(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Please see P2 in http://panda.unm.edu/pandaweb/graduate/prelims/SM_S09.pdf

"Starting with [itex]\mathbb{Z} (z_1,z_2)[/itex] above, derive expressions for the gas pressure..."

2. Relevant equations

3. The attempt at a solution

To find the pressure at the top and the bottom of the gas column, I tried to use [tex]F=-kT\ln \mathbb{Z}[/tex], where F is the free energy, and [tex]P=-\left(\frac{\partial F}{\partial V}\right)_T[/tex] by writing [itex]h=\frac{V}{A}[/itex] and got a horrible expression. So I don't think that is the way to go for a timed exam. Moreover, I'm not sure how I can get the pressure at a specific height from that.

Now, I'm thinking about starting from the probability [itex]p=\frac{exp[-\beta (\frac{p^2}{2m}+mgz)]}{\mathbb{Z}}[/itex], which directly gives the number of particles at height z. But how can I get the pressure from that?

The second part where I have to calculate the pressure at the top given the pressure at the bottom looks easier though, since I have the pressure at the bottom as a reference point.

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# Gas pressure in gravitational field from the partition function

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