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Heat capacity from energy

  1. Nov 2, 2008 #1
    Hi all,

    I have to show that the heat capacity can be expressed as

    Cv = Nk(1+1/45(Om/T)^2 + ...)

    where the internal energy is given as

    E = NkT*(1-(Om/(3T)-1/45(Om/T)^2)

    Normally I would just differentiate but if I do this I get something completely different - how to proceed any hints appreciated thanks in advance

    Best regards

  2. jcsd
  3. Nov 2, 2008 #2


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    Hi Magnus! :smile:
    erm … NkT*(1 - Om/(3T) - 1/45(Om/T)^2) = Nk(T - Om/3 - 1/45(Om/T)) :redface:
  4. Nov 2, 2008 #3
    yes of course... Thanks for the help. The partition function is also given in the exercise

    q_{rot} = \frac{T}{\omega}*(1+\frac{1}{3}(\frac{\omega}{T}+\frac{1}{15}(\frac{\omega}{T})^2+...)

    I presume the internal energy is given as

    E = -N(dLn Zrot / d beta)

    I would really like to know how to get from the partition function to the internal energy.
    The problem for me is how manage the differentiation of the serie. Any help or advise appreciated. Thanks in advance.


  5. Nov 2, 2008 #4


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    durrr … honestly no idea what that's all about …

    i thought this was a straightforward calculus problem! :redface:

    i think you'd better start a new thread, so as to get someone else to answer :smile:
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