1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hard thermo question.

  1. Oct 30, 2006 #1
    Well, it's hard to me at least :frown:
    [​IMG]
    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.
     
  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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Hard thermo question.
Loading...