Equations of state for a given system

[theboss368]

For a particular system it isfound that U=3/2 PV and P = AVT⁴/N. Find: the third equation of state; U(S,V,N); G(T,P,N); F(T,V,N); H(S,P,N); α(T,P); κ(T,P);and C_p(T,P).

 

I'm unsure of how to start, do I rearrange the equation for the parameters needed then put them together? Also the alpha kappa C_p parts have me a little baffled.

 

Would I need to do any major math or simple algebra

 

 

 

[mississippichem]

Are you familiar with the maxwell relations?

 

What is that pV term describing? Think about it. Then think about what differential you would integrate to get that pV term. How is that differential part of U(S, V, n). Finding the enthalpy should then be you're next step after finding the internal energy.

 

Please show some attempted work though or I can't continue to help.