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Statistical mechanics

  1. Feb 15, 2009 #1
    In adjacent containers of volume V1 and V2, there contains a gas of N molecules. The gas is free to move between the containers through a small hole in their common wall.

    What is the probability to find k molecules in the V1?

    Probability of one molecule to be in V1 is given by:
    [tex]P=\frac{V_1}{V_1+V_2} [/tex]

    Using the Poisson distribution, I think the probability that k molecules are in V1 should be:

    [tex]p_{poisson}(k)=\frac{a^k}{k!} e^{-a} [/tex]
    [tex]p(k)=\frac{\left( \frac{N V_1}{V_1+V_2} \right) ^k}{k!} e^{-\frac{N V_1}{V_1+V_2}} [/tex]

    Is this correct?

    My next step is to find the probability when V2 -> infinity, and N->infinity such that [tex]N/V=\rho[/tex] is finite.

    For this, I get:
    [tex]p(k)=\frac{\left( \rho \right) ^k}{k!} e^{-\rho} [/tex]

    Does this work make any logical sense at all? Comments are appreciated, thanks for the help!
     
  2. jcsd
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