Problem 4.52. Consider the system illustrated in Figure 4.91 The system consists of two dis- tinguishable particles, each of which can be in either of two boxes. The system is in thermal equilibrium with a heat bath at temperature T. Assume that the energy of a particle is zero if it is in the left box and r if it is in the right box. There is also a correlation energy term that increases the energy by A if the two particles are in the same box. (a) Enumerate the 22 = 4 microstates and their corresponding energy. (b) Calculate the partition function Z for arbitrary values of r and A and use your result to find the mean energy. (c) What is the probability that the system is in a particular microstate? (d) Suppose that r = 1 andA = 15. Sketch the qualitative behavior of the heat capacity C as a function of T.
Problem 4.52. Consider the system illustrated in Figure 4.91 The system consists of two dis- tinguishable particles, each of which can be in either of two boxes. The system is in thermal equilibrium with a heat bath at temperature T. Assume that the energy of a particle is zero if it is in the left box and r if it is in the right box. There is also a correlation energy term that increases the energy by A if the two particles are in the same box. (a) Enumerate the 22 = 4 microstates and their corresponding energy. (b) Calculate the partition function Z for arbitrary values of r and A and use your result to find the mean energy. (c) What is the probability that the system is in a particular microstate? (d) Suppose that r = 1 andA = 15. Sketch the qualitative behavior of the heat capacity C as a function of T.
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