Problem 3: Combining Boxes of Particles Consider two boxes A and B each identical to the box in HW Problem QPl with 50 particles in each box. As in QPI each particle is in one of two energy levels? E = l] or E = E and we can dene the \"energy excess\" for either box as s = (N1 ,_ No\"; where N1 particles have energy E = E and N0 particles have energy E = U. The two boxes are put into thermal contact so that energy can transfer from one box to the other (but no particles are transferred) with total energy U remaining constant during the transfer. (a) (2 points) What is the relation between SA and 35, the energy excess in Box A and in Box B, to maximize gm(N, U j, the combined multiplicity of the system. Justify your answer. (b) (2 points) Find the multiplicity 9(N, U) at equilibrium for the combined system. (c) (2 points) Explicitly determine the fundamental entropy 0' when U = 406 and at U = 425. Then use the change in entropy and the change in energy to estimate the fundamental temperature T. (d) (3 points) Repeat the calculations in Part (c) for U = lls and U = 625. Briey discuss why the temprerature becomes negative in this case whereas for two boxes with the particles in an innite square well potential, the temperature 1' is always positive