7.2.3Clausius-Clapeyron EquationA system filled with pure substance ,two phases: α + β at specifictemperatureandpressure.Given that : 1 mole substance transferred from α to β the variation of free enthalpy is:△GTn =Gβ-GαmmEquiibrium State: △Gr, =0 →G = G%(T,p=C)mmT→T+dTNewEquilibriumState:p→p+dp
7.2.3 Clausius-Clapeyron Equation A system filled with pure substance ,two phases: at specific temperature and pressure. Given that : 1 mole substance transferred from to , the variation of free enthalpy is: + G G G T p m m , = − Equilibrium State: , 0 G G G T p m m = → = (T,p=C) New Equilibrium State: p p p → + d T T T → +d
NewEquilibrium State+dGaY0Q→GGmmmGB+dGBQBmmmGBdGβGa+dGα一+(T+dT,p+dp=C)mmmm=dGβdGamm表明：由于压力和温度的变化而引起的自由变化，对于两相必须相等，这样才能建立起新的平衡压力与温度间必须遵守一定的规律
New Equilibrium State: d d mmm mmm GGG GGG → + → + d d d d m m m m m m G G G G G G + = + = (T+dT,p+dp=C) 表明: 由于压力和温度的变化而引起的自由焓变化， 对于两相必须相等,这样才能建立起新的平衡, 压力与温度间必须遵守一定的规律
For α and β :dG =Vαdp- SdTdGB =VBdp-SBdTVαdp-SadT =VPdp-SBdTSBSeASdpmmmVBVadTAVmmm△S. - Molar entropy difference between two phases△V.. - Molar volumetric change when phase-changingm
For and : d d d d d d m m m m m m G V p S T G V p S T = − = − d d d d d d m m m m m m m m m m V p S T V p S T p S S S T V V V − = − − = = − m m S V − − Molar entropy difference between two phases Molar volumetric change when phase-changing
2nd Law of Thermodynamics:ASAHdpmmASmTdTT△VmClausius-Clapeyron Equation can be applied to any two-phaseequilibrium of single composition such as evaporation,sublimation, melting and crystal transformation.·For evaporation and sublimation,pmeans Saturate Vapor Pressure;. for melting and crystal transformation,p means Balance Outer Pressure
2nd Law of Thermodynamics: m m H S T = d d m m p S T T V = Clausius-Clapeyron Equation can be applied to any two-phase equilibrium of single composition such as evaporation, sublimation, melting and crystal transformation. • For evaporation and sublimation, p means Saturate Vapor Pressure; • for melting and crystal transformation, p means Balance Outer Pressure
For evaporation and sublimation, gas is treated as Ideal-Gaand AH is not changed with temperatureR.TmAV~mpAHdTdpmT2R,pAHIn P2mRTPimAH+ClnpORR.Tm
For evaporation and sublimation, gas is treated as Ideal-Gas and is not changed with temperature H . 2 2 1 2 1 1 1 ln ( ) m m m m m m R T V p dp dT H p R T p H p R T T = = − − ln m m H p C R T OR = − +