Consider an ideal Fermi gas of spin 1/2 particles in a d-dimensional box of linear size L. The dispersion relation is given by e(p) = ap , with a, s > 0. You may call Aa the solid angle resulting from integration over the angle variables, e.g. 2x for d = 2, 4x for d = 3, etcetera. a) Find the density of states. b) Find the Fermi energy EF. c) Show that, at all temperatures, the internal energy of the gas is related to its pressure by PV o E. What is the constant of proportionality