# Homework Help: A slightly modified ideal gas

1. Apr 26, 2008

### luisgml_2000

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

$$\mathcal{H}=\frac{1}{2m}\sum p_i^2 + Wx$$

$$\Omega=V^{n}\int_{\mathcal{H} <E}dx d^{3N}p$$

$$S=klog\Omega$$

$$p/V=\frac{\partial S}{\partial V}$$

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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2. Apr 27, 2008

### luisgml_2000

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]?