物理化學(xué)英文課件：chapter04-1 Material Equilibrium

1、Chapter 4Material EquilibriumEquilibrium with respect to conversion of one set of chemical species to another setReaction: Equilibrium with respect to transport of matter between phase of the system without conversion of one species to anotherPhase:Physical ChemistryEntropy and EquilibriumThe intern

2、al energy (U) to identify permissible changesFirst law: The entropy (S) to identify the spontaneous changes among those permissible changes Second law:Material EquilibriumThe entropy (S) of an isolated system increases in the course of a spontaneous change: Stot 0The criterion for equilibrium in an

3、isolated system: maximization of the systems entropy SPhysical Chemistry(4.2)*a maximum at equilibriumEntropy and Equilibriumdq TdS(4.6)(4.7)(4.8)(4.9)dq = dU - dw TdSMaterial EquilibriumPhysical Chemistrydq = dU - dwThe Gibbs and Helmholtz Energies(4.10)dU TdS + SdT SdT + dwdU d(TS) SdT + dw(4.11)d

4、(U TS) SdT + dw(4.12)d(U TS) SdT - PdV(4.13)at constant T and V, dT=0, dV=0d(U TS) 0(4.14)P-V work onlydU TdS + dw(4.9)=: equilibriumP-V work onlyMaterial EquilibriumPhysical ChemistryA U - TSHelmholtz free energy(4.15)*dU d(TS) SdT d(PV) + VdPd(H TS) SdT - VdPd(U + PV TS) SdT + VdPat constant T and

5、 P, dT=0, dP=0d(H TS) 0(4.16)P-V work onlyConsider for constant T & P, dw = -PdV into (4.9)Material EquilibriumPhysical Chemistry(4.9)dU TdS + dwdU TdS + SdT SdT + PdV + VdP - VdPG H TS U + PV TSGibbs free energy(4.17)*dAT,V 0dGT,P 0Material EquilibriumPhysical ChemistryEquilibrium reachedConstant T

6、, PTimeGFig. 4.3G H TS U + PV TSGibbs free energy(4.17)*In a closed system capable of doing only P-V work, the constant-T-and-V material-equilibrium condition is the minimization of the Helmholtz function A, and the constant-T-and-P material-equilibrium condition is the minimization of the Gibbs fun

7、ction G.dA = 0at equilibrium, const. T, V (4.18)*dG = 0at equilibrium, const. T, P (4.19)*Material EquilibriumPhysical ChemistryG H TS U + PV TSGibbs free energy(4.17)*Consider a system in mechanical and thermal equilibrium which undergoes an irreversible chemical reaction or phase change at constan

8、t T and P.Material EquilibriumPhysical Chemistry(4.21)closed syst., const. T, V, P-V work onlyG = G2 G1 = (H2 TS2 ) (H1 TS1 ) = H TS(4.20)const. TMaterial EquilibriumPhysical Chemistryconst. T(4.12)(4.22)const. T, closed syst.It turns out that A carries a greater significance than being simply a sig

9、npost of spontaneous change:The change in the Helmholtz energy is equal to the maximum work the system can do:Material EquilibriumPhysical ChemistryG H TS U + PV TS(4.17)*G U TS + PV A + PV (4.12)(4.23)const. T and P, closed syst.If the P-V work is done in a mechanically reversible manner, then(4.24

10、)const. T and P, closed syst.orMaterial EquilibriumPhysical ChemistryWhen the change is reversibleThe maximum non-expansion work from a process at constant P and T is given by the value of GH U + PV G H TS(const. T, P)andThermodynamic Reactions for a System in EquilibriumBasic EquationsdU = TdS - Pd

11、V(4.25)*H U + PV(4.26)*A U TS(4.27)*G H - TS(4.28)*(4.29)*(4.30)*Material EquilibriumPhysical Chemistryclosed syst., rev. proc., P-V work onlyclosed syst., in equilib., P-V work onlyclosed syst., in equilib., P-V work only The rates of change of U, H, and S with respect to T can be determined from t

12、he heat capacities CP and CV.(4.31)*Key propertiesMaterial EquilibriumPhysical Chemistryclosed syst., in equilib.Basic EquationsHeat capacities(CP CV )The Gibbs EquationsdH = d(U + PV)(4.32)dH = TdS + VdPMaterial EquilibriumPhysical Chemistry= dU + d(PV)= dU + PdV + VdP= (TdS - PdV) + PdV + VdPdU =

13、TdS - PdV(4.25)*H U + PV(2.45)*dA = d(U - TS)dG = d(H - TS)(4.36)*dG = -SdT + VdP(4.35)dA = -SdT - PdV(4.32)dH = TdS + VdPdU = TdS - PdV(4.25)*Material EquilibriumPhysical Chemistry= dU - d(TS)= dU - TdS - SdT= (TdS - PdV) - TdS - SdT= dH - d(TS)= dH - TdS - SdT= (TdS + VdP) - TdS - SdT(4.36)*dG = -

14、SdT + VdP(4.35)dA = -SdT - PdV(4.34)dH = TdS + VdPdU = TdS - PdV(4.33)*The Gibbs EquationsMaterial EquilibriumPhysical Chemistryclosed syst., rev. proc., P-V work onlyFirst LawDefinitions (4.38)(4.37)(4.39)*The Power of thermodynamics:Material EquilibriumPhysical ChemistryDifficultly measured proper

15、ties to be expressed in terms of easily measured properties.The Maxwell RelationsIf Zf(x，y)，and Z has continuous second partial derivatives, thenThat isMaterial EquilibriumPhysical ChemistryThe Gibbs equation (4.33) for dU isdUTdSPdVdS0dV0V is held constant S is held constant(4.44)Material Equilibri

16、umPhysical Chemistry=dU = TdS - PdV(4.33)* These are the Maxwell Relations(4.45)(4.44)Material EquilibriumPhysical ChemistryThe first two are little used.The last two are extremely valuable.The equations relate the isothermal pressure and volume variations of entropy to measurable properties.Volume

17、dependence of UThe Gibbs equation (4.33) gives dUTdSPdVFrom (4.45)Divided (4.46) by dVT, the infinitesimal volume change at constant T, to give(4.47)For an isothermal process dUTTdSTPdVT (4.46)Material EquilibriumPhysical Chemistryfrom (4.34) dHTdSVdPPressure dependence of HTemperature dependence of

18、 UTemperature dependence of H(4.45)(4.48)Material EquilibriumPhysical ChemistryTemperature and Pressure dependence of GTemperature dependence of SPressure dependence of S(4.49)From (4.31)(4.51)The Gibbs equation (4.36) for dG isdG -SdT + VdPdT0dP0(4.38)(4.50)Material EquilibriumPhysical ChemistryJoule-Thomson Coefficient(2.64)*from (2.65)(4.52)(4.48)Material EquilibriumPhysical ChemistryHeat-Capacity Difference(2.60)(4.47)(4.53)Material EquilibriumPhysical Chemistry(4.53)As T 0, CP CVHeat-Capacity DifferenceMaterial EquilibriumPhysical