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a) Explain, in your own words, how entropy is used in statistical physics. b) Shannon's formula for the entropy of a set of probabilities is S = -kB Σ₁ P; log pj. Using this formula, derive Boltzmann's formula for the entropy of the microcanonical ensemble. c) Using Shannon's formula, derive an expression for the entropy of the canonical ensemble. d) Explain how your answer to (c) is related to the thermodynamic entropy.

a) Explain, in your own words, how entropy is used in statistical physics. b) Shannon's formula for the entropy of a set of probabilities is S = -kB Σ₁ P; log pj. Using this formula, derive Boltzmann's formula for the entropy of the microcanonical ensemble. c) Using Shannon's formula, derive an expression for the entropy of the canonical ensemble. d) Explain how your answer to (c) is related to the thermodynamic entropy.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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a) Explain, in your own words, how entropy is used in statistical physics. b) Shannon's formula for the entropy of a set of probabilities is S = -kB Σ₁ P; log pj. Using this formula, derive Boltzmann's formula for the entropy of the microcanonical ensemble. c) Using Shannon's formula, derive an expression for the entropy of the canonical ensemble. d) Explain how your answer to (c) is related to the thermodynamic entropy.
Transcribed Image Text:a) Explain, in your own words, how entropy is used in statistical physics. b) Shannon's formula for the entropy of a set of probabilities is S = -kB Σ₁ P; log pj. Using this formula, derive Boltzmann's formula for the entropy of the microcanonical ensemble. c) Using Shannon's formula, derive an expression for the entropy of the canonical ensemble. d) Explain how your answer to (c) is related to the thermodynamic entropy.
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