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Homework Help: 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
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