A binary alloy is composed of N~A atoms of type A and of N~B atoms of type B. Each A-type atom can exist in its ground state or in an excited state of energy ε (all other states are of such high energy that they can be neglected at the temperatures of interest). Each B-type atom similarly can exist in its ground state of energy zero or in an excited state of energy 2ε. The system is in equilibrium at temperature T.
a) Calculate the Helmholtz potential of the system.
b) Calculate the heat capacity of the system.