# Homework Help: Partition function of a gas

1. Sep 28, 2010

### rayman123

1. The problem statement, all variables and given/known data
The partition function of a given gas can be written
$$z=(\frac{V-Nb}{N})^{N}(\frac{mk_{B}T}{2\pi\hbar^2})^{\frac{3N}{2}}e^{{\frac{N^2a^2}{Vk_{B}T}}$$

2. Relevant equations

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

3. The attempt at a solution

mean energy
$$U=-\frac{\partial lnz}{\partial \beta}= \frac{3N}{2}{\frac{1}{\frac{mk_{B}T}{2\pi\hbar^2}}\cdot\frac{mk_{B}T}{2\pi\hbar^2}$$
taking $$\beta=\frac{1}{k_{B}T}$$
I get
$$\frac{3}{2}Nk_{B}T$$
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
$$\frac{1}{\beta}\frac{\partial lnz}{\partial V}= -\frac{N_{b}}{V-N_{B}}$$

can someone show me how to calculate it correctly?