# Pressure of Fermion Gas

1. Jun 19, 2016

### LizardWizard

The problem statement, all variables and given/known data
For a gas of N fermions of mass m confined in a volume V at a temperature $T<E_F/kB$, consider the quantity $<n_p>/V$ as you would a classical distribution f(p,q) in the system phase space. Show that the impulse transfer of the elastic collisions of the particles with the wall of the container with this f leads to the correct expression for the pressure of the gas.

The attempt at a solution
Now I might be wrong in assuming this but can I treat $<n_p>/V$ as the density of states? If so, for low temperatures we have
$g(\epsilon)=3N/2F (\epsilon/\epsilon_F)$
$U = \int_0^{\epsilon_F} d \epsilon g(\epsilon) \epsilon = 3N \epsilon_F/n$
$P=(dU/dV)_S=2N\epsilon_F/5$

I don't know if this is the correct approach to the problem, but I have no other idea where to start.

2. Jun 24, 2016