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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4. Show that the internal energy, U, of an Einstein crystal is given by:
3Nhv 3Nhvexp(-ßhv)
2 1-exp(-Bhv)
+
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 3Nhvexp(-ßhv) 2 1-exp(-Bhv) + 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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