Ultra Relativistic Free Electrons Gas

[Victor_Andrade]

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.

 

[dRic2]

Can you solve the problem for a *non* relativistic electron gas ?