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Partition function

  1. Jan 1, 2008 #1
    Is the energy given by the first or the second? I have seen both relationships in different websites, and I am confused.

    [tex] E = kT^2 \frac{\partial Z}{\partial T} [/tex]


    [tex] E = - \frac{\partial ln Z}{\partial \beta} [/tex]
  2. jcsd
  3. Jan 1, 2008 #2
    The first one should be

    [tex] E = kT^2 \frac{\partial \ln Z}{\partial T} [/tex]

    You can go from one to the other by the chain rule since [tex]\beta=\frac{1}{k\,T}[/tex]
  4. Jan 1, 2008 #3
    I did realise you can go from one to the other before I post this up. But the MIT website solution happily used the same equation (1) twice. For example, page 6 of http://web.mit.edu/Physics/graduate/gen1sol_S01.pdf
  5. Jan 1, 2008 #4
    It's simply wrong! :smile:
  6. Jan 2, 2008 #5


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    Homework Helper

    Yes, Rainbow Child is right.
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