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

1. ### yellowstone33

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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=-($$\delta$$A)/($$\delta$$V)T

P=NkT($$\delta$$lnZ)/($$\delta$$V)T

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

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

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