A simple system in which to study entropy and the Boltzmann distribution consists of N independent two state subsystems coupled thermally to a reservoir at temperature T The two states in each subsystem have energies 0 (by definition) and Find the partition function, the internal energy, and the entropy of the total system as a function of temperature Explain why the internal energy approaches N 2 as T Is this what you expected It may help if you explain why the entropy approaches Nk B ln 2 in the same limit

Question: A simple system in which to study entropy and the Boltzmann distribution consists of N independent two-state subsystems coupled thermally to a reservoir at temperature

A simple system in which to study entropy and the Boltzmann distribution consists of N independent two-state subsystems coupled thermally to a reservoir at temperature T. The two states in each subsystem have energies 0 (by definition) and ϵ. Find the partition function, the internal energy, and the entropy of the total system as a function of temperature. Explain why the internal energy approaches Nϵ/2 as T → ∞. Is this what you expected? It may help if you explain why the entropy approaches Nk_B ln 2 in the same limit.

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