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