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Homework Help: Entropy and Energy Density from a Partition Function

  1. Apr 6, 2008 #1
    1. The problem statement, all variables and given/known data

    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. Relevant 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!
  2. jcsd
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