Example 9.7: Electron contribution to capacity of heat In the case of some substances like O2 and NO there are additional contributions to thermodynamical properties resulting from two closely lying electronic levels, say 1, 2 with 2 − 1  kT, so that thermal excitation suffices in order to populate also the higher level. Establish the partition function for such a two-level system and calculate the electronic contribution Cel to the specific heat. What is the behaviour of Cel at high and at low temperatures T? What is the condition for a maximum of this quantity? For convenience set 1 = 0 and = 2 − 1. (Answer:

The maximum of Cel(T) is at temperature T = 1/kβ given by the solution of the equation 1 = (1/2) βtanh[{ β + ln(g1/g2)}/2], where g1, g2 are the degeneracies of the two levels).