7 Solution Thermodynamics & Phase EquilibriumObjective:· Basic conceptions of solution thermodynamics·Evaluation of Fugacity Coefficient and Activity Coefficient· Basic conceptions , principles and diaphragm of weaksolution ,ideal solution and non-ideal solution· Basic conceptions of gas-liquid phase equilibrium and itsevaluation
7 Solution Thermodynamics & Phase Equilibrium Objective: • Basic conceptions of solution thermodynamics • Evaluation of Fugacity Coefficient and Activity Coefficient • Basic conceptions , principles and diaphragm of weak solution ,ideal solution and non-ideal solution • Basic conceptions of gas-liquid phase equilibrium and its evaluation
7.1 Free Energy and Free Enthalpy7.1.1 Free EnergyConstant temperature + volumeclosedsystemConstant temperature + pressureEnergy transfer with surroundings1st Law of ThermodynamicsdU =Q-8WtotTotal Work ofReversibleProcessSystemdU = QRey -SWtotRevNon-expansionSWrorRev = pdV +#WWorkeRev
7.1 Free Energy and Free Enthalpy 7.1.1 Free Energy closed system Constant temperature + volume Constant temperature + pressure Energy transfer with surroundings 1 st Law of Thermodynamics d δ δ U Q W = − tot Reversible Process Rev Rev Rev Rev d δ δ δ d δ tot tot e U Q W W p V W = − = + Total Work of System Non-expansion Work
SQReydsSQRev,=TdS-TdU =TdS-pdV-SWeRevConstant temperature + volumedU = d(TS)-SWeRevU-TS=-8WeRevA=U-TSHelmholtzfreeenergy
Rev δ d Q S T = Rev d d d δ U T S p V W = − − e Rev δQ T S = d Constant temperature + volume Rev Rev d d( ) δ d( ) δ = − − = − e e U TS W U TS W A U TS = − Helmholtz free energy
Ais a State Property, so...物系的状态一定，则有确定的A值ii只要始终状态一定，则不论过程是否恒温恒容或是可逆A其为一定值。AA = △U - △(TS)ii只有在恒温恒容可逆过程中A才等于物系所做的最大非体积体积功。-Ar = WeRev自由能的减少等于物系所做的最大非体积功Constant temperature:T = T, = Tsuroundings == Constant
A is a State Property, so. i 物系的状态一定，则有确定的A值 ii 只要始终状态一定，则不论过程是否恒温恒容 或是可逆，其 为一定值。 iii 只有在恒温恒容可逆过程中， 才等于物系所 做的最大非体积体积功。 自由能的减少等于物系所做的最大非体积功。 A = − A U TS ( ) A − = A W T V e , Rev Constant temperature: 1 2 Constant T T T = = = Surroundings
Free Energy Criterion0
Free Energy Criterion , 0 AT V, 0 AT V, 0 = AT V Spontaneous Equilibrium Impossible
7.1.2 Free EnthalpyConstant temperature + pressuredU = d(TS)-d(pV)-SWtotRevd(U-TS+ pV)=-8WtotRev(H-TS)=-8Wo福tot RevG=U-TS+ pV=H-TS=A+pVGibbsfreeenergy-FreeEnthalpy
7.1.2 Free Enthalpy Constant temperature + pressure Rev Rev Rev d d( ) d( ) δ d( ) δ d( ) δ = − − − + = − − = − tot tot tot U TS pV W U TS pV W H TS W = − + = − = + G U TS pV H TS A pV Gibbs free energy －Free Enthalpy
G is a State Property, so..物系的状态一定，则有确定的G值ii只要始终状态一定，则不论过程是否恒温恒容或是可逆，其△G为一定值。△G = △H -△(TS)ili只有在恒温恒容可逆过程中，AG才等于物系所做的最大非体积体积功。-△Gr,p = WeRev自由焰的减少等于物系所做的最大非体积功。= ConstantConstant temperature: T = T, = Tsuroundings =
G is a State Property, so. i 物系的状态一定，则有确定的G值 ii 只要始终状态一定，则不论过程是否恒温恒容 或是可逆，其 为一定值。 iii 只有在恒温恒容可逆过程中， 才等于物系所 做的最大非体积体积功。 自由焓的减少等于物系所做的最大非体积功。 G = − G H TS ( ) G − = G W T p e , Rev Constant temperature: 1 2 Constant T T T = = = Surroundings
Free Enthalpy Criterion10AG.Spontaneous△Gr,p= 0Equilibrium.pImpossibleAG,7
Free Enthalpy Criterion , 0 GT p, 0 GT p, 0 = GT p Spontaneous Equilibrium Impossible
SummaryHH=U+PVUpVA=U-TSTSApvG=H-TS=U+ pV-TSTSG= A+pV
Summary H U PV A U TS G H TS U pV TS A pV = + = − = − = + − = + H pV U pV A TS G TS
7.2 Relationship between Thermodynamic PropertiesdU = TdS- pdVA=U-TSdA=dU-TdS-SdTdA=-pdV- SdTdH = TdS +VdpG=H-TSdG= dH -TdS-SdTdG = Vdp- SdT
7.2 Relationship between Thermodynamic Properties d d d d d d d d d d d d d d d d d d d d U T S p V A U TS A U T S S T A p V S T H T S V p G H TS G H T S S T G V p S T = − = − = − − = − − = + = − = − − = −