Show that the internal energy, U, of an Einstein crystal is given by: U 3Nhv 3Nhvexp(-ßhv) 2 1-exp(-ßhv) + Hint: The following identity will avoid you having to use the chain rule: In(1 − @7(x)) = ¯¯(ƒ '(x)) e´ f(x) 1-e d (1)(1 dx
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