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(a) Given that the Helmholtz energy can be written as A=-N system k B ln Z Obtain simplified expressions for both A and S of

(a) Given that the Helmholtz energy can be written as

A=-NsystemkBlnZ

Obtain simplified expressions for both A and S of an Einstein solid.

(b) Show that the entropy approaches 0 as the temperature approaches 0 in such a solid.

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