Hard thermo question.

  • Thread starter mewmew
  • Start date
  • #1
114
0
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:

Answers and Replies

  • #2
114
0
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.
 
  • #3
quasar987
Science Advisor
Homework Helper
Gold Member
4,784
18
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:
  • #4
114
0
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.
 

Related Threads on Hard thermo question.

  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
911
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
4K
Replies
5
Views
2K
Replies
6
Views
5K
Top