5. (25 points) In this problem we will consider the distribution of energy, microstates, macrostates, and entropy. To do this, consider a simple model consisting of two boxes each with 10 bins (degrees of freedom) in which to put energy. To keep these large A numbers as small as possible, we will assume that each bin can hold only one packet of energy, and that energy packets are indistinguishable Potentially Useful Things: W = MV W = NIn 2 MI B S = KB In W W = NI(M-N)! (a) Suppose we have 4 packets of energy total. In how many ways can we distribute them so that they are all in box A? (5 pts) packet of energy = degree of freedom place to put energy) (b) How many ways can we distribute the 4 packets in the total system of box A + box B? (5 pts) (c) If the system with all 4 packets and all 20 degrees of freedom from both boxes was in thermal equilibrium, would you expect to find the 4 flames distributed all in box A, as in the macrostate from part (a), upon observation at a random time? Explain why you think so. (5 pts) (d) The states described in the questions of (a) and (b) are macrostates, while each configuration that contributes is a microstate. What is the entropy of the macrostate in (b) in meV/K (m: milli)? (5 pts) KB = 0.0862 me V/K S = k. in WU (e) The temperature of a system is related to the average energy in one degree of freedom by = 1/2 k.T. If each of energy packets contains an energy of 25me V (again, milli-electron-Volts), what is the temperature of box A in the macrostate from part (a), in Kelvin? (5 pts) k = CamScanner