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Homework Help: A slightly modified ideal gas

  1. Apr 26, 2008 #1
    1. The problem statement, all variables and given/known data

    A system is contained within the walls of a box and a movable piston. An object weighing W is placed on the piston. If you regard the gas and the piston as an isolated system, use the microcanonical ensemble to deduce the equation of state for p (pressure). Take a look at the picture.


    2. Relevant equations

    [tex]\mathcal{H}=\frac{1}{2m}\sum p_i^2 + Wx[/tex]

    [tex]\Omega=V^{n}\int_{\mathcal{H} <E}dx d^{3N}p[/tex]

    [tex]S=klog\Omega[/tex]

    [tex]p/V=\frac{\partial S}{\partial V}[/tex]

    3. The attempt at a solution

    The only thing I need to solve this problem is to write down the hamiltonian of this system. I'd like to know if the expression that I have written is correct; in that case, I don't know how to evaluate the integral for the number of microstates.

    thanks!
     

    Attached Files:

  2. jcsd
  3. Apr 27, 2008 #2
    I'm sure that the hamiltonian of this system is as written above. Do you have any ideas for solving the integral for [tex] \Omega[\tex]?
     
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