)4.158268650[(×+−T=268650-270.98T·T=991KT991K.2MnO(S)+C(S)=2Mn(S)+CO2(g)º·)/ln(0'0PPRTGGCO+∆=∆=]1013251333.0ln314.8)0.149374510[(×+−T=374510-261.58T·T=991K·07MgOCaOCa2SiO4SiS+O2=SiO2Sº·Sil+O2=SiO2Sº·2Mgg+O2=2MgOSº·2CaOS+SiO2S=Ca2SiO4Sº·1SiMgOSil+2MgOS=2Mgg+SiO2SSiO2Sil+2MgOS=2Mgg+SiO2lººº·º1011Ca2SiO42CaOS+Sil+MgOS=2Mgg+Ca2SiO4Sºººº·º2CaOS+SiS+MgOS=2Mgg+Ca2SiO4Sºººº·)/ln(0'0PPRTGGMg+∆=∆=]101325ln314.8)7.216396640[(2MgpT×+−1aA+dD=qQ+RrPA´PD´PQ´PR´PAPDPQPR1-55])/()/()/()/(ln[00000aAdDrRqQPPPPPPPPRTG−=∆1-56aAdDrRqQPPPPPPPPK)/()/()/()/(0000=KRTGln0−=∆1-57KºKKK1-571-55JRTKRTGlnln+−=∆1-58KJK=JKJ11122ºº''0lnBTARBRTARTGK+=−−=∆−=1-593CaCO3S=CaOS+CO2gKP=PCO2KPCO2PCO2PCO2CO2PCO2PCO2CaCO3PCO2=PCO2PCO2PCO2CaOCO2CaCO3CaCO31183K101325Pa1183K1----20lnRTHdTKd∆=º1213º23C+CO2=2COCONb2O5NbNb2O5+5CS=2NbS+5CONb2O5•16xi%iiiinnxΣ=100)(%×Σ=iimminimiC123CdniniGdPTGdTTGdGnjPTCiniTniP,,1,,)()()(∑=∂∂+∂∂+∂∂=1-60niPTniG,,)(∂∂dniIiGiµ1314njVTnjPSnjVSiniGniHniU,,,,,,)()()(∂∂=∂∂=∂∂=µ(1-61)1-60idniGdnidGiΣ=Σ=µ(1-62)1-61ni1-62iniGniGiΣ=Σ=µ(1-63)GiµiGiiiiinnµγµ=)((1-64))()(iiiiinGnG=γ(1-65)1APAPºAAAAxPP0=(1-71)BBBCKP=(1-72)2(1-73)0=∆MV(1-74)0=∆MH(1-75)iiMxnRTGlnΣ=∆(1-76)iiMxnRSlnΣ−=∆1415MnO-FeO1fBaBBBBxfa=(1-77)BBBBBBaPxfPP00==1-78CSiO22CS+SiO2=[Si]+2COS[]G2)/(ln00SiOSiCOaaPPRTGG⋅+∆=∆(1-79)2IP0,PPaRi=1lim,1=→iRixixa1lim1=→ixiγ(1-80)iIHHiHiKPa,,=1lim,0=→iHixixa1lim0=→ixif(1-81)fi1%3,%%,,0iHiHRiiiakaKaPP===(1-82)][%,%%0ifkxfKxPPiiiHiiii===γ(1-83)iiHiRifaaγ=,,(1-84)1516x0iγi0iiiHiRifaaγγ==0,,(1-85)iHiHiMMKkaa1001%,%,==(1-86)MiM1i1412342),,,(ln43222xxxff=(1-87)x2x3x4∑∑∑∑+∂∂∂+∂∂+∂∂+===kjkjnjjjnjjjxxxxfxxfxxfff22222222222lnln21ln).0,0,0(lnln(1-88)).0,0,0(ln2f+∂∂+∂∂+∂∂=∂∂=∑=442332222222lnlnlnlnlnxxfxxfxxfxxffnjjj(1-89)01)ln(→∂∂=xiijixfε+++=4423322222lnxxxfεεε(1-90)+∂∂+∂∂+∂∂=∂∂=∑=]4[%]4[%ln]3[%]3[%ln]2[%]2[%ln][%][%lnln222222fffjjffnj(1-91)01)][%ln(→∂∂=xijijfe+++=]4[%]3[%]2[%ln4232222eeef(1-92)1617jiεjie81830K1%V2O5S)()(23)(2522sOVgOsV=+10,9.2471231350−⋅+−=∆molJTG)(][3][252sOVOV=+1Vs=[V]101,6.4520711−⋅−−=∆molJTG21/2O2=[O]102,89.2117150−⋅−−=∆molJTG32Vs+3/2O2=V2O5s103,9.2471231350−⋅+−=∆molJTG3-21-32=10,77.347838480−⋅+−=∆molJTGK=585960[%V][%O]][%],[%][][OaVaOV==323][2][)(][%][%152OVaaaKOVsOV==[%O]=0.011950.01195%9SiO2+2CS=[Si]+2COPCO=175.5PaaSiO2=0.097[%C]=4.0,1500288.0=CSie11.0=SiSieSiO2+2CS=[Si]+2CO·60.2031140lg+−=TKCSiOCOSiaaPPSifK2)]([%0=17182lg)lg(2]lg[%lglg0SiOCOSiaPPSifK−++=)097.0lg()325.1035.175lg(2]lg[%0.4288.0][%11.060.20177331140−++×+=+−SiSi0394.0][%11.0]lg[%=−+SiSi[%Si]=1.64171Nm-1-2AA·G=-WA·G1RTMrPP⋅=ρσ2ln0(1-94a)1819P0PrM∞Kelvin)11(2ln2121rrRTMPPrr−=ρσ(1-94b)Pr1Pr2r1r2r21-93a-r02aZnO+C=Zng+COb310-5cmCaSO418.2mol·L-1210-4cm15.33mol·L-1CaCO31-11-1CaCO3,kPaTº50060070080090010001.01×10-20.2132.3317.288.13441.98×10-20.3753.9526.3131496AlMgZrC·(1-94)V1-941920)344(32VGrrnG∆+=∆πσπ(1-95)nr1-2rKrKVKGr∆−=σ2(1-96)1-2·dCdRTCCRTddσσ⋅−=−=Γln(1-97)C------R--------2021k2k2=bbPbP+=11θ(1-98)18G1-4——Zn-2eZn2+——Cu2++2e——Cu2++2e1-4——2Cl--2e2122···mol-1ººSTGP∆−=∂∂)(PTGZFS)(∂∂=∆PTGZEFZEFH)(∂∂+−=∆(1-102)3aA+bB=gG+rRbBaArRgGaaaaRTGG⋅⋅+∆=∆ln0bBaArRqGaaaaZFRTEE⋅⋅−=ln0(1-103)1-103E=2223++−=+MMMMMMaaFRTln20ϕϕ(1-104)aaFRTMMMMln20−=++ϕϕ(1-105)−−++−++→γγγγγγMMAMaB−−++±±±⋅==⋅=γγγγaaamaB(1-106)γγγ1)(−−++±⋅=aaaγγγγγγ1)(−−++±⋅=γγγ1)(−−++±⋅=mmm(1-107)221BBzmΣ=Ι(1-108)MBBZBIA!lg−=±γ(1-109)A1—IZZA⋅⋅⋅−=−+±γlg(1-110)—A10298K0.01mol·kg-1NaNO30.0011mol·kg-1M