Question

basic Molecular Thermodynamics

2. This problem focuses on a system that contains two indistinguishable bosons. If there are two energy levels available for each of them, then the list of possible states will look like the list in the table in Problem 1, except that the two-particle states numbered 2 and 3 are not different states, in this case. There is only one state that has one of the bosons in ɛj and one in ɛ2, because the bosons cannot be told apart. a) Write the partition function for two indistinguishable bosons, if there are two energy states available. (Include only one of the two-particle states 2 and 3.) b) Show that this time, the partition function does not factorize into Q= [exp(-ɛ1/kT) + exp(-82/kT)] [exp(-ɛ1/kT) + exp(-€2/kT)] c) Next, consider the case with two indistinguishable bosons and three energy states that are available to each boson, ɛ1, E2, and ɛ3. Write the partition function in this case. d) Does the partition function in part c) factorize into Qa[exp(-81/kT) + exp(-82/kT) + exp(-83/kT)] [exp(-81/kT) + exp(-ɛ/kT) + exp(-83/kT)] ?

Answer 1

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