Boltzmann distribution - Derive equation of state of a gas from Helmholtz free energy


by yellowstone33
Tags: boltzmann, derive, distribution, energy, equation, free, helmholtz, state
yellowstone33
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#1
Mar15-11, 12:04 AM
P: 1
1. The problem statement, all variables and given/known data

Show that the equation of state of an ideal gas with N molecules in a container of volume V at temperature T is P=NkT. Use the result derived earlier.

The result is A=-NkTlnZ, where Z is the partition function and A is the Helmholtz free energy.

2. Relevant equations

3. The attempt at a solution

P=-([tex]\delta[/tex]A)/([tex]\delta[/tex]V)T

P=NkT([tex]\delta[/tex]lnZ)/([tex]\delta[/tex]V)T

Here, I'm stuck. Surely, ([tex]\delta[/tex]lnZ)/([tex]\delta[/tex]V)T=0?

It seems so trivial. I don't understand what I'm missing. Thank you in advance.
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