Question about Maxwell equation in thermal physics

[Clara Chung]

Homework Statement

Homework Equations

The Attempt at a Solution

How to do part ii)?
I differentiate part i with respect to p
(∂H/∂P)_T = T (∂S/∂P)_T + V ...(1)
Then I used the equation given in the question,
Applying maxwell equation I got
(∂T/∂V)_S = -(∂P/∂S)_V ...(2)
I planned to substitute (2) into (1), However the subscript of
-(∂P/∂S)_V is V , but the subscript of (∂S/∂P)_T is T which are not the same
What should I do?

 

[Chestermiller]

What is the expression for dS interns of dT and dP?

 

[Clara Chung]

What is the expression for dS interns of dT and dP?

Do I need the expression according to the information given by the question or from dQrev/T?

 

[Chestermiller]

Do I need the expression according to the information given by the question or from dQrev/T?

Neither. Purely from mathematics.

 

[Clara Chung]

Neither. Purely from mathematics.

If it is purely from mathematics.. I think I can do it like this
G=H-TS
dG=dH-TdS-SdT
dG=VdP-SdT
so
(∂V/∂T)_P = - (∂S/∂P)_T
Now I can put it into (∂H/∂P)_T = T (∂S/∂P)_T + V ...(1)
So
(∂H/∂P)_T = -T(∂V/∂T)_P + V
Thanks for helping!