Apply Eqs 7 7 and 7 10 directly to Eqs 7 5 and 7 6 and derive the relations of Eqs 7 13 and 7 14 Eq 7 5 d Pdv sdT Eq 7 6 dg vdP sdT Eq 7 10 dz (z x)y dx (z y)x dy Eq 7 13 (P T)v (s v)T Eq 7 14 (v T)P (s P)T

Question: Apply Eqs. 7.7 and 7.10 directly to Eqs. 7.5 and 7.6 and derive the relations of Eqs. 7.13 and 7.14. Eq. 7.5 d = Pdv

Apply Eqs. 7.7 and 7.10 directly to Eqs. 7.5 and 7.6 and derive the relations of Eqs. 7.13 and 7.14.
Eq. 7.5
dα = Pdv - sdT
Eq. 7.6
dg = vdP - sdT
Eq. 7.10
dz = (∂z / ∂x)y dx + (∂z / ∂y)x dy
Eq. 7.13
(∂P/∂T)v = (∂s/∂v)T
Eq. 7.14
(∂v/∂T)P = - (∂s/∂P)T

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