Question

3. Consider a gas of fermion at
a) Express the mean number of particle , and mean energy by polylogarithm function

a) For a gas of fermion with density of state , show that the chemical potential is given by
b) At finite temperature find the occupation number of the quantum state with energy $\varepsilon$. Explain qualitatively how this distribution would influence on the specific heat of the system.

T7 0 Lin-). n-1 1 fn(z)= T(n) 1 da g(e (kBT)2g(EF) g(EF) (T) EF 6 TT T 0

Answer 1

fo Fermi Coao, ** e have ,T) Leg(+) and, N 2 pookloles, Amd, Maan mD fo Tal air and 21TK2 mkT 0*+1 gnd,(2- 32 2 PAS

The average oceupadtin nad 20 m23 And dw g Tr ist TntegralJdaca du

Aio,u Srecifi heat C2 g