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Boltzmann distribution  Derive equation of state of a gas from Helmholtz free energy 
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Mar1511, 12:04 AM

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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=([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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