Statistical Thermodynamics

Fundamentals and Applications

By: Normand Laurendeau

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Hardcover | 17 March 2006

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466 Pages

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This 2006 textbook discusses the fundamentals and applications of statistical thermodynamics for beginning graduate students in the physical and engineering sciences. Building on the prototypical Maxwellâ"Boltzmann method and maintaining a step-by-step development of the subject, this book assumes the reader has no previous exposure to statistics, quantum mechanics or spectroscopy. The book begins with the essentials of statistical thermodynamics, pauses to recover needed knowledge from quantum mechanics and spectroscopy, and then moves on to applications involving ideal gases, the solid state and radiation. A full introduction to kinetic theory is provided, including its applications to transport phenomena and chemical kinetics. A highlight of the textbook is its discussion of modern applications, such as laser-based diagnostics. The book concludes with a thorough presentation of the ensemble method, featuring its use for real gases. Numerous examples and prompted homework problems enrich the text.

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'... presents a general and complete overview of statistical thermodynamics mainly for beginners or engineers, linking this science to quantum mechanics and to classical thermodynamics ... Throughout the whole book, the author presents many figures which illustrate the concepts he introduces. He draws the computations with precise details and illustrates these computations with their physical background.' Alain Brillard, Zentralblatt MATH

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Non-Fiction Science Physics Thermodynamics & Heat Engineering & Technology Mechanical Engineering & Materials Materials Science Engineering Thermodynamics Mechanics of Fluids Mechanical Engineering

Preface	p. xv
Introduction	p. 1
The Statistical Foundation of Classical Thermodynamics	p. 1
A Classification Scheme for Statistical Thermodynamics	p. 3
Why Statistical Thermodynamics?	p. 3
Fundamentals of Statistical Thermodynamics
Probability and Statistics	p. 7
Probability: Definitions and Basic Concepts	p. 7
Permutations and Combinations	p. 10
Probability Distributions: Discrete and Continuous	p. 11
The Binomial Distribution	p. 13
The Poisson Distribution	p. 15
The Gaussian Distribution	p. 16
Combinatorial Analysis for Statistical Thermodynamics	p. 18
Distinguishable Objects	p. 19
Indistinguishable Objects	p. 20
Probability Theory and Statistical Mathematics (Chapter 2)	p. 23
The Statistics of Independent Particles	p. 29
Essential Concepts from Quantum Mechanics	p. 30
The Ensemble Method of Statistical Thermodynamics	p. 31
The Two Basic Postulates of Statistical Thermodynamics	p. 32
The M-B Method: System Constraints and Particle Distribution	p. 33
The M-B Method: Microstates and Macrostates	p. 33
The Most Probable Macrostate	p. 35
Bose-Einstein and Fermi-Dirac Statistics	p. 37
Bose-Einstein Statistics	p. 37
Fermi-Dirac Statistics	p. 38
The Most Probable Particle Distribution	p. 39
Entropy and the Equilibrium Particle Distribution	p. 40
The Boltzmann Relation for Entropy	p. 40
Identification of Lagrange Multipliers	p. 41
The Equilibrium Particle Distribution	p. 42
Thermodynamic Properties in the Dilute Limit	p. 45
The Dilute Limit	p. 45
Corrected Maxwell-Boltzmann Statistics	p. 46
The Molecular Partition Function	p. 47
The Influence of Temperature	p. 49
Criterion for Dilute Limit	p. 50
Internal Energy and Entropy in the Dilute Limit	p. 51
Additional Thermodynamic Properties in the Dilute Limit	p. 53
The Zero of Energy and Thermodynamic Properties	p. 55
Intensive Thermodynamic Properties for the Ideal Gas	p. 56
Statistical Modeling for Thermodynamics (Chapters 3-4)	p. 59
Quantum Mechanics and Spectroscopy
Basics of Quantum Mechanics	p. 69
Historical Survey of Quantum Mechanics	p. 69
The Bohr Model for the Spectrum of Atomic Hydrogen	p. 72
The de Broglie Hypothesis	p. 76
A Heuristic Introduction to the Schrodinger Equation	p. 78
The Postulates of Quantum Mechanics	p. 80
The Steady-State Schrodinger Equation	p. 83
Single-Particle Analysis	p. 84
Multiparticle Analysis	p. 85
The Particle in a Box	p. 86
The Uncertainty Principle	p. 90
Indistinguishability and Symmetry	p. 92
The Pauli Exclusion Principle	p. 94
The Correspondence Principle	p. 95
Quantum Analysis of Internal Energy Modes	p. 97
Schrodinger Wave Equation for Two-Particle System	p. 97
Conversion to Center-of-Mass Coordinates	p. 98
Separation of External from Internal Modes	p. 99
The Internal Motion for a Two-Particle System	p. 99
The Rotational Energy Mode for a Diatomic Molecule	p. 100
The Vibrational Energy Mode for a Diatomic Molecule	p. 104
The Electronic Energy Mode for Atomic Hydrogen	p. 108
The Electronic Energy Mode for Multielectron Species	p. 115
Electron Configuration for Multielectron Atoms	p. 116
Spectroscopic Term Symbols for Multielectron Atoms	p. 118
Electronic Energy Levels and Degeneracies for Atoms	p. 119
Electronic Energy Levels and Degeneracies for Diatomic Molecules	p. 121
Combined Energy Modes for Atoms and Diatomic Molecules	p. 123
Selection Rules for Atoms and Molecules	p. 124
The Spectroscopy of Diatomic Molecules	p. 129
Rotational Spectroscopy Using the Rigid-Rotor Model	p. 130
Vibrational Spectroscopy Using the Harmonic-Oscillator Model	p. 131
Rovibrational Spectroscopy: The Simplex Model	p. 132
The Complex Model for Combined Rotation and Vibration	p. 136
Rovibrational Spectroscopy: The Complex Model	p. 138
Electronic Spectroscopy	p. 141
Energy-Mode Parameters for Diatomic Molecules	p. 144
Quantum Mechanics and Spectroscopy (Chapters 5-7)	p. 147
Statistical Thermodynamics in the Dilute Limit
Interlude: From Particle to Assembly	p. 157
Energy and Degeneracy	p. 157
Separation of Energy Modes	p. 159
The Molecular Internal Energy	p. 160
The Partition Function and Thermodynamic Properties	p. 161
Energy-Mode Contributions in Classical Mechanics	p. 163
The Phase Integral	p. 164
The Equipartition Principle	p. 166
Mode Contributions	p. 167
Thermodynamic Properties of the Ideal Gas	p. 169
The Monatomic Gas	p. 169
Translational Mode	p. 169
Electronic Mode	p. 173
The Diatomic Gas	p. 175
Translational and Electronic Modes	p. 176
The Zero of Energy	p. 176
Rotational Mode	p. 178
Quantum Origin of Rotational Symmetry Factor	p. 182
Vibrational Mode	p. 184
Rigorous and Semirigorous Models for the Diatomic Gas	p. 187
The Polyatomic Gas	p. 192
Rotational Contribution	p. 194
Vibrational Contribution	p. 196
Property Calculations for Polyatomic Molecules	p. 198
Thermodynamic Properties of the Ideal Gas (Chapters 8-9)	p. 201
Statistical Thermodynamics for Ideal Gas Mixtures	p. 205
Equilibrium Particle Distribution for the Ideal Gas Mixture	p. 205
Thermodynamic Properties of the Ideal Gas Mixture	p. 208
The Reacting Ideal Gas Mixture	p. 211
Equilibrium Particle Distribution for Reactive Ideal Gas Mixture	p. 211
Equilibrium Constant: Introduction and Development	p. 213
Equilibrium Constant: General Expression and Specific Examples	p. 214
Dissociation of a Homonuclear Diatomic	p. 217
The Homonuclear-Heteronuclear Conversion Reaction	p. 219
The Ionization Reaction	p. 220
Concentration and Temperature Measurements	p. 223
Mode Temperatures	p. 224
Radiative Transitions	p. 225
Spectral Transfer of Radiation	p. 227
The Einstein Coefficients	p. 228
Line Broadening	p. 229
Absorption Spectroscopy	p. 230
Emission Spectroscopy	p. 234
Emissive Diagnostics	p. 234
The Problem of Self-Absorption	p. 235
Fluorescence Spectroscopy	p. 237
Sodium D-Line Reversal	p. 240
Advanced Diagnostic Techniques	p. 241
Chemical Equilibrium and Diagnostics (Chapters 10-11)	p. 243
Statistical Thermodynamics Beyond the Dilute Limit
Thermodynamics and Information	p. 251
Reversible Work and Heat	p. 251
The Second Law of Thermodynamics	p. 252
The Boltzmann Definition of Entropy	p. 253
Information Theory	p. 254
Spray Size Distribution from Information Theory	p. 256
Elements of the Solid State	p. 259
Statistical Thermodynamics of the Crystalline Solid	p. 259
Einstein Theory for the Crystalline Solid	p. 262
Debye Theory for the Crystalline Solid	p. 263
Critical Evaluation of the Debye Formulation	p. 266
The Band Theory of Metallic Solids	p. 268
Thermodynamic Properties of the Electron Gas	p. 270
The Metallic Crystal near Absolute Zero	p. 273
Equilibrium Radiation	p. 275
Bose-Einstein Statistics for the Photon Gas	p. 275
Photon Quantum States	p. 276
The Planck Distribution Law	p. 276
Thermodynamics of Blackbody Radiation	p. 278
The Influence of Wavelength for the Planck Distribution	p. 280
The Solid State and Radiation (Chapters 13-14)	p. 283
Nonequilibrium Statistical Thermodynamics
Elementary Kinetic Theory	p. 289
The Maxwell-Boltzmann Velocity Distribution	p. 289
The Maxwell-Boltzmann Speed Distribution	p. 291
The Maxwell-Boltzmann Energy Distribution	p. 294
Molecular Effusion	p. 295
The Ideal Gas Pressure	p. 298
Kinetics of Molecular Transport	p. 301
Binary Collision Theory	p. 301
Fundamentals of Molecular Transport	p. 305
The Mean Free Path	p. 305
The Molecular Flux	p. 307
Transport Properties	p. 309
Rigorous Transport Theory	p. 311
Dimensionless Transport Parameters	p. 312
Collision Integrals	p. 313
The Lennard-Jones Potential	p. 314
Rigorous Expressions for Transport Properties	p. 316
Chemical Kinetics	p. 319
The Bimolecular Reaction	p. 319
The Rate of Bimolecular Reactions	p. 320
Chemical Kinetics from Collision Theory	p. 321
The Significance of Internal Energy Modes	p. 324
Chemical Kinetics from Transition State Theory	p. 325
Kinetic Theory and Molecular Transport (Chapters 15-17)	p. 331
The Ensemble Method of Statistical Thermodynamics
The Canonical and Grand Canonical Ensembles	p. 339
The Ensemble Method	p. 339
The Canonical Ensemble	p. 340
The Equilibrium Distribution for the Canonical Ensemble	p. 341
Equilibrium Properties for the Canonical Ensemble	p. 342
Independent Particles in the Dilute Limit	p. 345
Fluctuations in Internal Energy	p. 347
Grand Canonical Ensemble	p. 349
The Equilibrium Distribution for the Grand Canonical Ensemble	p. 351
Equilibrium Properties for the Grand Canonical Ensemble	p. 352
Independent Particles in the Dilute Limit Revisited	p. 355
Applications of Ensemble Theory to Real Gases	p. 359
The Behavior of Real Gases	p. 359
Equation of State for Real Gases	p. 360
Canonical Partition Function for Real Gases	p. 361
The Virial Equation of State	p. 362
The Second Virial Coefficient	p. 364
Rigid-Sphere and Square-Well Potentials	p. 366
Implementation of Lennard-Jones Potential	p. 367
The Third Virial Coefficient	p. 369
Properties for Real Gases	p. 371
	p. 375
Whence and Whither	p. 379
Reprising the Journey	p. 379
Preparing for New Journeys	p. 383
The Continuing Challenge of Thermodynamics	p. 385
Appendices
Physical Constants and Conversion Factors	p. 389
Series and Integrals	p. 390
Periodic Table	p. 391
Mathematical Procedures	p. 393
Thermochemical Data for Ideal Gases	p. 396
Summary of Classical Thermodynamics	p. 409
Review of Classical Mechanics	p. 415
Review of Operator Theory	p. 418
The Spherical Coordinate System	p. 421
Electronic Energy Levels	p. 424
Energy-Mode Parameters for Molecules	p. 427
Normal Mode Analysis	p. 430
Tabulation of Debye Function	p. 433
Maxwell-Boltzmann Energy Distribution	p. 434
Force Constants for the Lennard-Jones Potential	p. 436
Collision Integrals for Calculating Transport Properties from the Lennard-Jones Potential	p. 437
Reduced Second Virial Coefficient from the Lennard-Jones Potential	p. 438
References and Acknowledgments	p. 439
Index	p. 445
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Statistical Thermodynamics

Fundamentals and Applications

At a Glance

Hardcover

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