## Which should I use to prove this?

(∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume

s(P,v)
Tds= du +pdv
h= u + pv
h(P,v)
u(P,v)
or other formula?
How am I going to choose ? Please guide

Thank

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 Quote by Outrageous (∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume s(P,v) Tds= du +pdv h= u + pv h(P,v) u(P,v) or other formula?
I'm not expert on gas theory, so I'll just treat this as an algebraic question.
Of those 'formulae', only two are equations. One of those two involves h, not mentioned anywhere else. So that leaves Tds= du +pdv as the only candidate.
What would the constant volume version of that equation look like?

 Quote by haruspex I'm not expert on gas theory, so I'll just treat this as an algebraic question. Of those 'formulae', only two are equations. One of those two involves h, not mentioned anywhere else. So that leaves Tds= du +pdv as the only candidate. What would the constant volume version of that equation look like?
The others also can become equation like s is function of v and p
So ∂s=(∂s/∂p)dp + (∂s/∂v)dv
Then h=u + pv , can be dh= du + Pdv + vdp
This is all just dealing with mathematics , please teach me how to choose
Do you mean why did I put constant volume there? It means by keeping volume constant then only differentiate.
Thank

## Which should I use to prove this?

 Quote by Outrageous (∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume s(P,v) Tds= du +pdv h= u + pv h(P,v) u(P,v) or other formula? How am I going to choose ? Please guide Thank
Have you considered using the Maxwell relations?

BiP

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 Quote by Outrageous Do you mean why did I put constant volume there?
No, I mean take this equation: Tds= du +pdv
and turn it into an equation involving partial derivatives, v being constant.

 Quote by Bipolarity Have you considered using the Maxwell relations? BiP
 Quote by haruspex No, I mean take this equation: Tds= du +pdv and turn it into an equation involving partial derivatives, v being constant.
I am not really understand what is Maxwell ,
I only can get (∂s/∂P) at constant volume = (1/T)(∂h/∂P)constant volume -(v/T)

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