Question

Solid state physics Ashcroft Chapter 2 Problem 2.2 (especially part F)

Solid state Physics (1st Edition) Chapter 2, Problem 2P (2 Bookmarks) Show all steps ON Problem Thermodynamics of the Free and Independent Electron Gas (a) Deduce from the thermodynamic identities Os си T (2.96) From Eqs. (2.56) and (2.57), and from the third law of thermodynamics (s0 as T0) that the entropy density, s- S/V is given by dk In-In - (2.97) Where f (E(k)) is the Fermi function (Eq.(2.56). (b) Since the pressure P satisfies Eq.(B.5) in Appendix B, P=-(U-TS-un), deduce from (2.97) that In exp- (2.98) Show that (2.98) implies that P is a homogeneous function of μ and T of degree 5/2: that is for any constant A.

Answer 1

Part F: Show by, retaining further terms in the sommefeld expansions of u and n that correct to order 7^3 the electronic heat capacity is given by C_v = pi^2/3 k_B T_g [epsilon_f] - pi^4/90 k_B T^3_g [epsilon_f} [15 (g (epsilon_f)/g (epsilon_f))^2 - 21 g (epsilon_f)/g (epsilon_f)] mu (T) does not have any elastic expansion about T almostequalto, why Because expansion does not work in 2 Dimensional