4. Entropy for a Two-Level System a) Write the partition function for a system with only two levels, a ground state ( = 0) and a single excited state (& = A). We will refer to this as a "two-level system". b) Using your partition function, derive and expression for the internal energy, E, and entropy, S, for the two-level system. c) Plot the entropy, S, as a function of the ratio kT/A. Explain the limiting behavior at high and low temperature. ds d) Plot the function as a function of the ratio kT/A. Does this function have a maximum? If dT so, explain its physical origins