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A slightly modified ideal gas

1. Homework Statement

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. Homework 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!
 

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Answers and Replies

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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