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Consider a system of N distinguishable atoms, each of which can be in only one of...

Consider a system of N distinguishable atoms, each of which can be in only one of two states: the lowest energy state with energy 0, and an excited state with energy ɛ > 0. When there are n atoms in the excited state (and N-1 atoms in the lowest state), the total energy is U = nɛ.

1. Calculate the entropy S/k = ln(Ω(n)) and find the value of n for which it is maximum.

2. Find an expression for temperature T as a function of n, N, and ɛ.

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