- Title Pages
- Deadication
- Preface to the Second Edition
- Preface to the First Edition
- 1 Introduction
- 2 The Classical Ideal Gas
- 3 Discrete Probability Theory
- 4 The Classical Ideal Gas: Configurational Entropy
- 5 Continuous Random Numbers
- 6 The Classical Ideal Gas: Energy Dependence of Entropy
- 7 Classical Gases: Ideal and Otherwise
- 8 Temperature, Pressure, Chemical Potential, and All That
- 9 The Postulates and Laws of Thermodynamics
- 10 Perturbations of Thermodynamic State Functions
- 11 Thermodynamic Processes
- 12 Thermodynamic Potentials
- 13 The Consequences of Extensivity
- 14 Thermodynamic Identities
- 15 Extremum Principles
- 16 Stability Conditions
- 17 Phase Transitions
- 18 The Nernst Postulate: The Third Law of Thermodynamics
- 19 Ensembles in Classical Statistical Mechanics
- 20 Classical Ensembles: Grand and Otherwise
- 21 Refining the Definition of Entropy
- 22 Irreversibility
- 23 Quantum Ensembles
- 24 Quantum Canonical Ensemble
- 25 Black-Body Radiation
- 26 The Harmonic Solid
- 27 Ideal Quantum Gases
- 28 Bose–Einstein Statistics
- 29 Fermi–Dirac Statistics
- 30 Insulators and Semiconductors
- 31 Phase Transitions and the Ising Model
- Appendix Computer Calculations and Python
- Index

# The Classical Ideal Gas: Configurational Entropy

# The Classical Ideal Gas: Configurational Entropy

- Chapter:
- (p.43) 4 The Classical Ideal Gas: Configurational Entropy
- Source:
- An Introduction to Statistical Mechanics and Thermodynamics
- Author(s):
### Robert H. Swendsen

- Publisher:
- Oxford University Press

This chapter derives the part of the entropy that is generated by the positions of particles, or the configurational entropy. The remaining part of the entropy, which is generated by the momenta of the particles, is derived in Chapter 6. While both derivations are unconventional, they are based directly on an 1877 paper by Boltzmann that discusses the exchange of energy between two or more systems. The dependence of the entropy on the number of particles is derived solely by assuming that the probability of a given particle being in a specified volume is proportional to that volume. No quantum mechanics is required for this derivation, and the result is valid for both distinguishable and indistinguishable particles.

*Keywords:*
entropy, classical mechanics, Boltzmann, discrete probability, particle exchange, distinguishable particles, indistinguishable particles

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .

- Title Pages
- Deadication
- Preface to the Second Edition
- Preface to the First Edition
- 1 Introduction
- 2 The Classical Ideal Gas
- 3 Discrete Probability Theory
- 4 The Classical Ideal Gas: Configurational Entropy
- 5 Continuous Random Numbers
- 6 The Classical Ideal Gas: Energy Dependence of Entropy
- 7 Classical Gases: Ideal and Otherwise
- 8 Temperature, Pressure, Chemical Potential, and All That
- 9 The Postulates and Laws of Thermodynamics
- 10 Perturbations of Thermodynamic State Functions
- 11 Thermodynamic Processes
- 12 Thermodynamic Potentials
- 13 The Consequences of Extensivity
- 14 Thermodynamic Identities
- 15 Extremum Principles
- 16 Stability Conditions
- 17 Phase Transitions
- 18 The Nernst Postulate: The Third Law of Thermodynamics
- 19 Ensembles in Classical Statistical Mechanics
- 20 Classical Ensembles: Grand and Otherwise
- 21 Refining the Definition of Entropy
- 22 Irreversibility
- 23 Quantum Ensembles
- 24 Quantum Canonical Ensemble
- 25 Black-Body Radiation
- 26 The Harmonic Solid
- 27 Ideal Quantum Gases
- 28 Bose–Einstein Statistics
- 29 Fermi–Dirac Statistics
- 30 Insulators and Semiconductors
- 31 Phase Transitions and the Ising Model
- Appendix Computer Calculations and Python
- Index