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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder
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Consider an Einstein solid for which both N and q are much

Chapter 3, Problem 36P

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QUESTION:

Problem 36P

Consider an Einstein solid for which both N and q are much greater than 1. Think of each oscillator as a separate “particle.”

(a) Show that the chemical potential is

(b) Discuss this result in the limits N ≫ q and N ≪ q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?

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QUESTION:

Problem 36P

Consider an Einstein solid for which both N and q are much greater than 1. Think of each oscillator as a separate “particle.”

(a) Show that the chemical potential is

(b) Discuss this result in the limits N ≫ q and N ≪ q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?

ANSWER:

Step 1 of 5

Part (a)

The expression for the solid which contains oscillators and energy units is,

                                                       

The entropy of a system can be expressed as,

                                                                 

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