Property Relation S.J.T.0. Phase Transformation and Applications dU=TdS-Pdv -T =-P dF =-SdT-Pdv 〔) =-S =-P dG =-SdT +Vap =-S =V dH TaS +Vap 〔) -T ap a as aP)s as as U aT) aP SJTU Thermodynamics of Materials Spring2012©X.J.Jin Lecture 6 Property Relation Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2012 © X. J. Jin Lecture 6 Property Relation II Property Relation S S V P V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ S S P V PT ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T V P V S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ T T P V PS ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − dU = TdS − PdV dF = −SdT − PdV dG = −SdT +VdP dH = TdS +VdP 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.0. Phase Transformation and Applications p.65,2.13 s-ss=-() EX:ideal gas PV=RT 8 RdP ds= 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 -n--19.14J/(@ol-K) SJTU Thermodynamics of Materials Spring2012©X.J.Jin Lecture 6 Property Relation Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2012 © X. J. Jin Lecture 6 Property Relation II 恒温下熵变的计算(1) T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − ∫ ∫ ⎟⎠⎞ ⎜⎝⎛ ∂∂ − = = − 21 21 2 1 PP P dP TV S S d S EX: ideal gas dP P R d S P R P S P R T V PV RT P T ⎟ = − = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ = For a change in pressure from 1 atm to 10 atm at constant pressure. R P R J ( ) mol K PdP S RPP Δ = − = − = − = − ⋅ ∫ ln ln10 19.14 / 101 21 恒温下，当压力改变时，将引起熵变 p.65, 2.13
恒温下熵变的计算（③） S.J.T.0. Phase Transformation and Applications ap s,-s-=() EX:solid the volumetric thermal expansion coefficient, For a change in pressure from 1 atm to 10 atm at constant pressure.The molar volume and volumetric thermal expansion coefficient are constant over the pressure range of interest. AS=-JVaydP=-Vay(P,-P)=-9Var H SJTU Thermodynamics of Materials Spring2012©X.J.Jin Lecture 6 Property Relation Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2012 © X. J. Jin Lecture 6 Property Relation II 恒温下熵变的计算(3) T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − ∫ ∫ ⎟⎠⎞ ⎜⎝⎛ ∂∂ − = = − 21 21 2 1 PP P dP TV S S d S EX: solid the volumetric thermal expansion coefficient, For a change in pressure from 1 atm to 10 atm at constant pressure. The molar volume and volumetric thermal expansion coefficient are constant over the pressure range of interest. V V P P S VαV dP Vα (P2 P1) 9Vα 2 1 Δ = − = − − = − ∫ αV V P P V V TV TV V α ⎟ = α ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ = 1