华东理工大学：物理化学（中英文） 5. The Second Law: the machinery

p The fundamental equations The First Law: dU=dg+dw H For a reversible change in a composition, and in the pl closed system of constant absence of any non-expansion P A TS work d w=-pdy and dq =tds G TS du=Tds -pdv dv is an exact differential, its value is independent of pa 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 6 The First Law: dU =dq+dw H pV U pV A TS G TS For a reversible change in a closed system of constant composition, and in the absence of any non-expansion work: d w = -pdV and dq =TdS dU=TdS-pdV dU is an exact differential, its value is independent of path. The fundamental equations

p The fundamental equations H=U+p, A=0-TS, G=U+pV-TS dh= dU+ pdy+ vd Pv U = (dS pd)+pdv+ vdp y A TS Tds +yd G IS dg= dU+pdv+ vdp -tds- sdT (TdS pdn)+pd+ vdp-TdS- SdT -vdp -sdT da= dU-Tds-SdT =(d pdv)-TdS- SdT pdv-sdT 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 7 H pV U pV A TS G TS dH = dU+ pdV + Vdp =(TdS-pdV)+ pdV + V dp H=U+pV, A=U-TS, G=U+pV-TS dA= dU-TdS-SdT = (TdS -pdV) -TdS- SdT dG = dU+pdV+ Vdp –TdS- SdT = (TdS-pdV) +pdV+ Vdp –TdS- SdT = TdS +V dp = Vdp -SdT = -p dV -SdT The fundamental equations

p The fundamental equations du=Tds -pdy H dH=TdS+vdp p dG=vdp- SdT V A TS dA=-pdv-sdT IS The fundamental equations 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 8 dU=TdS -pdV dH=TdS+Vdp dG=Vdp-SdT dA=-pdV-SdT H pV U pV A TS G TS The fundamental equations The fundamental equations

O 5.1 Properties of the internal energy 1). The Maxwell relations z=f(x,y) dx⊥ J gdx+ hdy z where 8= a ay x 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 9 5.1 Properties of the internal energy 1). The Maxwell relations = gdx + hdy z = f (x, y) y y z x x z z y x d d d            +        = y x y z h x z g            =        where =

O 5.1 Properties of the internal energy ) The Maxwell relations The first derivative of g with respect to v, and h to x 0 z axa g 0z ax)y ayax dz=gdx hdy 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 10 1). The Maxwell relations x y z y g x    =           2 y x z x h y     =        2 x y x h y g         =           dz = gdx + hdy The first derivative of g with respect to y, and h to x 5.1 Properties of the internal energy