Answer Happy

Let N be the 5. Consider a nonrelativistic degenerate free electron gas in two dimensions. number of electrons, each of mass m and contained in an area A. (a) Calculate the density of states of the electrons. [5 points] (b) Calculate the Fermi energy & of the electron gas. [7 points] (c) Calculate the total energy E of the gas and the average energy per electron, both at T = 0 K. [7 points] (d) Assume KT << μ~Ep, calculate the energy E(T) of the gas to the order (kT/E)². [10 points) (e) Use the above result to obtain the heat capacity of the electrons at low temperatures. Give a physical explanation to your result. [7 points] (f) Calculate the low temperature entropy and free energy of the system. [7 points] (g) Calculate the pressure of the electron gas to the order (kT/ɛp)². [7 points]