Consider a system that may be unoccupied with energy zero or occupied by one particle in either of two states, one of energy zero and one of energy e. Find the Gibbs sum for this system [use fugacity 1 = exp(Bu) to express the Gibbs sum]. Note that the system can hold a maximum of one particle. 2-b. Find the thermal average occupancy of the system (N) in terms of 1 and Gibbs sum. 2-c. Find the thermal average occupancy of the state at energy E. 2-d. Find the expression for the thermal average energy of the system. 2-e. Allow the possibility that the orbitals at energy 0 and € may be occupied each by one particle at the same time. Then show that Gibbs sum = 1 + 1 + 1 exp(-E/T) + 12 exp(-€/T) = (1 + 1) [1 + 1 exp(-4/1)] Here, because the Gibbs sum can be factored as shown, we have in effect two independent systems.
