
Published online:
20 February 2020
Published in print:
10 December 2019
Online ISBN:
9780191887703
Print ISBN:
9780198853237
Contents
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7.1 Entropy of a Composite System of Classical Ideal Gases 7.1 Entropy of a Composite System of Classical Ideal Gases
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7.2 Equilibrium Conditions for the Ideal Gas 7.2 Equilibrium Conditions for the Ideal Gas
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7.2.1 Equilibrium with Respect to Energy 7.2.1 Equilibrium with Respect to Energy
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7.2.2 Equilibrium with Respect to the Number of Particles 7.2.2 Equilibrium with Respect to the Number of Particles
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7.3 The Volume-Dependence of the Entropy 7.3 The Volume-Dependence of the Entropy
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7.4 Asymmetric Pistons 7.4 Asymmetric Pistons
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7.5 Indistinguishable Particles 7.5 Indistinguishable Particles
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7.6 Entropy of a Composite System of Interacting Particles 7.6 Entropy of a Composite System of Interacting Particles
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7.6.1 The Ideal Gas Revisited 7.6.1 The Ideal Gas Revisited
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7.6.2 Generalizing the Entropy to Interacting Particles 7.6.2 Generalizing the Entropy to Interacting Particles
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7.7 The Second Law of Thermodynamics 7.7 The Second Law of Thermodynamics
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7.8 Equilibrium between Subsystems 7.8 Equilibrium between Subsystems
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7.9 The Zeroth Law of Thermodynamics 7.9 The Zeroth Law of Thermodynamics
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7.10 Problems 7.10 Problems
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PROBLEM 7.1 General forms for the entropy PROBLEM 7.1 General forms for the entropy
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PROBLEM 7.2 The ‘traditional’ expression for the entropy of an ideal gas of distinguishable particles PROBLEM 7.2 The ‘traditional’ expression for the entropy of an ideal gas of distinguishable particles
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Chapter
7 Classical Gases: Ideal and Otherwise
Get access
Pages
81–98
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Published:December 2019
Cite
Swendsen, Robert H., 'Classical Gases: Ideal and Otherwise', An Introduction to Statistical Mechanics and Thermodynamics, 2nd edn (Oxford , 2019; online edn, Oxford Academic, 20 Feb. 2020), https://doi.org/10.1093/oso/9780198853237.003.0007, accessed 8 May 2025.
Abstract
As preparation for the derivation of the entropy for systems with interacting particles, the position and momentum variables are treated simultaneously, in this chapter, for the ideal gas. Releasing a constraint on the exchange of volume between two systems leads to an entropy maximum, just as the release of an energy- or particle-number constraint. This same principle is shown to be true for asymmetric pistons, which allow the total volume to change. The entropy of systems with interacting particles is then derived. The Second Law of Thermodynamics is established for general systems. Finally, the Zeroth Law of Thermodynamics is derived.
An Introduction to Statistical Mechanics and Thermodynamics. Robert H. Swendsen, Oxford University Press (2020). © Robert H. Swendsen. DOI: 10.1093/oso/9780198853237.001.0001
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