Consider N identical harmonic oscillators (as in the Einstein floor). Let the allowed energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on.

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Consider N identical harmonic oscillators (as in the Einstein floor). Let the allowed energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on.

A) Find the Helmholtz free energy of this system.

B) Derive the expression that gives the entropy of this system as a function of temperature.

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