2. a system consists of n non-interacting, localised objects, each of which can exist in one of three quantum states with energies 0, ε , ε (ie., the two upper energy levels are doubly degenerate). derive expressions for the following quantities in terms of ε and t with simplified high and low temperature limits. (a) the single particle partition function (b) the number of particles with energy ε (c) the total energy of the system (d) the helmholtz free energy of the system (e) the entropy of the system (at high temperatures only)