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

The partition function of a given gas can be written

[tex] z=(\frac{V-Nb}{N})^{N}(\frac{mk_{B}T}{2\pi\hbar^2})^{\frac{3N}{2}}e^{{\frac{N^2a^2}{Vk_{B}T}}[/tex]

2. Relevant equations

[tex]lnz= Nln(\frac{V-Nb}{N})+\frac{3N}{2}ln(\frac{mk_{B}T}{2\pi\hbar^2})+\frac{N^2a^2}{Vk_{B}T}}[/tex]

3. The attempt at a solution

mean energy

[tex] U=-\frac{\partial lnz}{\partial \beta}= \frac{3N}{2}{\frac{1}{\frac{mk_{B}T}{2\pi\hbar^2}}\cdot\frac{mk_{B}T}{2\pi\hbar^2}[/tex]

taking [tex] \beta=\frac{1}{k_{B}T}[/tex]

I get

[tex]\frac{3}{2}Nk_{B}T[/tex]

is this correct?

it seems like the minus from the formula for the mean energy is missing....it the whole calculation correct?

1. The problem statement, all variables and given/known data

calculate the pressure of the gas

now i have

[tex] \frac{1}{\beta}\frac{\partial lnz}{\partial V}= -\frac{N_{b}}{V-N_{B}}[/tex]

can someone show me how to calculate it correctly?

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# Homework Help: Partition function of a gas

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