Homework Help: 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

Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?