2. Consider a system consisting of a set of N distinguishable, noninteracting particles, each of which has two energy levels: a ground state, which can be taken to have zero energy, and an excited state of energy . The system is prepared in a macrostate in which the energy is U = q. (a) Find an expression for the number of microstates for the system above consistent with N particles and an energy U, and show that for this system N U = 1+ e/(kT)' Discuss the low- and high-temperature limits of this expression.