上海交通大学：《材料热力学》教学资源_07电子教案（英文课件）lecture 6 property relation II

Contents of Today S.J.T.U. Phase Transformation and Applications Review previous Property relation Functions F and G Partial molar quantities Property relation derived from U,H,F,and G etc. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Contents of Today Review previous Property relation Functions F and G Partial molar quantities Property relation derived from U, H, F, and G etc

3.2 The Functions F and G(3) S.J.T.U. Phase Transformation and Applications U PV TS H=U+PV G=H-TS F=U-TS SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications 3.2 The Functions F and G (3) ≡ −TSUF ≡ −TSHG ≡ + PVUH

3.2 The Functions F and G(4) S.J.T.U. Phase Transformation and Applications dU Tds-Pdv dF =-SdT-Pdv H dG =-SdT +VdP S dH Tds VdP F U SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications 3.2 The Functions F and G (4) = − PdVTdSdU = − − PdVSdTdF −= +VdPSdTdG = +VdPTdSdH

3.3 Chemical Potentials (5) S.J.T.U. Phase Transformation and Applications &G OF T,P,n≠n aG OF aH aU On; =4 i T P.ni+ni Oni P,S,n,≠n oni V,S,n≠n The chemical potential of the component i. G Used extensively in the treatment of the thermodynamics of solutions and of chemical reactions. U SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications 3.3 Chemical Potentials (5) ij nnVT ij i nnPT i n F n G ≠ ≠ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ,, ,, i i nnPT ij i nnVT ij i nnSP ij i nnSV ij n U n H n F n G = μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ,, ≠ ,, ≠ ,, ≠ ,, ≠ μi The chemical potential of the component i. Used extensively in the treatment of the thermodynamics of solutions and of chemical reactions

Review S.J.T.U. Phase Transformation and Applications 当系统由始态I经过某一过程变到终态Ⅱ后，如能使系统再回到原态，同时 也消除了原过程对环境所产生的一切影响，则原来过程称为可逆过程。 H=U+PV dU=TdS-Pdv PV G=H-TS dF =-SdT-Pav TS F=U-TS dG=-SdT +VdP G H dH TdS +VdP U The chemical potential of the component i. OG OF aH aU on O =4 iP,S,nj≠n oni )v.s.n,+n SJTU Thermodynamics of Materials Spring2006©X.J.Jim Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Review ≡ −TSUF ≡ −TSHG ≡ + PVUH 当系统由始态I经过某一过程变到终态II后，如能使系统再回到原态，同时 也消除了原过程对环境所产生的一切影响，则原来过程称为可逆过程。 = − PdVTdSdU = − − PdVSdTdF = − +VdPSdTdG = +VdPTdSdH i i nnPT ij i nnVT ij i nnSP ij i nnSV ij n U n H n F n G = μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ,, ≠ ,, ≠ ,, ≠ ,, ≠ μi The chemical potential of the component i

Index of nomenclature S.J.T.U. Phase Transformation and Applications Entropy of Mixing混合熵 ·Partial Molar Quantities偏摩尔量 .). p.65,2.13 O△G aCp =△V ap 8) Os aH OH S,o SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Index of nomenclature • Entropy of Mixing混合熵 • Partial Molar Quantities偏摩尔量 T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − = 0 ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ T VU p.65, 2.13 V p G T Δ= ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂Δ∂ T p pC ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ S pT ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ S T ⎟⎠⎞ ⎜⎝⎛ ∂∂σ T p V V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ − 1 H S T ⎟⎠⎞ ⎜⎝⎛ ∂∂ σ εH S , ⎟⎠⎞ ⎜⎝⎛ ∂∂

Partial Molar Quantities S.J.T.U. Phase Transformation and Applications The partial derivative of that quantity with respect to mass(number of moles)at constant temperature and constant pressure,and the mass of all other materials in the system. The partial molar volume of material a in a solution. Va= av Pure a > The partial molar volume would be equal to the molar volume. Constant T and P The chemical potential is the partial molar Gibbs free energy.(Only) a SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Partial Molar Quantities The partial derivative of that quantity with respect to mass (number of moles) at constant temperature and constant pressure, and the mass of all other materials in the system. a nnPT cb ,,,, " a n V V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = The partial molar volume of material a in a solution. a nnPT cb ,,,, " a n V VSlope ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ == na V Constant T and P Pure a The partial molar volume would be equal to the molar volume. The chemical potential is the partial molar Gibbs free energy. (Only)

Property Relations (1) S.J.T.U. Phase Transformation and Applications OM aN dz Mdx Ndy dU=Tas-Pav dH TaS +Vdp dF =-SdT-Pdv 〔部) as dG =-SaT+Vap as H SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Property Relations (1) = + NdyMdxdz = − PdVTdSdU = +VdPTdSdH = − − PdVSdTdF = − +VdPSdTdG x y x N y M ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ S S V P V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ S S P V P T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T V P V S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ −

Property Relation S.J.T.U. Phase Transformation and Applications dU Tds-Pdy =T =-P av dF =-SdT-Pdv =-S =-P dG =-SdT +Vap =-S =V dH Tas +Vap -T =V av 二 S aP) as as v at SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications Property Relation S S V P V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ S S P V PT ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T V P V S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T P V PS ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − = − PdVTdSdU = − − PdVSdTdF = − +VdPSdTdG = +VdPTdSdH P V U T S U V S ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ P V F S T F V T ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ V P G S T G P T ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ V P H T S H P S ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂

恒温下熵变的计算(1) S.J.T.U. Phase Transformation and Applications or) 3s-=-) dp p.65,2.13 EX:ideal gas R R PV-RT =- ds= D 恒温下，当压力改变时，将引起熵变 For a change in pressure from 1 atm to 10 atm at constant pressure. H AS--RP--RIn P--RIn10--19.14J/(mol-K) SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 6 property relation applications

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 6 property relation applications 恒温下熵变的计算(1) T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − ∫∫ ⎟⎠⎞ ⎜⎝⎛ ∂∂ −==− 21 21 12 PP P dP TV SdSS EX: ideal gas dP P R Sd P R P S P R T V RTVP P T ⎟ −= −= ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ = For a change in pressure from 1 atm to 10 atm at constant pressure. RPR ( ) KmolJ PdP RS PP −=−=−=−=Δ ⋅ ∫ ln /14.1910ln 101 21 恒温下，当压力改变时，将引起熵变 p.65, 2.13