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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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 and A = 15. Sketch the qualitative behavior of the heat capacity C as a
function of T.
Transcribed Image Text: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 and A = 15. Sketch the qualitative behavior of the heat capacity C as a function of T.
Figure 4.9: The two particles considered in Problem 4.521 The two distinguishable particles can
each be in one of the two boxes. The energy of the system depends on which box the particles
оссиру.
Transcribed Image Text:Figure 4.9: The two particles considered in Problem 4.521 The two distinguishable particles can each be in one of the two boxes. The energy of the system depends on which box the particles оссиру.
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