Thermodynamics, Statistical Physics, and Quantum Mechanics

198 SOLUTIONS

b) From (S.4.81.1) we may find the partition function Z:

where we define The sum (S.4.81.2) may be easily calculated:

The mean magnetic moment per dipole is given by

Since the atoms do not interact,

For J = 1/2,

This result can be obtained directly from (S.4.81.3) and (S.4.81.4):