# Entropy and Energy Density from a Partition Function

1. Homework Statement

Partition Function: Z = 1/N! [8 pi V (kT/hc)^3]^N
There are several parts to this but here are the parts I'm struggling with:
a) Compute the entropy of the system S.
b) Computer the energy density u and compare the result with the corresponding results for a nonrelativistic gas and radiation (a "photon gas").

2. Homework Equations

S = Bk (U-F) = - (partial F w/ respect to T)
S = k ln Z

u = U/V

3. The Attempt at a Solution

I got that U = 3 NkT. So is u just 3Nkt/V? How do I find this for a nonrelativistic gas and radiation?

I also computed cv = 3Nk and cp = 4Nk but don't know what to do from there.

Much appreciate the help!