# Pressure of Fermion Gas

Homework Statement
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.