Statistical thermodynamics: understanding the properties of macroscopic systems
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2013
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 519 - 520 |
| Physical Description: | XIII, 534 S. graph. Darst. 24 cm |
| ISBN: | 9781466510678 1466510676 |
Staff View
MARC
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| 020 | |a 1466510676 |c (hbk.) £49.99 |9 1-466-51067-6 | ||
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| 245 | 1 | 0 | |a Statistical thermodynamics |b understanding the properties of macroscopic systems |c Lukong Cornelius Fai ; Gary Matthew Wysin |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2013 | |
| 300 | |a XIII, 534 S. |b graph. Darst. |c 24 cm | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
.......................................................................................................................xi
Authors
...................................................................................................................xiii
Chapter
1
Basic Principles of Statistical Physics.
.1
1.1
Microscopic
and Macroscopic Description of States
................1
1.2
Basic Postulates
.........................................................................2
1.3
Gibbs Ergodic Assumption
........................................................3
1.4
Gibbsian Ensembles
..................................................................4
1.5
Experimental Basis of Statistical Mechanics
............................5
1.6
Definition of Expectation Values
...............................................6
1.7
Ergodic Principle and Expectation Values
................................9
1.8
Properties of Distribution Functions
.......................................14
1.8.1
About Probabilities
.....................................................14
1.8.2
Normalization Requirement of
Distribution Functions
................................................15
1.8.3
Property of Multiplicity of Distribution
Functions
....................................................................15
1.9
Relative Fluctuation of an Additive
Macroscopic Parameter
...........................................................16
1.9.1
Questions and Answers
..............................................20
1.10
Liouville Theorem
...................................................................26
1.10.1
Questions and Answers
..............................................30
1.11
Gibbs Microcanonical Ensemble
.............................................39
1.12
Microcanonical Distribution in Quantum Mechanics
.............44
1.13
Density Matrix
.........................................................................48
1.14
Density Matrix in Energy Representation
...............................51
1.15
Entropy
....................................................................................56
1.15.1
Entropy of Microcanonical Distribution
....................58
1.15.2
Exact and Inexact Differentials
..............................60
1.15.3
Properties of Entropy
.................................................61
Chapter
2
Thermodynamic Functions
................................................................67
2.1
Temperature
.............................................................................67
2.2
Adiabatic Processes
.................................................................72
2.3
Pressure
...................................................................................73
2.3.1
Questions on Stationary Distributions Functions
and Ideal Gas Statistics
..............................................75
2.4
Thermodynamic Identity
.........................................................84
2.5
Laws of Thermodynamics
.......................................................88
VI
Contents
2.5.1
First
Law of Thermodynamics
...................................89
2.5.2
Second Law of Thermodynamics
..............................91
2.6
Thermodynamic Potentials, Maxwell Relations
.....................93
2.7
Heat Capacity and Equation of State
.......................................98
2.8
Jacobian Method
....................................................................100
2.9
Joule-Thomson Process
........................................................105
2.10
Maximum Work
....................................................................109
2.11
Condition for Equilibrium and Stability in an
Isolated System
......................................................................113
2.12
Thermodynamic Inequalities
................................................118
2.13
Third Law of Thermodynamics
............................................121
2.13.1
Nernst Theorem
........................................................122
2.14
Dependence of Thermodynamic Functions
on Number of Particles
..........................................................124
2.15
Equilibrium in an External Force Field
.................................129
Chapter
3
Canonical Distribution
.....................................................................135
3.1
Gibbs Canonical Distribution
................................................135
3.2
Basic Formulas of Statistical Physics
....................................139
3.3
Maxwell Distribution
.............................................................160
3.4
Experimental Basis of Statistical Mechanics
........................179
3.5
Grand Canonical Distribution
...............................................180
3.6
Extrémům
of Canonical Distribution Function
.....................185
Chapter
4
Ideal Gases
.......................................................................................189
4.1
Occupation Number
...............................................................189
4.2
Boltzmann Distribution
.........................................................191
4.2.1
Distribution with Respect to Coordinates
................195
4.3
Entropy of a Nonequilibrium Boltzmann Gas
.......................196
4.4
Free Energy of the Ideal Boltzmann Gas
..............................200
4.5
Equipartition Theorem
..........................................................223
4.6
Monatomic Gas
.....................................................................227
4.7
Vibrations of Diatomic Molecules
.........................................231
4.8
Rotation of Diatomic Molecules
............................................235
4.9
Nuclear Spin Effects
..............................................................239
4.10
Electronic Angular Momentum Effect
..................................244
4.11
Experiment and Statistical Ideas
...........................................245
4.11.1
Specific Heats
...........................................................246
Chapter
5
Quantum Statistics of Ideal Gases
...................................................247
5.1
Maxwell-Boltzmann, Bose-Einstein, and
Fermi-Dirac Statistics
...........................................................247
5.2
Generalized Thermodynamic Potential
for a Quantum Ideal Gas
.......................................................248
5.3
Fermi-Dirac and Bose-Einstein Distributions
.....................249
Contents
VII
5.4
Entropy of Nonequilibrium Fermi and
Bose
Gases
..............252
5.4.1
Fermi Gas
.................................................................252
5.4.2
Bose
Gas
...................................................................256
5.5
Thermodynamic Functions for Quantum Gases
...................258
5.6
Properties of Weakly Degenerate Quantum Gases
...............263
5.6.1
Fermi Energy
............................................................263
5.7
Degenerate Electronic Gas at Temperature
Different from Zero
...............................................................266
5.8
Experimental Basis of Statistical Mechanics
........................271
5.9
Application of Statistics to an Intrinsic Semiconductor
........272
5.9.1
Concentration of Carriers
.........................................273
5.10
Application of Statistics to Extrinsic Semiconductor
............279
5.11
Degenerate
Bose
Gas
.............................................................284
5.11.1
Condensation of
Bose
Gases
....................................284
5.12
Equilibrium or Black Body Radiation
...................................288
5.12.1
Electromagnetic Eigenmodes of aCavity
................288
5.13
Application of Statistical Thermodynamics
to Electromagnetic Eigenmodes
............................................294
Chapter
6
Electron Gas in a Magnetic Field
.....................................................305
6.1
Evaluation of Diamagnetism of a Free Electron Gas;
Density Matrix for a Free Electron Gas
................................305
6.2
Evaluation of Free Energy
.....................................................316
6.3
Application to a Degenerate Gas
...........................................318
6.4
Evaluation of Contour Integrals
............................................320
6.5
Diamagnetism of a Free Electron Gas; Oscillatory Effect....
324
Chapter
7
Magnetic and Dielectric Materials
...................................................329
7.1
Thermodynamics of Magnetic Materials in a
Magnetic Field
.......................................................................329
7.2
Thermodynamics of Dielectric Materials in an
Electric Field
..........................................................................333
7.3
Magnetic Effects in Materials
...............................................336
7.4
Adiabatic Cooling by Demagnetization
................................340
Chapter
8
Lattice Dynamics
.............................................................................343
8.1
Periodic Functions of a Reciprocal Lattice
...........................343
8.2
Reciprocal Lattice
.................................................................343
8.3
Vibrational Modes of a Monatomic Lattice
..........................347
8.3.1
Linear Monatomic Chain
.........................................348
8.3.2
Density of States
.......................................................358
8.4
Vibrational Modes of a Diatomic Linear Chain
....................359
8.5
Vibrational Modes in a Three-Dimensional Crystal
.............364
8.5.1
Properties of the Dynamical Matrix
........................369
viii
Contents
8.5.2
Cyclic Boundary for Three-Dimensional Cases
......373
8.5.2.1
Born-Von
Karman
Cyclic Condition
.......373
8.6
Normal Vibration of a Three-Dimensional Crystal
..............375
Chapter
9
Condensed Bodies
............................................................................389
9.1
Application of Statistical Thermodynamics to Phonons
.......389
9.2
Free Energy of Condensed Bodies in the
Harmonic Approximation
.....................................................391
9.3
Condensed Bodies at Low Temperatures
..............................394
9.4
Condensed Bodies at High Temperatures
.............................397
9.5
Debye Temperature Approximation
......................................398
9.6
Volume Coefficient of Expansion
..........................................403
9.7
Experimental Basis of Statistical Mechanics
........................405
Chapter
10
Multiphase Systems
..........................................................................407
10.1
Clausius-Clapeyron Formula
................................................407
10.2
Critical Point
..........................................................................413
Chapter
11
Macroscopic Quantum Effects: Superfluid Liquid Helium
.............421
11.1
Nature of the Lambda Transition
..........................................421
11.2
Properties of Liquid Helium
..................................................424
11.3
Landau Theory of Liquid He II
.............................................425
11.4
Superfluidity of Liquid Helium
.............................................430
Chapter
12 Nonideal
Classical Gases
.................................................................435
12.1
Pair Interactions Approximation
...........................................435
12.2
Van
Der Waals
Equation
.......................................................441
12.3
Completely Ionized Gas
........................................................442
Chapter
13
Functional Integration in Statistical Physics
....................................449
13.1
Feynman Path Integrals
.........................................................449
13.2
Least Action Principle
...........................................................450
13.3
Representation of Transition Amplitude through
Functional Integration
...........................................................456
13.3.1
Transition Amplitude in Hamiltonian Form
............460
13.3.2
Transition Amplitude in Feynman Form
..................463
13.3.3
Example: A Free Particle
.........................................472
13.4
Transition Amplitudes Using Stationary Phase Method
.......473
13.4.1
Motion in Potential Field
..........................................473
13.4.2
Harmonic Oscillator
.................................................476
Contents ix
13.5
Representation of Matrix Element of Physical Operator
through Functional Integral
...................................................479
13.6
Property of Path Integral Due to Events Occurring
in Succession
.........................................................................481
13.7
Eigenvectors
..........................................................................482
13.8
Transition Amplitude for Time-Independent Hamiltonian
.....483
13.9
Eigenvectors and Energy Spectrum
......................................485
13.9.1
Harmonic Oscillator Solved via
Transition Amplitude
...............................................485
13.9.2
Coordinate Representation of Transition
Amplitude of Forced Harmonic Oscillator
..............488
13.9.3
Matrix Representation of Transition Amplitude
of Forced Harmonic Oscillator
................................490
13.10 Schrödinger
Equation
............................................................494
13.11
Green Function for
Schrödinger
Equation
............................496
13.12
Functional Integration in Quantum Statistical Mechanics....
497
13.13
Statistical Physics in Representation of Path Integrals
..........497
13.14
Partition Function of Forced Harmonic Oscillator
...............503
13.15
Feynman Variational Method
................................................504
13.15.1
Proof of Feynman Inequality
...................................506
13.15.2
Application of Feynman Inequality
.........................507
13.16
Feynman Polaron Energy
......................................................509
References
.............................................................................................................519
Index
......................................................................................................................521
PHYSICS
STATISTICAL
THERMODYNAMICS
UNDERSTANDING THE PROPERTIES OF
MACROSCOPIC SYSTEMS
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:
THE MACROSCOPIC
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.
К1Ч7Ч5
CRC
Press
Taylor
&
Francis Group
зр
informa
reness
www.tayiorandfrancisgroup-com
6000
Broken Sound Parkway, NW
Suite
300,
Boca Raton. FL
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4RN. UK
www.crcpress.com
|
| any_adam_object | 1 |
| author | Fai, Lukong Cornelius Wysin, Gary Matthew |
| author_facet | Fai, Lukong Cornelius Wysin, Gary Matthew |
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| id | DE-604.BV040639547 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:28:03Z |
| institution | BVB |
| isbn | 9781466510678 1466510676 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025466636 |
| oclc_num | 826854322 |
| open_access_boolean | |
| owner | DE-11 DE-703 |
| owner_facet | DE-11 DE-703 |
| physical | XIII, 534 S. graph. Darst. 24 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Fai, Lukong Cornelius Verfasser aut Statistical thermodynamics understanding the properties of macroscopic systems Lukong Cornelius Fai ; Gary Matthew Wysin Boca Raton, Fla. [u.a.] CRC Press 2013 XIII, 534 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 519 - 520 Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Statistical thermodynamics. Statistische Thermodynamik (DE-588)4126251-7 s DE-604 Wysin, Gary Matthew Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025466636&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025466636&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Fai, Lukong Cornelius Wysin, Gary Matthew Statistical thermodynamics understanding the properties of macroscopic systems Statistische Thermodynamik (DE-588)4126251-7 gnd |
| subject_GND | (DE-588)4126251-7 |
| title | Statistical thermodynamics understanding the properties of macroscopic systems |
| title_auth | Statistical thermodynamics understanding the properties of macroscopic systems |
| title_exact_search | Statistical thermodynamics understanding the properties of macroscopic systems |
| title_full | Statistical thermodynamics understanding the properties of macroscopic systems Lukong Cornelius Fai ; Gary Matthew Wysin |
| title_fullStr | Statistical thermodynamics understanding the properties of macroscopic systems Lukong Cornelius Fai ; Gary Matthew Wysin |
| title_full_unstemmed | Statistical thermodynamics understanding the properties of macroscopic systems Lukong Cornelius Fai ; Gary Matthew Wysin |
| title_short | Statistical thermodynamics |
| title_sort | statistical thermodynamics understanding the properties of macroscopic systems |
| title_sub | understanding the properties of macroscopic systems |
| topic | Statistische Thermodynamik (DE-588)4126251-7 gnd |
| topic_facet | Statistische Thermodynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025466636&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025466636&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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