《物理化学 Physical Chemistry》课程教学资源（英文版）The Second Law（The Machinery）

Th e second law The machinery

The Second Law The Machinery

The Fundamental equations du= tds-pdV dh= tds+ vdp da=-SdT-pdV dg=-sdt+ vdp

The Fundamental Equations • dU = TdS - pdV • dH = TdS + Vdp • dA = -SdT - pdV • dG = -SdT + Vdp

Maxwell relations- Derivation oUOU IS+ dv=-lds+ pdv C S aT C

Maxwell Relations - Derivation               2 2 U S V U V S dU U S dS U V dV TdS pdV T V p S V S S V       =       =       +       = − +        = −      

Maxwell Relations- Summary T OS T OS Os T T S T p

Maxwell Relations - Summary p T V T S p S V p S T V V S T p S V p T S p V T         = −                 =                 =                 = −                        

Thermodynamic eg'n. of state dU=丌nV+CaT

Thermodynamic Eq’n. of State        T T T V T V U V T p T p dU dV C dT        =       − = +

Variation ofg with Temperature G刃 gas G > liquid as id Solle solid

Variation of G with Temperature   G T S S S S p gas liquid solid       = −   gas liquid solid T G

Variation ofg with pressure aG gas G > > ga qu SO liquid olid

Variation of G with Pressure   G p V V V V T gas liquid solid       =   gas liquid solid p G

Gibbs-Helmholz equation aG G-h S 刀T 1 OG G H TO t OG/T) JH

Gibbs-Helmholz Equation       G T S G H T T G T G T H T G T T H T p p p       = − = −       − = −       = − 1 2 2 2 ( / )

Temperature dependence of ag (△G/7)△H △HdT d(△G/7)=-」72 △G(72)△G(T) =△H 12,T1

Temperature dependence of DG   ( / ) ( / ) ( ) ( ) D D D D D D D G T T H T d G T HdT T G T T G T T H T T p T T T T       = − = − − = −         2 2 2 2 1 1 2 1 1 2 1 2 1 1

Pressure dependence of ag BAG =△→dAG=△p p △G(p2)=△G(n)+|4W如 for gases:△G(P2)=△G(P1)+ nItin(P2/p1) for solids and liquids,△G(P2)△G(P1)

Pressure dependence of DG   D D D D D D D D D D D G p V d G Vdp G p G p Vdp G p G p nRT p p G p G p T p p p p p p       =  = = + = +     1 2 1 2 1 2 2 1 2 1 2 1 2 1 ( ) ( ) ( ) ( ) ln( / ) ( ) ( ) for gases: for solids and liquids