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

[Dai_Yue]

Homework Statement

The function G is given in the question: [tex]G(P,T) = \frac{-aT^2} {P}, [/tex]
where a is a positive constant.

Homework Equations

[tex] dG = Vdp - SdT, [/tex]
and probably [tex] S(V,T) = (\frac{\partial S}{\partial T})_V dT + (\frac{\partial S}{\partial V})_T dV [/tex]

The Attempt at a Solution

[tex]C_v dT = TdS, [/tex]

∴​

[tex](\frac{\partial S}{\partial T})_vdT = \frac {C_v}{T}[/tex]
.. 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 [tex](\frac{\partial S}{\partial T})_pdT = \frac {C_p}{T}[/tex]
, which turned into something like [itex] \frac{-2aT}{P} [/itex] but I don't know how I would find [itex]C_v[/itex] without being given a starting function of V and T like Helmholt's energy. Because I'm looking for [itex]C_v[/itex] I'm 90% sure that the function will be a function of V & T, not P & T.

Pls help thx

 

[Chestermiller]

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