Show that the average energy of a system depends on the temperature, even though the energies of the accessible states do not, by considering a system with two accessible states having energies 0 and 0.1 eV, respectively.
(a) What is the probability for the system to be in the excited state at 300 K? At 600 K?
(b) What is the average internal energy of the system at each of these two temperatures?
(c) Does the average energy increase with T, even though the energies of the individual states do not?