Eight indistinguishable independent molecules (N=8) can occupy discrete and equidistant non-degenerate energy levels with energies 0, , 2 , or 3 . Consider the initial microstate to be determined by level occupancies (no, n1, n2, n3) = (4, 3, 1, 0), which gives the total energy of the microstate E(4,3,1,0) = 5 . a) what is the most probable configuration (no, n1, n2, n3) that can be reached by exciting one of the molecules to the next higher level, bringing the total energy E to 6 ? (Explain your answers)

b) What is the most probable configuration that can be reached if one of the excited molecules descends to the nearest lower level giving up energy and reducing the total energy E to 4? c) Suppose the system is brought in equilibrium with a bath at temperature T. Equilibration allows exchange of energy between the system and the bath but N and V remain fixed. Express the Helmholtz free energy F(N,V,T) in terms of for given system at temperature T= /k!