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

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

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4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhv exp(-ßhv) 1- exp(-Bhv) + 2 U = Hint: The following identity will avoid you having to use the chain rule: d |In(1-ef(x)) = −(ƒ '(x)) e² dx 1-e
Transcribed Image Text:4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhv exp(-ßhv) 1- exp(-Bhv) + 2 U = Hint: The following identity will avoid you having to use the chain rule: d |In(1-ef(x)) = −(ƒ '(x)) e² dx 1-e
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Hence show that (u/beta)

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