Problems and Solutions on Thermodynamics and Statistical Mechanics

262 Pwblema d Sdutiona on Therdpam'ca^8 Statistical Mechanica

while some electrons occupy states of E > E~. The number of electrons with
E > E~ is given by

The number of vacancies for e < 0 is given by

By n, = np, we have p = cg/2 when a = b. We also obtain the equation to

determine p when a # b,

For a > b, we have

so that B + eg - p > E + p, i.e., p < ~~12. Hence p shifts to lower energies.

For a < b, p > E~ 12, p shifts to higher energies.

(c) When T = 0, by

we obtain

p shifts to lower energies as T increases.