HW05 2"'1 law of thermodynamics (Ch20) 1. PROBLEMS Consider an Einstein solid in the macrostate N = 1 and U = 515' (a) Make a list of every microstate (in the form 041, for instance). What is the multiplicity w(5E, 1) of this macrostate? (b) Check your multiplicity using the equation w(U, N) = W q!(3N1)! (c) What happens to the multiplicity if you increase the energy of the solid? Use StatMech to generate tables/graphs for the following ve Einstein solid pairs in thermal contact. In each case choose U = 100B. (1) NA = 50,N3 = 50 (2) NA = 60, NB = 40 (3) NA = 70,N3 = 30 (4) NA = 80, N3 = 20 (5) NA = 90, N3 = 10 (a) At equilibrium, compare the energy per solid (HA and U3). Is the total energy shared equally between two different sized solids? (b) Compare the average energy per atom (UA / N A and U 3 / N3) for the value of UA corresponding to the peak probability. State a simple rule describing how UA/NA compares to U3 /N3 at equilibrium. Two systems are in thermal contact. The entropy of a certain macropartition of the combined system is 102k3. The entropy of another macropartition is 204.163. How much more likely is the system to be in the second macropartition than the rst? (A \"macropartition\" is a particular way the total energy is divided between the two systems.) Object A has its entropy increase quite a bit when we give it a certain tiny amount of energy, whereas object B has its entropy increase by a much smaller amount with the same gi. Which has the higher temperature? The multiplicity of an ideal monatomic gas of N molecules, internal energy U, and volume V turns out to be w(U, V. N) = CVNU3N/2 where C depends only on N. (a) Use the \"entropy\" denition of temperature to determine how the internal energy depends on temperature. (b) Use the Boltzmann entropy formula 5' = kB In w to calculate the entropy change of an ideal gas in a reversible adiabatic process. A refrigerator has a coefcient of performance of 2. 1. In each cycle it absorbs 34 k] of heat from the cold reservoir. (3) How much mechanical energy is required each cycle to operate the refrigerator? (b) During each cycle, how much heat is discarded to the high-temperature reservoir