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Finding temperature from entropy

  1. Dec 10, 2008 #1
    Hi all,

    I have determined the entropy previously which gives the following results

    S = k*(N Log N - n Log n -(N-n)*Log(N-n)

    I have furthermore deduced the relation between state n and the energy as

    [tex]n = \frac{E+N*\epsilon}{2*\epsilon}[/tex]

    I know that the temperature is

    [tex]\frac{\partial S}{\partial E}=\frac{1}{T}[/tex]

    I am not quite sure how to proceed - I could replace small n with an expression containing the energy but what about capital N - should I isolate that from the relation and insert that into the entropy expression and then differentiate with respect to the energy - any hints or commands appreciated thanks in advance.

  2. jcsd
  3. Dec 10, 2008 #2


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    Gold Member

    Replacing 'n' in your expression for the entropy seems like a good start to me. The next question is "which variables are held fixed when you compute the partial derivative of S with respect to E"? ...Surely if 'N' is fixed during this differentiation, the problem is simplified.:wink:
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