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E-raamat: Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems

(University of Dschang, Cameroon and The Abdus Salam International Centre For Theoretical Physics, Trieste, Italy), (Kansas State University, Manhattan, USA)
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  • Ilmumisaeg: 19-Oct-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781466510685
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 19-Oct-2012
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781466510685
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Fai (condensed matter physics, U. of Dschang, Cameroon) and Wysin (physics, Kansas State U.) present a textbook for graduate and practicing theoretical physicists who are already familiar with statistical thermodynamics, particularly its experimental dimension. Knowing the microscopic constituents of a system permits its macroscopic parameters to be evaluated using statistical thermodynamics, he says. Among his topics are thermodynamic functions, the quantum statistics of ideal gases, magnetic and dielectric materials, multiphase systems, and functional integration in statistical physics. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

Statistical thermodynamics and the related domains of statistical physics and quantum mechanics are very important in many fields of research, including plasmas, rarefied gas dynamics, nuclear systems, lasers, semiconductors, superconductivity, ortho- and para-hydrogen, liquid helium, and so on. Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems provides a detailed overview of how to apply statistical principles to obtain the physical and thermodynamic properties of macroscopic systems.

Intended for physics, chemistry, and other science students at the graduate level, the book starts with fundamental principles of statistical physics, before diving into thermodynamics. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and Lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The book concludes with an examination of statistical thermodynamics using functional integration and Feynman path integrals, and includes a wide range of problems with solutions that explain the theory.

Arvustused

"... recommended for various levels of study: from a general course to the ground specialized course of theoretical physics. Moreover, a large number of problems based on physical situations supplied with detailed solutions determine an exceptional usefulness of this book due to the development of practical skills." Zentralblatt MATH 1305

Preface xi
Authors xiii
Chapter 1 Basic Principles of Statistical Physics
1(66)
1.1 Microscopic and Macroscopic Description of States
1(1)
1.2 Basic Postulates
2(1)
1.3 Gibbs Ergodic Assumption
3(1)
1.4 Gibbsian Ensembles
4(1)
1.5 Experimental Basis of Statistical Mechanics
5(1)
1.6 Definition of Expectation Values
6(3)
1.7 Ergodic Principle and Expectation Values
9(5)
1.8 Properties of Distribution Functions
14(2)
1.8.1 About Probabilities
14(1)
1.8.2 Normalization Requirement of Distribution Functions
15(1)
1.8.3 Property of Multiplicity of Distribution Functions
15(1)
1.9 Relative Fluctuation of an Additive Macroscopic Parameter
16(10)
1.9.1 Questions and Answers
20(6)
1.10 Liouville Theorem
26(13)
1.10.1 Questions and Answers
30(9)
1.11 Gibbs Microcanonical Ensemble
39(5)
1.12 Microcanonical Distribution in Quantum Mechanics
44(4)
1.13 Density Matrix
48(3)
1.14 Density Matrix in Energy Representation
51(5)
1.15 Entropy
56(11)
1.15.1 Entropy of Microcanonical Distribution
58(2)
1.15.2 Exact and "Inexact" Differentials
60(1)
1.15.3 Properties of Entropy
61(6)
Chapter 2 Thermodynamic Functions
67(68)
2.1 Temperature
67(5)
2.2 Adiabatic Processes
72(1)
2.3 Pressure
73(11)
2.3.1 Questions on Stationary Distributions Functions and Ideal Gas Statistics
75(9)
2.4 Thermodynamic Identity
84(4)
2.5 Laws of Thermodynamics
88(5)
2.5.1 First Law of Thermodynamics
89(2)
2.5.2 Second Law of Thermodynamics
91(2)
2.6 Thermodynamic Potentials, Maxwell Relations
93(5)
2.7 Heat Capacity and Equation of State
98(2)
2.8 Jacobian Method
100(5)
2.9 Joule--Thomson Process
105(4)
2.10 Maximum Work
109(4)
2.11 Condition for Equilibrium and Stability in an Isolated System
113(5)
2.12 Thermodynamic Inequalities
118(3)
2.13 Third Law of Thermodynamics
121(3)
2.13.1 Nernst Theorem
122(2)
2.14 Dependence of Thermodynamic Functions on Number of Particles
124(5)
2.15 Equilibrium in an External Force Field
129(6)
Chapter 3 Canonical Distribution
135(54)
3.1 Gibbs Canonical Distribution
135(4)
3.2 Basic Formulas of Statistical Physics
139(21)
3.3 Maxwell Distribution
160(19)
3.4 Experimental Basis of Statistical Mechanics
179(1)
3.5 Grand Canonical Distribution
180(5)
3.6 Extremum of Canonical Distribution Function
185(4)
Chapter 4 Ideal Gases
189(58)
4.1 Occupation Number
189(2)
4.2 Boltzmann Distribution
191(5)
4.2.1 Distribution with Respect to Coordinates
195(1)
4.3 Entropy of a Nonequilibrium Boltzmann Gas
196(4)
4.4 Free Energy of the Ideal Boltzmann Gas
200(23)
4.5 Equipartition Theorem
223(4)
4.6 Monatomic Gas
227(4)
4.7 Vibrations of Diatomic Molecules
231(4)
4.8 Rotation of Diatomic Molecules
235(4)
4.9 Nuclear Spin Effects
239(5)
4.10 Electronic Angular Momentum Effect
244(1)
4.11 Experiment and Statistical Ideas
245(2)
4.11.1 Specific Heats
246(1)
Chapter 5 Quantum Statistics of Ideal Gases
247(58)
5.1 Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac Statistics
247(1)
5.2 Generalized Thermodynamic Potential for a Quantum Ideal Gas
248(1)
5.3 Fermi--Dirac and Bose--Einstein Distributions
249(3)
5.4 Entropy of Nonequilibrium Fermi and Bose Gases
252(6)
5.4.1 Fermi Gas
252(4)
5.4.2 Bose Gas
256(2)
5.5 Thermodynamic Functions for Quantum Gases
258(5)
5.6 Properties of Weakly Degenerate Quantum Gases
263(3)
5.6.1 Fermi Energy
263(3)
5.7 Degenerate Electronic Gas at Temperature Different from Zero
266(5)
5.8 Experimental Basis of Statistical Mechanics
271(1)
5.9 Application of Statistics to an Intrinsic Semiconductor
272(7)
5.9.1 Concentration of Carriers
273(6)
5.10 Application of Statistics to Extrinsic Semiconductor
279(5)
5.11 Degenerate Bose Gas
284(4)
5.11.1 Condensation of Bose Gases
284(4)
5.12 Equilibrium or Black Body Radiation
288(6)
5.12.1 Electromagnetic Eigenmodes of a Cavity
288(6)
5.13 Application of Statistical Thermodynamics to Electromagnetic Eigenmodes
294(11)
Chapter 6 Electron Gas in a Magnetic Field
305(24)
6.1 Evaluation of Diamagnetism of a Free Electron Gas; Density Matrix for a Free Electron Gas
305(11)
6.2 Evaluation of Free Energy
316(2)
6.3 Application to a Degenerate Gas
318(2)
6.4 Evaluation of Contour Integrals
320(4)
6.5 Diamagnetism of a Free Electron Gas; Oscillatory Effect
324(5)
Chapter 7 Magnetic and Dielectric Materials
329(14)
7.1 Thermodynamics of Magnetic Materials in a Magnetic Field
329(4)
7.2 Thermodynamics of Dielectric Materials in an Electric Field
333(3)
7.3 Magnetic Effects in Materials
336(4)
7.4 Adiabatic Cooling by Demagnetization
340(3)
Chapter 8 Lattice Dynamics
343(46)
8.1 Periodic Functions of a Reciprocal Lattice
343(1)
8.2 Reciprocal Lattice
343(4)
8.3 Vibrational Modes of a Monatomic Lattice
347(12)
8.3.1 Linear Monatomic Chain
348(10)
8.3.2 Density of States
358(1)
8.4 Vibrational Modes of a Diatomic Linear Chain
359(5)
8.5 Vibrational Modes in a Three-Dimensional Crystal
364(11)
8.5.1 Properties of the Dynamical Matrix
369(4)
8.5.2 Cyclic Boundary for Three-Dimensional Cases
373(1)
8.5.2.1 Born--Von Karman Cyclic Condition
373(2)
8.6 Normal Vibration of a Three-Dimensional Crystal
375(14)
Chapter 9 Condensed Bodies
389(18)
9.1 Application of Statistical Thermodynamics to Phonons
389(2)
9.2 Free Energy of Condensed Bodies in the Harmonic Approximation
391(3)
9.3 Condensed Bodies at Low Temperatures
394(3)
9.4 Condensed Bodies at High Temperatures
397(1)
9.5 Debye Temperature Approximation
398(5)
9.6 Volume Coefficient of Expansion
403(2)
9.7 Experimental Basis of Statistical Mechanics
405(2)
Chapter 10 Multiphase Systems
407(14)
10.1 Clausius--Clapeyron Formula
407(6)
10.2 Critical Point
413(8)
Chapter 11 Macroscopic Quantum Effects: Superfluid Liquid Helium
421(14)
11.1 Nature of the Lambda Transition
421(3)
11.2 Properties of Liquid Helium
424(1)
11.3 Landau Theory of Liquid He II
425(5)
11.4 Superfluidity of Liquid Helium
430(5)
Chapter 12 Non ideal Classical Gases
435(14)
12.1 Pair Interactions Approximation
435(6)
12.2 Van Der Waals Equation
441(1)
12.3 Completely Ionized Gas
442(7)
Chapter 13 Functional Integration in Statistical Physics
449(70)
13.1 Feynman Path Integrals
449(1)
13.2 Least Action Principle
450(6)
13.3 Representation of Transition Amplitude through Functional Integration
456(17)
13.3.1 Transition Amplitude in Hamiltonian Form
460(3)
13.3.2 Transition Amplitude in Feynman Form
463(9)
13.3.3 Example: A Free Particle
472(1)
13.4 Transition Amplitudes Using Stationary Phase Method
473(6)
13.4.1 Motion in Potential Field
473(3)
13.4.2 Harmonic Oscillator
476(3)
13.5 Representation of Matrix Element of Physical Operator through Functional Integral
479(2)
13.6 Property of Path Integral Due to Events Occurring in Succession
481(1)
13.7 Eigenvectors
482(1)
13.8 Transition Amplitude for Time-Independent Hamiltonian
483(2)
13.9 Eigenvectors and Energy Spectrum
485(9)
13.9.1 Harmonic Oscillator Solved via Transition Amplitude
485(3)
13.9.2 Coordinate Representation of Transition Amplitude of Forced Harmonic Oscillator
488(2)
13.9.3 Matrix Representation of Transition Amplitude of Forced Harmonic Oscillator
490(4)
13.10 Schrodinger Equation
494(2)
13.11 Green Function for Schrodinger Equation
496(1)
13.12 Functional Integration in Quantum Statistical Mechanics
497(1)
13.13 Statistical Physics in Representation of Path Integrals
497(6)
13.14 Partition Function of Forced Harmonic Oscillator
503(1)
13.15 Feynman Variational Method
504(5)
13.15.1 Proof of Feynman Inequality
506(1)
13.15.2 Application of Feynman Inequality
507(2)
13.16 Feynman Polaron Energy
509(10)
References 519(2)
Index 521
Lukong Cornelius Fai is with ICTP Trieste, Italy and the University of Dschang, Cameroon. Gary Wysin is with Kansas State University, USA.