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Entropy And Energy Representation

  1. Dec 13, 2012 #1
    How do I go from the entropy of a system, S(U,V,N), to its internal energy, U(S,V,N)?
    For instance, for an ideal classical gas, we have

    S=(3/2)N*R*ln(U/N) + N*R(V/N) + N*R*c

    where R is the Boltzmann constant, N is the particle number, V is the volume and "c" is a constant.

    How can I convert this to U(S,V,N) ?

    The unswer is U=N*(U/N)^(2/3)*exp[(2/3)*(S/(N*R)-c)]

  2. jcsd
  3. Dec 13, 2012 #2


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    Staff: Mentor

    This is just algebra. Isolate ln(U/N), use e^() on both sides and multiply with N.
  4. Dec 13, 2012 #3
    my bad. thanks!
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