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Einstein's Other Theory : The Planck-Bose-Einstein Theory of Heat Capacity - Donald W. Rogers

Einstein's Other Theory

The Planck-Bose-Einstein Theory of Heat Capacity

Hardcover Published: 14th March 2005
ISBN: 9780691118260
Number Of Pages: 181

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Einstein's theories of relativity piqued public curiosity more than any other mathematical concepts since the time of Isaac Newton. Scientists and non-scientists alike struggled, not so much to grasp as to believe the weird predictions of relativity theory--shrinking space ships, bending light beams, and the like. People all over the world watched with fascination as Einstein's predictions were relentlessly and unequivocally verified by a hundred experiments and astronomical observations.

In the last decade of the twentieth-century, another of Einstein's theories has produced results that are every bit as startling as the space-time contractions of relativity theory. This book addresses his other great theory, that of heat capacity and the Bose-Einstein condensate. In doing so, it traces the history of radiation and heat capacity theory from the mid-19th century to the present. It describes early attempts to understand heat and light radiation and proceeds through the theory of the heat capacity of solids. It arrives at the theory of superconductivity and superfluidity--the astonishing property of some liquids to crawl spontaneously up and out of their containers, and the ability of some gases to cause light to pause and take a moment's rest from its inexorable flight forward in time. Couched in the terminology of traditional physical chemistry, this book is accessible to chemists, engineers, materials scientists, mathematicians, mathematical biologists, indeed to anyone with a command of first-year calculus. In course work, it is a collateral text to third semester or advanced physical chemistry, introductory statistical mechanics, statistical thermodynamics, or introductory quantum chemistry. The book connects with mainstream physical chemistry by treating boson and fermion influences in molecular spectroscopy, statistical thermodynamics, molecular energetics, entropy, heat capacities (especially of metals), superconductivity, and superfluidity.

Industry Reviews

"It is rarely remembered in popular science circles that Einstein did much basic work on Brownian motion, produced a theory of solid-state heat capacities, and combined with the Indian physicist Satyendranath Bose to produce the so-called Bose-Einstein statistics as well. This book aims to examine these topics, apart from Brownian motion, in conjunction with Planck's contribution to the theory of black-body radiation... This book [is] ... highly recommended."--Jeremy Dunning-Davies, Chemistry World "[T]he one point that [this book] makes about Einstein is a significant one: that his contributions to quantum mechanics, and particularly to quantum statistical mechanics, are arguably at least as revolutionary as those he made via his much more famous relativity theory."--Philip Anderson, Times Higher Education Supplement

Prefacep. xiii
Failure of the Dulong-Petit Lawp. 1
Crystals: Einstein's Viewp. 2
Problemsp. 2
Classical Harmonic Motionp. 4
Wave Equations: The Vibrating Stringp. 7
Wave Motionp. 9
Solving the Wave Equation: Separation of Variablesp. 11
The Time-Independent Wave Equation X(x)p. 12
The Time-Dependent Wave Equation T(t)p. 15
Superpositionsp. 16
A Two-Dimensional Wave Equationp. 17
The Time-Independent Wave Functions X(x[subscript 1]) and X(x[subscript 2])p. 18
A Three-Dimensional Wave Equationp. 20
The Boltzmann Distributionp. 21
Degrees of Freedomp. 23
Kinetic Energy per Degree of Freedomp. 24
Boltzmann's Constantp. 26
The Translational Energyp. 27
The Energy of a Vibrational State Is k[subscript B]Tp. 27
Trouble Brewingp. 28
Problemsp. 29
Experimental Background
Thermal Radiation in a Chamber or Cavityp. 30
Kirchhoff's Law: Absorptivityp. 33
The Intensity of Radiationp. 34
The Stefan-Boltzmann Law: Emissivityp. 36
Stefan's Lawp. 36
The Blackbody Radiation Spectrump. 41
Measurement of the Blackbody Spectrump. 43
Astrophysical Data from the COBE Satellitep. 46
Problemsp. 48
The Planck Equation
The Paschen-Wien Lawp. 49
Fitting the Curvep. 51
The Number Density of Oscillatory Modesp. 56
The Rayleigh-Jeans Equationp. 60
The Planck Equationp. 62
Immediate Deductions from Planck's Lawp. 67
Problemsp. 68
The Einstein's Equation
The Einstein Modelp. 70
Einstein's First Derivation: The Heat Capacity of Diamondp. 71
The Einstein Temperaturep. 73
Difficulties with the Einstein Theoryp. 75
Problemsp. 76
The Debye Equation
The Debye Modelp. 77
The Debye Equationp. 79
The Debye Temperaturep. 82
The Integral Dp. 84
Very-Low-Temperature Behavior of the Debye Equationp. 84
The Speed of Sound in Solidsp. 86
The Debye Third-Power Lawp. 90
Third-Law Entropiesp. 90
Problemsp. 92
Quantum Statistics
The Photoelectric Effectp. 94
The Photon Gasp. 96
Bose's Letter to Einsteinp. 97
The Quantum Harmonic Oscillatorp. 98
The Total Vibrational Energyp. 101
Heat Capacityp. 101
Bosons and Fermionsp. 103
Permutations and Combinationsp. 104
Configurationsp. 105
Stirling's Approximationp. 107
Constraintsp. 107
The Classical Boltzmann Distributionp. 108
Fine Structurep. 110
The Classical Case: A More General Derivationp. 112
Fermi-Dirac Countingp. 113
The Fermi-Dirac Distribution Functionp. 116
Bose-Einstein Countingp. 117
The Bose-Einstein Statistical Weights W[subscript B]p. 119
The Bose-Einstein Distribution Functionp. 120
Summary Equationsp. 121
An Alternative Derivation for Fermions and Bosonsp. 121
Fermions (Again)p. 123
Bosons (Again)p. 123
Reduction to the Classical Casep. 125
The Entropyp. 126
A Note from Classical Thermodynamics: The Fundamental Equationp. 129
Problemsp. 129
Consequences of the Fermi-Dirac Distribution
The Electron Gasp. 132
The Fermi Seap. 132
The Fermi Distributionp. 135
The Electronic Contribution to Solid-State Heat Capacityp. 136
The Ground State of a Fermi Gasp. 137
The Number of Orbitals in the Ground Statep. 139
The Total Energy of Electrons in the Ground Statep. 140
The Density of Statesp. 141
The Energy of an Electron Gasp. 144
The Low-Temperature Heat Capacity of an Electron Gasp. 145
The Debye-Sommerfeld Equationp. 146
Problemsp. 148
Consequences of the Bose-Einstein Distribution
Of Waves and Particlesp. 149
Bose: The Density of Photon Modesp. 150
Why Is [mu] = 0 for Photons?p. 152
Phononsp. 154
The Influence of Symmetry Numbers on Rotational Spectroscopyp. 155
The Vibrational Partition Function q[subscript vib]p. 157
The Rotational Partition Function q[subscript rot]p. 158
Symmetry Numbersp. 159
Bosons, Fermions, and Tripletsp. 161
The Einstein Coefficientsp. 162
Lasersp. 164
The Bose-Einstein Condensationp. 165
The Bose-Einstein Condensation of Metal Vapor (Nobel Prize, 2001)p. 165
Ballistic Expansionp. 167
Macroscopic Quantum Effectsp. 168
Superfluidityp. 168
Order Parametersp. 170
Superconductivityp. 171
Stopped Lightp. 172
Vorticesp. 173
Problemsp. 175
Bibliographyp. 177
Indexp. 179
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780691118260
ISBN-10: 0691118264
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 181
Published: 14th March 2005
Country of Publication: US
Dimensions (cm): 24.18 x 16.76  x 1.98
Weight (kg): 0.44