Calculate the following for this system in terms of t v

Question

For a certain system, the energy of each state s is given by

where β₀ and V₀ are fixed constants and C_s is a constant whose value depends on the state. Calculate the following for this system in terms of T, V, N:

(a) the partition function,

(b) the average internal energy,

(c) the average pressure,

(d) the average chemical potential,

(e) the standard deviation σ for fluctuations in internal energy,

(f) the average entropy