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Homework Help: Thermodynamical fluctuations, mean square deviation help!

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Recalling that k=R/Na (Na is Avogadro's number), show that the density of fluctuations of an ideal gas are given by :

    <(dp)^2> / p^2 = 1 / (N*Na) where p is the density (mass/V)

    That is, the relative mean square density deviation is the reciprocal of the number of molecules in the subsystem.

    2. Relevant equations

    <(dN)^2> = <N^2> - <N>^2 from my book

    3. The attempt at a solution

    I have no idea where to even begin with this..I have a whole series of problems that ask me to find the "mean square deviation of ____". I understand what an expectation value is, and that i have the given equation for the value.

    But HOW do I find <P> or <P^2> ?? Normally I would take the value*probability (sum of X*P(X) right?) but in this case....what is my probability? what is my value??

    Where do I even start!?!?

    Plz help I have 4 problems like this and am stuck in the exact same place on all 4.
  2. jcsd
  3. Nov 13, 2008 #2
    You may look up "grand canonical ensemble" or "grand partition function" in any thermodynamics textbook. It'll help.
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