1. Limited time only! Sign up for a free 30min personal 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!

Partition function of a gas

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data
    The partition function of a given gas can be written
    [tex] z=(\frac{V-Nb}{N})^{N}(\frac{mk_{B}T}{2\pi\hbar^2})^{\frac{3N}{2}}e^{{\frac{N^2a^2}{Vk_{B}T}}[/tex]

    2. Relevant equations

    [tex]lnz= Nln(\frac{V-Nb}{N})+\frac{3N}{2}ln(\frac{mk_{B}T}{2\pi\hbar^2})+\frac{N^2a^2}{Vk_{B}T}}[/tex]

    3. The attempt at a solution

    mean energy
    [tex] U=-\frac{\partial lnz}{\partial \beta}= \frac{3N}{2}{\frac{1}{\frac{mk_{B}T}{2\pi\hbar^2}}\cdot\frac{mk_{B}T}{2\pi\hbar^2}[/tex]
    taking [tex] \beta=\frac{1}{k_{B}T}[/tex]
    I get
    is this correct?
    it seems like the minus from the formula for the mean energy is missing....it the whole calculation correct?

    1. The problem statement, all variables and given/known data
    calculate the pressure of the gas

    now i have
    [tex] \frac{1}{\beta}\frac{\partial lnz}{\partial V}= -\frac{N_{b}}{V-N_{B}}[/tex]

    can someone show me how to calculate it correctly?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Partition function Date
Deriving Fermi-Dirac Distribution misunderstanding Mar 14, 2018
Partition Function at a Fixed Pressure Oct 16, 2017
Mean energy using the partition function Sep 23, 2017
Partition function May 31, 2017