- Title Pages
- Dedication
- Preface
- Acknowledgments
- 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 Irreversibility
- 22 Quantum Ensembles
- 23 Quantum Canonical Ensemble
- 24 Black-Body Radiation
- 25 The Harmonic Solid
- 26 Ideal Quantum Gases
- 27 Bose–Einstein Statistics
- 28 Fermi–Dirac Statistics
- 29 Insulators and Semiconductors
- 30 Phase Transitions and the Ising Model
- Appendix: Computer Calculations and VPython
- Index

# Ideal Quantum Gases

# Ideal Quantum Gases

- Chapter:
- (p.308) 26 Ideal Quantum Gases
- Source:
- An Introduction to Statistical Mechanics and Thermodynamics
- Author(s):
### Robert H. Swendsen

- Publisher:
- Oxford University Press

This chapter develops the basic equations that will be used to analyse the Fermi-Dirac and Bose-Einstein gases. The representation of many-particle states in terms of products of single-particle states is presented. The reasons for using the quantum grand canonical ensemble are given, and a general expression for the grand canonical partition function is derived. The essential equations for fermions, bosons, and distinguishable particles are developed, and the basic strategy for using them to solve problems is given.

*Keywords:*
quantum gases, single-particle states, many-particle states, grand canonical partition function, fermions, bosons, distinguishable particles, Bose-Einstein gases

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- Title Pages
- Dedication
- Preface
- Acknowledgments
- 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 Irreversibility
- 22 Quantum Ensembles
- 23 Quantum Canonical Ensemble
- 24 Black-Body Radiation
- 25 The Harmonic Solid
- 26 Ideal Quantum Gases
- 27 Bose–Einstein Statistics
- 28 Fermi–Dirac Statistics
- 29 Insulators and Semiconductors
- 30 Phase Transitions and the Ising Model
- Appendix: Computer Calculations and VPython
- Index