Since

(5.132)

and

(5.133)

Eq. (5.130) becomes

(5.134)

The mean energy of an electron is:

(5.135)

At absolute zero,

(5.136)

Since at absolute zero there are no electrons with ε > ε_m0. ε < ε_m0 at T = 0 K, we have from Eq. (5.134)

∴	(5.137)     (5.138)

The average energy at absolute zero equals th of maximum energy.

Any other temperature is the average energy of the electron at

(5.139)

The total energy U = Nε and the heat capacity

(5.140)

where n is the number of moles. The molar specific heat is represented by

(5.141)

The MB statistics gives a value

(5.142)

which is independent of temperature.