How to derive U(S(V,T),V) from U(S,V,N)?

[Persefonh]

Homework Statement

My question is how can one derive U(S(V,T),V) from the relation U(S,V,N).This is the beginning of a given solution which is not explained in more detail.

Homework Equations

The Attempt at a Solution

I can understand U(S,V,N) as dU=TdS-pdV+μdN but not the transition: U(S,V,N)-->U(S(V,T),V).
A full solution of this exercise is given at http://www.thphys.uni-heidelberg.de/~amendola/statphys/problems-students.pdf on page 3.

 

[jitu16]

Are you referring to eqn 13?? If that's the case here's explanation:

$\frac{\partial U(S,V)}{\partial V}= \frac{\partial U}{\partial S} \frac{\partial S}{\partial V}+\frac{\partial U}{\partial V} \frac{\partial V}{\partial V} =\frac{\partial U}{\partial S} \frac{\partial S}{\partial V}+\frac{\partial U}{\partial V}$

This is a simple chain rule. If you don't know chain rule, review your calculus course, I don't think you'll go anywhere without that.

 

[Persefonh]

Thank you for your reply.I am not referring to equation 13, but before that.
The exercise starts with U(S(V,T),V). My question is how one can derive that from U(S,V,N)?

 

[jitu16]

Entropy is a function of T,V or T,P.
If you still can't recall,
$S=-\frac{\partial G(T,V)}{\partial T}$ and,
$S=-\frac{\partial A(T,P)}{\partial T}$

 

[BvU]

Hello Persephone, welcome to PF !

Could it be as simple as N is constant, hence $U(S, V, N) = U(S, V)$ ?

 

[Persefonh]

Thanks BvU!