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