Consider the same system as in the previous problem. Assume that N ...

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Consider the same system as in the previous problem. Assume that N is large.

(a) Working in the canonical ensemble, find the Helmholtz free energy A(T, N) as a function of temperature T and number N.

Previous problem's system:

Consider a system of N distinguishable non-interacting objects, each of which can be in one of two possible states, "up" and "down", with energies + and -8. Assume that N is large.

(b) Starting from A(T, N) of part (a), find the canonical entropy and express it as a function of the average energy E and number N. Show that your result agrees with your answer for the entropy in the microcanonical ensemble, as computed in problem 3, in the large N limit.

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