Problem :
Consider two spin systems A and A' placed in an external field H. System A consist of N weakly interacting localized particles of spin 1/2 and magntic moment u. Similarly, system A' consists of N' weakly interacting localized particles of spin 1/2 and magnetic moment u'. The two systems are initially isolated with respective total energies bNuH and b'N'u'H. They are then placed in thermal contact with each other. Suppose that |b|<<1 and |b'|<<1 so that the simple expressions of Problem 2.4c can be used for the densities of stats of the two systems.
In the most probable situation corresponding to the final thermal equilibrium, how is the energy Et of systemA related to the energy Et' of system A' ?