# Ultra Relativistic Free Electrons Gas

Homework Statement:
A dispersion relation of a ultra-relativistic free electrons gas is given by $$e_{k} = c\hbar{\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{2}}}$$

Determine the number and density of orbitals. Show that pressure p is related to energy U by pV=U/3. Determine the energy U in the degenerate free electron regime.
Relevant Equations:
##e_{k} = c\hbar{\sqrt{k_{x}^{2}+k_{y}^{2}+k_{z}^{2}}}##
I don't know how to approach this problem.