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3) Consider a system consisting of one particle with two states, one of energy 0 and one of
energy +ɛ.
a)
Write down the partition function Z for this system.
b)
Show that the average energy for this system can be written as

Derive an expression for the entropy S.
d)
Derive an approximate expression for the entropy in the high-temperature limit.
e)
Derive an approximate expression for the entropy in the low-temperature limit.

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