Statistical Thermodynamics: Boltzmann Distribution

A system has three energy levels: ε0 = 0, ε1 = 100 J/mol, ε2 = 500 J/mol, each non-degenerate. (a) Calculate the partition function at T = 298 K. (b) Calculate the probability of finding the system in each energy level. (c) Calculate the average energy ⟨E⟩ at 298 K. (d) How do the populations change as T → ∞? (e) Derive the expression for entropy S in terms of the partition function and show that S → k ln(W) as T → ∞.