Problems and Solutions on Thermodynamics and Statistical Mechanics

2 78 Problems 8 Solutions on Thermodytomics d Statistical Mechanics

ii2

2m

and the kinetic energy of an electron is E = -k2. Combining, we get

At T = 0 K, the N electrons fill up the energy levels from zero to EF =

h"

-k>, i.e.,

2m

EF 2

N = D(&)d&= ;D(EF)EF

Jo

2m

(a) The specific heat is

where kB is Boltzmann's constant.

(b) The magnetic susceptibility is

where pB is the Bohr magneton.

(c), (d) The average kinetic energy is

2 3

ED(&)& = -D(EF)E; = -NEF ,

(Ek) = I"' 5 5

and the pressure on the walls of the box is

2105

fermions is confined to a volume V. Calculate

the zero temperature limit of (a) the chemical potential, (b) the average

An ideal gas of N spin