Consider a two-state system discussed in class with two energy levels Ey, E,. T'here are three states with energy E; (i.e. the degeneracy of the excited state is 3). Assume a large number of N noninteracting distinguishable particles which populate :hese levels. The system is in contact with a reservoir at temperature T'. (a) Write an explicit algebraic expression for the partition function of a single particle in this sytem. Write out any summations explicitly (b) Write an explicit algebraic expression for the total internal energy of the system U = NE, where E is the average energy each atom. Write out any summations explicitly (c) In the limit of very large temperature T oo, what is the probability that a particle is found in one particular excited state {1 with energy E1? Explain your reasoning