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Homework Help: Hard thermo question.

  1. Oct 30, 2006 #1
    Well, it's hard to me at least :frown:
    http://img169.imageshack.us/img169/206/questionzg0.png [Broken]
    We are using Schroeders book and this problem was given to us from I assume the book by Reif. We haven't seem to have gotten far enough along in Schroeders book to have gone over this though.

    I can do part A, but part B and C I am clueless on. I know that T = partial derivative of U/S but it doesn't seem to be helping me very much. Thanks in advance for any pointers.
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 30, 2006 #2
    Ok, I found B more or less, by taking n=E/e. My equation for T looks pretty nasty because my multiplicity from part A was relatively nasty. I am still pretty much completely stuck on how to do C though.
     
  4. Oct 31, 2006 #3

    quasar987

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    What do you get for A? I get

    [tex]\Omega(N,n)=\binom{N}{N-n}=\frac{N!}{n!(N-n)!}[/tex]

    (the number of ways to pick the position of the N-n atomes that are not in an interstititiisal position.

    Temperature is [tex]\frac{1}{kT}=\frac{\partial \Omega(N,n)}{\partial E}[/tex].

    I guess you said, [tex]n=n(E)=E/\epsilon[/tex], so then

    [tex]\frac{\partial \Omega(N,n)}{\partial E}=\frac{\partial \Omega(N,n)}{\partial n}\frac{\partial n}{\partial E}= \frac{\partial \Omega(N,n)}{\partial n}\frac{1}{\epsilon}[/tex]

    But do you know how to take the derivative of a factorial?
     
    Last edited: Oct 31, 2006
  5. Oct 31, 2006 #4
    Sorry, I Should have been more specific. I took a Sterling approximation of the factorials of the form Ln(x!)= x Ln(x) - x, expanded each term, substituted in n = E/epsilon and differentiated. This was messy though and I am not sure the desired method.
     
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