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Partition function

  • Thread starter touqra
  • Start date
  • #1
284
0
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]

or

[tex] E = - \frac{\partial ln Z}{\partial \beta} [/tex]
 

Answers and Replies

  • #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]
 
  • #3
284
0
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]
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
 
Last edited by a moderator:
  • #4
It's simply wrong! :smile:
 
  • #5
mjsd
Homework Helper
726
3
Yes, Rainbow Child is right.
 

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