1 In This Problem You Will Derive The Average Energy Of A System In The Canonical Ensemble A First Note That The Inte 1 (71.46 KiB) Viewed 27 times
1. In this problem you will derive the average energy of a system in the canonical ensemble. a. First note that the internal energy of the system fluctuates in the canonical ensemble because the system and bath can exchange energy. The average internal energy by definition is U = Es UgP, with s a microstate of the system, U, the internal energy of the system in that microstate, and Ps the probability that the system will be in that microstate. Substitute in the expression derived in class for the probability the system is in microstate s. It is best if you use B = t. = KT. b. Show that a U= (1052) Z V.N c. Next show using the chain rule that a a as -T2 at and a a = -k82 aT
d. Next compute the heat capacity at constant volume of a system in the canonical ensemble by assuming that au Cu = at VEN Your answer should be in terms of log Z, B, and derivatives with respect to ß.
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