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Statistical Mechanics, Kinetic theory, and Stochastic Processes
1st Edition - January 1, 1972
Author: C.V. Heer
Hardback ISBN:
9 7 8 - 0 - 1 2 - 3 3 6 5 5 0 - 7
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 4 4 1 - 4
Statistical Mechanics, Kinetic Theory, and Stochastic Processes presents the statistical aspects of physics as a "living and dynamic" subject. In order to provide an elementary… Read more
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Statistical Mechanics, Kinetic Theory, and Stochastic Processes presents the statistical aspects of physics as a "living and dynamic" subject. In order to provide an elementary introduction to kinetic theory, physical systems in which particle-particle interaction can be neglected are considered. Transport phenomena in the free-molecular flow region for gases and the transport of thermal radiation are discussed. Discrete random processes such as random walk, binomial and Poisson distributions, and throwing of dice are studied by means of the characteristic function. Comprised of 11 chapters, this book begins with an introduction to the mass point gas as well as some elementary properties of space and velocity distributions. The discussion then turns to radiation and its interaction with an atom; probability, statistics, and conditional probability; intermolecular interactions; transport phenomena; and statistical thermodynamics. Molecular systems at low densities are also considered, together with non-ideal and real gases; liquids and solids; and stochastic processes, noise, and fluctuations. In particular, the response of atoms and molecules to perturbations and scattering by crystals, liquids, and high-pressure gases are examined. This monograph will be useful for undergraduate students, practitioners, and researchers in physics.
Preface
List of Symbols
I Mass Point Gas
1.1 Introduction
1.2 Uniform Space Distributions
1.3 Nonuniform Space Distributions
1.4 Average or Expected Value of Observable Quantities
1.5 Average or Expected Free Paths
1.6 Mass Point Gas
1.7 Effusive Flow of a Mass Point Gas
1.8 Pressure of a Mass Point Gas
1.9 Speed Distribution Function
1.10 Momentum Transfer and Heat Transfer in Free Molecular Flow
1.11 Free Molecular Flow
References
II Radiation
2.1 Introduction
2.2 Electromagnetic Radiation
2.3 Thermal Radiation
2.4 Surface Absorption and Emission of Thermal Radiation
2.5 Radiation Pressure
2.6 Experimental Verification of the Frequency Distribution of Thermal Radiation
2.7 Radiation Temperature
2.8 Interaction of Radiation with an Atom
2.9 Thermal Radiation in Enclosures Containing Matter
2.10 Absorption and Emission of Radiation by Matter
2.11 Motion through Thermal Radiation
References
III Probability, Statistics, And Conditional Probability
3.1 Introduction
3.2 Integral-Valued Random Variables
3.3 Useful Mathematical Formulas
3.4 Random Walk
3.5 Binomial and Poisson Distributions
3.6 Central Limit Theorem
3.7 Conditional Probability
3.8 Physical Processes Continuous in Space and Time
3.9 Random Walk with Absorbing Boundaries
3.10 Some Probability Laws Frequently Encountered in Physics
References
General References
IV Intermolecular Interactions
4.1 Introduction
4.2 Classical Elastic Collisions
4.3 Quantum Aspects of Elastic Collisions
4.4 Cross Sections for Diffusion and Viscosity
4.5 Elastic and Inelastic Binary Collisions
4.6 Inelastic Scattering Cross Section
4.7 Atomic Cross Sections from Atomic Beam Experiments
4.8 Interaction of Molecules with Solid Surfaces
References
V Transport Phenomena
5.1 Introduction
5.2 Elementary Theory of Transport
5.3 Gas Dynamics
5.4 Nonequilibrium Properties of the Distribution Function
5.5 General Transport Equations
5.6 Equilibrium Mixture of Two Gases
5.7 Diffusion
5.8 Sound Waves in Gases
References
VI Statistical Thermodynamics
6.1 Introduction
6.2 Laws of Thermodynamics
6.3 Thermodynamic Functions
6.4 Statistical Physics
References
General References
VII Molecular Systems At Low Densities
7.1 Nearly Ideal Gases
7.2 Photon Gas
7.3 Bose and Fermi Distributions
7.4 Chemical Reactions
7.5 Thermal Ionization and Excitation of Atoms
7.6 Thermodynamic Properties of Heteronuclear Diatomic Molecules
7.7 Homonuclear Diatomic Molecules
7.8 Equipartition Theorem
7.9 Gases at Very High Temperatures
7.10 Paramagnetism
References
VIII Nonideal And Real Gases
8.1 Nonideal Gases
8.2 Cluster Expansion
8.3 Equation of State and Second Virial Coefficient
8.4 Second Virial Coefficients for Classical, Fermi-Dirac, and Bose-Einstein Gases
8.5 Second Virial Coefficient for Molecular Gases with Interaction
8.6 Intermolecular Potentials
8.7 Degenerate Fermi-Dirac Gas—Electrons in Metals and in Very Dense Matter
8.8 Degenerate Bose-Einstein Gas
References
IX Gases, Liquids, And Solids
9.1 Introduction
9.2 Thermodynamic Aspects of Equilibrium between Phases
9.3 Phonon Gas
9.4 Thermodynamic Systems that Are Composed of Different Particles
9.5 The Third Law of Thermodynamics
9.6 Binary Mixtures
9.7 A Combinatorial Problem
9.8 Experimental Critical Points
9.9 Surface-Gas-Phase Equilibrium
References
X Stochastic Processes, Noise, And Fluctuations
10.1 Introduction
10.2 Thermal Motion of a One-Dimensional System
10.3 Random Pulses
10.4 Correlation Function and Spectral Density
10.5 Response of a Simple Harmonic Oscillator to Random Pulses and Thermal Noise
10.6 Correlation Function and Spectral Density for Brownian Motion
10.7 Response of Electrical Circuits to Random Pulses and Thermal Noise
10.8 Fluctuation Dissipation Theorem
10.9 Fluctuations in Thermal Radiation
10.10 General Theory of Fluctuations in Statistical Thermodynamics
10.11 Correlation of Fluctuations and Measurement with Waves
10.12 Nonlinear Physical Systems
10.13 Characteristic Functions for Random Pulses
10.14 Random Processes
References
XI Stochastic Processes In Quantum Systems
11.1 Introduction
11.2 Elementary Theory of Transition Rates
11.3 Density Matrix and the Response of Atoms and Molecules to Perturbations
11.4 Natural Line Width
11.5 Recoilless Emission and the Mössbauer Effect
11.6 Damping and the Golden Rule for Transition Rates
11.7 Theory for Broadening of Spectral Lines in Gases
11.8 Scattering by Crystals, Liquids, and High-Pressure Gases
References
Appendix A: Fundamental Constants
Appendix B: Gaussian Integrals
Index
- No. of pages: 618
- Language: English
- Published: January 1, 1972
- Imprint: Academic Press
- Hardback ISBN: 9780123365507
- eBook ISBN: 9780323144414