Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mean Occupation Number of Non-interacting quantum fluids

  1. Mar 7, 2014 #1
    Hi, I get two contradicting sections of the book "Concepts in Thermal Physics":

    Earlier in the section they used the grand partition function to derive the mean occupation number ##<n_i> = -\frac{1}{\beta}\frac{\partial ln Z}{\partial E_i}##

    Later in the section, they said ##<n_k> = \frac{1}{\beta}\frac{\partial Z_k}{\partial \mu}##

    Why does the first expression take the differential of ##ln Z## and the second expression simply takes the differential of ##Z##?

    mbu0yf.png
     
  2. jcsd
  3. Mar 8, 2014 #2
    If it helps, it was earlier defined that ##Z = \Pi_i\left( 1 \pm e^{\beta(\mu - E_i)}\right)^{\pm 1}##
     
  4. Mar 11, 2014 #3
    bumpp
     
  5. Mar 11, 2014 #4
    It should be ln Z, it's just an error in the book. And the author is aware of it already, see this errata.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Mean Occupation Number of Non-interacting quantum fluids
Loading...