Hardcover
Published: 14th March 2005
ISBN: 9780691118260
Number Of Pages: 181
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.
"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
Preface | p. xiii |
History | |
Failure of the Dulong-Petit Law | p. 1 |
Crystals: Einstein's View | p. 2 |
Problems | p. 2 |
Background | |
Classical Harmonic Motion | p. 4 |
Wave Equations: The Vibrating String | p. 7 |
Wave Motion | p. 9 |
Solving the Wave Equation: Separation of Variables | p. 11 |
The Time-Independent Wave Equation X(x) | p. 12 |
The Time-Dependent Wave Equation T(t) | p. 15 |
Superpositions | p. 16 |
A Two-Dimensional Wave Equation | p. 17 |
The Time-Independent Wave Functions X(x[subscript 1]) and X(x[subscript 2]) | p. 18 |
A Three-Dimensional Wave Equation | p. 20 |
The Boltzmann Distribution | p. 21 |
Degrees of Freedom | p. 23 |
Kinetic Energy per Degree of Freedom | p. 24 |
Boltzmann's Constant | p. 26 |
The Translational Energy | p. 27 |
The Energy of a Vibrational State Is k[subscript B]T | p. 27 |
Trouble Brewing | p. 28 |
Problems | p. 29 |
Experimental Background | |
Thermal Radiation in a Chamber or Cavity | p. 30 |
Kirchhoff's Law: Absorptivity | p. 33 |
The Intensity of Radiation | p. 34 |
The Stefan-Boltzmann Law: Emissivity | p. 36 |
Stefan's Law | p. 36 |
The Blackbody Radiation Spectrum | p. 41 |
Measurement of the Blackbody Spectrum | p. 43 |
Astrophysical Data from the COBE Satellite | p. 46 |
Problems | p. 48 |
The Planck Equation | |
The Paschen-Wien Law | p. 49 |
Fitting the Curve | p. 51 |
The Number Density of Oscillatory Modes | p. 56 |
The Rayleigh-Jeans Equation | p. 60 |
The Planck Equation | p. 62 |
Immediate Deductions from Planck's Law | p. 67 |
Problems | p. 68 |
The Einstein's Equation | |
The Einstein Model | p. 70 |
Einstein's First Derivation: The Heat Capacity of Diamond | p. 71 |
The Einstein Temperature | p. 73 |
Difficulties with the Einstein Theory | p. 75 |
Problems | p. 76 |
The Debye Equation | |
The Debye Model | p. 77 |
The Debye Equation | p. 79 |
The Debye Temperature | p. 82 |
The Integral D | p. 84 |
Very-Low-Temperature Behavior of the Debye Equation | p. 84 |
The Speed of Sound in Solids | p. 86 |
The Debye Third-Power Law | p. 90 |
Third-Law Entropies | p. 90 |
Problems | p. 92 |
Quantum Statistics | |
The Photoelectric Effect | p. 94 |
The Photon Gas | p. 96 |
Bose's Letter to Einstein | p. 97 |
The Quantum Harmonic Oscillator | p. 98 |
The Total Vibrational Energy | p. 101 |
Heat Capacity | p. 101 |
Bosons and Fermions | p. 103 |
Permutations and Combinations | p. 104 |
Configurations | p. 105 |
Stirling's Approximation | p. 107 |
Constraints | p. 107 |
The Classical Boltzmann Distribution | p. 108 |
Fine Structure | p. 110 |
The Classical Case: A More General Derivation | p. 112 |
Fermi-Dirac Counting | p. 113 |
The Fermi-Dirac Distribution Function | p. 116 |
Bose-Einstein Counting | p. 117 |
The Bose-Einstein Statistical Weights W[subscript B] | p. 119 |
The Bose-Einstein Distribution Function | p. 120 |
Summary Equations | p. 121 |
An Alternative Derivation for Fermions and Bosons | p. 121 |
Fermions (Again) | p. 123 |
Bosons (Again) | p. 123 |
Reduction to the Classical Case | p. 125 |
The Entropy | p. 126 |
A Note from Classical Thermodynamics: The Fundamental Equation | p. 129 |
Problems | p. 129 |
Consequences of the Fermi-Dirac Distribution | |
The Electron Gas | p. 132 |
The Fermi Sea | p. 132 |
The Fermi Distribution | p. 135 |
The Electronic Contribution to Solid-State Heat Capacity | p. 136 |
The Ground State of a Fermi Gas | p. 137 |
The Number of Orbitals in the Ground State | p. 139 |
The Total Energy of Electrons in the Ground State | p. 140 |
The Density of States | p. 141 |
The Energy of an Electron Gas | p. 144 |
The Low-Temperature Heat Capacity of an Electron Gas | p. 145 |
The Debye-Sommerfeld Equation | p. 146 |
Problems | p. 148 |
Consequences of the Bose-Einstein Distribution | |
Of Waves and Particles | p. 149 |
Bose: The Density of Photon Modes | p. 150 |
Why Is [mu] = 0 for Photons? | p. 152 |
Phonons | p. 154 |
The Influence of Symmetry Numbers on Rotational Spectroscopy | p. 155 |
The Vibrational Partition Function q[subscript vib] | p. 157 |
The Rotational Partition Function q[subscript rot] | p. 158 |
Symmetry Numbers | p. 159 |
Bosons, Fermions, and Triplets | p. 161 |
The Einstein Coefficients | p. 162 |
Lasers | p. 164 |
The Bose-Einstein Condensation | p. 165 |
The Bose-Einstein Condensation of Metal Vapor (Nobel Prize, 2001) | p. 165 |
Ballistic Expansion | p. 167 |
Macroscopic Quantum Effects | p. 168 |
Superfluidity | p. 168 |
Order Parameters | p. 170 |
Superconductivity | p. 171 |
Stopped Light | p. 172 |
Vortices | p. 173 |
Problems | p. 175 |
Bibliography | p. 177 |
Index | p. 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