(a) Find the entropy of a set of N oscillators of frequency as a function of...

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(a) Find the entropy of a set of N oscillators of frequency ω as a function of the total quantum number n. Use the multiplicity function (1.55) and make the Stirling approximation log N! ≈ N log N – N. Replace N – 1 by N.
(b) Let U denote the total energy nhω of the oscillators. Express the entropy as σ(U, N). Show that the total energy at temperature τ is
U = Nhω / ex(hω/τ)–1 (42)
This is the Plank result; it is derived again in Chapter 4 by a powerful method that does not require us to find the multiplicity function.

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Thermal Physics

ISBN: 978-0716710882

2nd Edition

Authors: Charles Kittel, Herbert Kroem

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