Consider a degenerate electron gas in which essentially all of the electrons are highly relativistic (ϵ ≫ mc2), so that their energies are ϵ = pc (where p is the magnitude of the momentum vector).

(a) Modify the derivation given above to show that for a relativistic electron gas at zero temperature, the chemical potential (or Fermi energy) is given by µ = hc(3N/8πV)1/3.

(b) Find a formula for the total energy of this system in terms of N and µ.