版权所有：华东理工大学物理化学教研室 11 1). The Maxwell relations dz = gdx + hdy V V U S S U U V S d d ⎟ d ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = dU = TdS − pdV p V U T h S U g V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = = ⎠⎞ ⎜⎝⎛ ∂∂ = , S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ x y xh yg ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 11 1). The Maxwell relations dz = gdx + hdy V V U S S U U V S d d ⎟ d ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = dU = TdS − pdV p V U T h S U g V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = = ⎠⎞ ⎜⎝⎛ ∂∂ = , S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ x y xh yg ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 12 1). The Maxwell relations dU = TdS − pdV S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ S S p V p T ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ V V T S T p ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ Maxwell relations x y x h y g ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ( ) ( )x y h z y g z x = ∂ ∂ = ∂ ∂ dz = gdx + hdy 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 12 1). The Maxwell relations dU = TdS − pdV S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ S S p V p T ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ V V T S T p ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ Maxwell relations x y x h y g ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ( ) ( )x y h z y g z x = ∂ ∂ = ∂ ∂ dz = gdx + hdy 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 13 dU = TdS − pdV S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ S S p V p T ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ V V T S T p ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ p V U T S U V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , V p H T S H p S = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , S T A p V A T V ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ , S T A V p G T p ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ , 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 13 dU = TdS − pdV S S V p V T ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ S S p V p T ⎟⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ V V T S T p ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ p V U T S U V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , V p H T S H p S = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , S T A p V A T V ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ , S T A V p G T p ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ , 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 14 2). The variation of internal energy with volume T T V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ The internal pressure is defined as π = Since V V U S S U U V S d d ⎟ d ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = If divide both sides of equation by dV with the constraint of constant T T V T V S U V S S U V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 14 2). The variation of internal energy with volume T T V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ The internal pressure is defined as π = Since V V U S S U U V S d d ⎟ d ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = If divide both sides of equation by dV with the constraint of constant T T V T V S U V S S U V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 15 2). The variation of internal energy with volume T V T V S U V S S U V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ p VU T SU V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , p V S T T ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ = V V T S Tp ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ p Tp T V⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ = Therefore: p Tp T V T ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ π = 5.1 Properties of the internal energy
版权所有：华东理工大学物理化学教研室 15 2). The variation of internal energy with volume T V T V S U V S S U V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ p VU T SU V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , p V S T T ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ = V V T S Tp ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ p Tp T V⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ = Therefore: p Tp T V T ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ π = 5.1 Properties of the internal energy