The internal energy of a 3-D gas of N electrons is equal to total kinetic energy of the system and given by U = S g@N()ede. At OK, the system is in its ground state and the energy is given by : E a- Find the number of quantum states N(e) b- Find the density of state g(e) (Hint: use g(e) = dN/de) - Proof that the density of state can be written as: g(e) = 3 d- At 0 K, we only need to evaluate from 0 to the Fermi energy and the no becomes a step function and U. = (g()ede. Show that the kinetic energy of a three-dimensional gas of N free electrons is U. = NE 8. Find the relation connecting P and V for the electron gas 10U f- Show that the bulk modules B is given by 97