Find Cv as a function of V & T (or P & T) given G(P,T)?

1. Feb 29, 2016

Dai_Yue

1. The problem statement, all variables and given/known data
The function G is given in the question: $$G(P,T) = \frac{-aT^2} {P},$$
where a is a positive constant.
2. Relevant equations
$$dG = Vdp - SdT,$$
and probably $$S(V,T) = (\frac{\partial S}{\partial T})_V dT + (\frac{\partial S}{\partial V})_T dV$$
3. The attempt at a solution
$$C_v dT = TdS,$$
∴​
$$(\frac{\partial S}{\partial T})_vdT = \frac {C_v}{T}$$
.. and that's about as far as I got.

I could find C_p by taking a partial derivative of G with respect to T and get $$(\frac{\partial S}{\partial T})_pdT = \frac {C_p}{T}$$
, which turned into something like $\frac{-2aT}{P}$ but I don't know how I would find $C_v$ without being given a starting function of V and T like Helmholt's energy. Because I'm looking for $C_v$ I'm 90% sure that the function will be a function of V & T, not P & T.

Pls help thx

2. Mar 2, 2016

Staff: Mentor

In order to get Cv, you are going to have to get U. U can be obtained from knowledge of H and PV. Do you know how to get H if you know G(P,T)? Do you know how to get V if you know G(P,T)?

Chet