On the Trail of Blackbody Radiation: Max Planck and the Physics of his Era

224 Pages·2022·7.923 MB·English

by  Don S. Lemons, William R. Shanahan, Louis J. Buchholtz

On The Trail of Blackbody Radiation

On the Trail of Blackbody Radiation
Max Planck and the Physics of His Era
Don S. Lemons, William R. Shanahan, and Louis J. Buchholtz
illustrated by Marta Gyeviki
The MIT Press
Cambridge, Massachusetts
London, England
© 2022 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any
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The MIT Press would like to thank the anonymous peer reviewers who
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Library of Congress Cataloging- in- Publication Data
Names: Lemons, Don S. (Don Stephen), 1949- author. | Shanahan,
William R., author. | Buchholtz, Louis J., author.
Title: On the trail of blackbody radiation : Max Planck and the
physics of his era / Don S. Lemons, William R. Shanahan, and
Louis J. Buchholtz ; Illustrated by Marta Gyeviki.
Description: Cambridge, Massachusetts : The MIT Press, [2022] |
Includes bibliographical references and index.
Identifiers: LCCN 2021035122 | ISBN 9780262047043 (hardcover)
Subjects: LCSH: Blackbody radiation.
Classification: LCC QC484 .L46 2022 | DDC 530.12—dc23/
eng/20211014
LC record available at https://lccn.loc.gov/2021035122
10 9 8 7 6 5 4 3 2 1
Dedications
Don S. Lemons: To his wife Allison and sons Nathan and
Micah
William R. Shanahan: To his wife Katie
Louis J. Buchholtz: To his wife Barbara, daughter Clara,
and son Will

Contents
Preface xi
A Brief Guide to the Trail xv
1 The Prehistory of Blackbody Radiation 1
1.1 Pictet’s Experiment and Prevost’s Exchanges 1
1.2 Reflectors, Absorbers, and Emitters of Radiant Heat 4
1.3 Blackbodies and Blackbody Radiation 5
2 Classical Thermodynamics 7
2.1 Why Thermodynamics? 7
2.2 Equilibrium and the Zeroth Law of Thermodynamics 8
2.3 The First Law of Thermodynamics 10
2.4 Thermodynamic Temperature 12
2.5 The Second Law of Thermodynamics 14
2.6 The Fluid System 16
2.7 Example: The Ideal Gas 17
2.8 The Adiabatic Invariant of an Ideal Gas 19
2.9 The Entropy of an Ideal Gas 20
2.10 Relations among Different Forms of the Adiabatic
Invariant 22
3 Kirchhoff’s Law, 1859 25
3.1 Blackbody Radiation and the Laws of
Thermodynamics 25
viii Contents
3.2 The Energy Density of Blackbody Radiation 25
3.3 The Spectral Energy Density 29
3.4 Kirchhoff’s Law of Thermal Radiation 29
4 The Stefan-B oltzmann Law, 1884 33
4.1 Radiation Pressure 33
4.2 The Stefan-B oltzmann Law 36
4.3 The Adiabatic Invariant of Blackbody Radiation 38
4.4 An Alternate Derivation of the Stefan- Boltzmann Law 39
4.5 The Entropy of Blackbody Radiation 42
4.6 The Universality of Blackbody Radiation 43
4.7 Boltzmann’s 1884 Derivation 44
5 Wien’s Contributions, 1893–1 896 51
5.1 Spectral Energy Density 51
5.2 Cumulative Spectral Energy Density 52
5.3 Thermodynamic Adiabatic Invariants 53
5.4 Wien’s Electromagnetic Adiabatic Invariant 56
5.5 Wien’s Displacement Law 59
5.6 A Dimensional Consequence of Wien’s Displacement
Law 62
5.7 A Practical Consequence of Wien’s Displacement Law 63
5.8 Wien’s 1896 Distribution 64
5.9 Wien’s 1893 Derivation 65
6 The Damped, Driven, Simple Harmonic Oscillator 69
6.1 Planck Resonator 69
6.2 Simple Harmonic Oscillator 70
6.3 The Damped, Simple Harmonic Oscillator 72
6.4 The Damped, Driven, Simple Harmonic Oscillator 73
6.5 Lorentzian Approximation for Weak Damping 75
7 The Fundamental Relation 79
7.1 The Fundamental Relation 79