2D Fermion Gas

1. Jun 18, 2016

LizardWizard

The problem statement, all variables and given/known data

For a gas of N fermions with mass M in 2D in a region of area A in thermal equilibrium at temperature T, we are asked to find $U/N$ in fuction of $T$ and $a=A/N$.

The attempt at a solution

I used $U=\sum(<n_i>\epsilon_i) = \sum(\exp(\beta(\mu-\epsilon_i))\epsilon_i = \exp(\mu\beta)\sum(\exp(-\epsilon_i\beta)\epsilon_i$
from which $\exp(\mu\beta)=n/\lambda$ where $n=N/V$ and $\lambda=mkT/2\pi\hbar^2$

Now as you can tell expressing this in terms of $a$ is awkward to say the least, did I go wrong in the calculations somewhere?

2. Jun 19, 2016

LizardWizard

Never mind, it was right all along I just got confused for some reason.