An account of Max Planck’s construction of his theory of blackbody radiation, summarizing the established physics on which he drew.
In the last year of the nineteenth century, Max Planck constructed a theory of blackbody radiation—the radiation emitted and absorbed by nonreflective bodies in thermal equilibrium with one another—and his work ushered in the quantum revolution in physics. In this book, three physicists trace Planck’s discovery. They follow the trail of Planck’s thinking by constructing a textbook of sorts that summarizes the established physics on which he drew. By offering this account, the authors explore not only how Planck deployed his considerable knowledge of the physics of his era but also how Einstein and others used and interpreted Planck’s work.
Planck did not set out to lay the foundation for the quantum revolution but to study a universal phenomenon for which empirical evidence had been accumulating since the late 1850s. The authors explain the nineteenth-century concepts that informed Planck’s discovery, including electromagnetism, thermodynamics, and statistical mechanics. In addition, the book offers the first translations of important papers by Ludwig Boltzmann and Wilhelm Wien on which Planck’s work depended.
Author(s): Don S. Lemons, William R. Shanahan, Louis J. Buchholtz
Publisher: The MIT Press
Year: 2022
Language: English
Pages: 223
City: Cambridge
Contents
Preface
A Brief Guide to the Trail
1 The Prehistory of Blackbody Radiation
1.1 Pictet’s Experiment and Prevost’s Exchanges
1.2 Reflectors, Absorbers, and Emitters of Radiant Heat
1.3 Blackbodies and Blackbody Radiation
2 Classical Thermodynamics
2.1 Why Thermodynamics?
2.2 Equilibrium and the Zeroth Law of Thermodynamics
2.3 The First Law of Thermodynamics
2.4 Thermodynamic Temperature
2.5 The Second Law of Thermodynamics
2.6 The Fluid System
2.7 Example: The Ideal Gas
2.8 The Adiabatic Invariant of an Ideal Gas
2.9 The Entropy of an Ideal Gas
2.10 Relations among Different Forms of the Adiabatic Invariant
3 Kirchhoff’s Law, 1859
3.1 Blackbody Radiation and the Laws of Thermodynamics
3.2 The Energy Density of Blackbody Radiation
3.3 The Spectral Energy Density
3.4 Kirchhoff’s Law of Thermal Radiation
4 The Stefan-BoltzmannLaw, 1884
4.1 Radiation Pressure
4.2 The Stefan-Boltzmann Law
4.3 The Adiabatic Invariant of Blackbody Radiation
4.4 An Alternate Derivation of the Stefan-Boltzmann Law
4.5 The Entropy of Blackbody Radiation
4.6 The Universality of Blackbody Radiation
4.7 Boltzmann’s 1884 Derivation
5 Wien’s Contributions, 1893–1896
5.1 Spectral Energy Density
5.2 Cumulative Spectral Energy Density
5.3 Thermodynamic Adiabatic Invariants
5.4 Wien’s Electromagnetic Adiabatic Invariant
5.5 Wien’s Displacement Law
5.6 A Dimensional Consequence of Wien’s Displacement Law
5.7 A Practical Consequence of Wien’s Displacement Law
5.8 Wien’s 1896 Distribution
5.9 Wien’s 1893 Derivation
6 The Damped, Driven, Simple Harmonic Oscillator
6.1 Planck Resonator
6.2 Simple Harmonic Oscillator
6.3 The Damped, Simple Harmonic Oscillator
6.4 The Damped, Driven, Simple Harmonic Oscillator
6.5 Lorentzian Approximation for Weak Damping
7 The Fundamental Relation
7.1 The Fundamental Relation
7.2 The Planck Resonator Model
7.3 The Weakly Damped Planck Resonator
7.4 The Damped, Driven Planck Resonator
7.5 Resonator Responding to a Spectrum
8 Planck’s Zeroth Derivation, 1900
8.1 The Zeroth Derivation
8.2 The Thermodynamics of Planck Resonators
8.3 An Irreversible Process and an Incorrect Deduction
8.4 The Wien Distribution
8.5 Planck’s “Lucky Intuition”
8.6 Planck’s New Task
9 Boltzmann’s Statistical Mechanics
9.1 Boltzmann’s Physics
9.2 Boltzmann’s Legacy
9.3 Boltzmann’s First Calculation
9.4 A Continuation of Boltzmann’s First Calculation
9.5 The Boltzmann Factor
10 Planck’s “First Derivation,” 1900–1901
10.1 The “First Derivation”
10.2 Planck’s Program
10.3 Boltzmann’s Entropy and Planck’s Combinatorics
10.4 The Program Completed
10.5 Planck’s Natural Units
10.6 The Status of “Energy Elements”
11 Einstein’s Response, 1905–1907
11.1 Einstein’s Initial Response to Planck’s Quantum
11.2 The Entropy of Blackbody Radiation in the Wien Limit
11.3 The Photoelectric Effect
11.4 The Einstein Solid
12 Einstein on Emission and Absorption, 1917
12.1 Einstein’s “Quantum Theory of Radiation”
12.2 Einstein’s Derivation
12.3 Einstein’s Derivation Made Classical?
12.4 Einstein’s Missing Quantum Hypothesis
The Big Ideas
Acknowledgments
Annotated Bibliography
Appendix A English Translation of “A Derivation of Stefan’s Law, Concerning the Temperature Dependence of Thermal Radiation, from the Electromagnetic Theory of Light” by Ludwig Boltzmann in Graz (1884)
Appendix B English Translation of “A NewRelationship between Blackbody Radiation andthe Second Law of Thermodynamics” by WillyWien in Charlottenburg (1893)
§I Process Description
§2 Calculation of the Energy Distribution’s Alteration Using the Doppler Principle
Appendix C An Electromagnetic AdiabaticInvariant
Appendix D An Ideal Gas “Displacement Law”
Notes
Preface
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
The Big Ideas
Appendix A
Appendix B
Appendix C
Index
