Thermodynamics and Statistical Mechanics

by Greiner, Walter

• ISBN13: 9780387942995
• ISBN10: 0387942998
• Format: Paperback
• Copyright: 1995-05-01
• Publisher: Springer Verlag

Summary

The series of texts Classical Theoretical Physics is based on thehighly successful series of courses given by Walter Greiner andhis colleagues at the Johann Wolfgang Goethe University inFrankfurt am Main, Germany. Intended for advanced undergraduatesand beginning graduate students, the volumes in this series willprovide not only a complete survey of classical theoreticalphysics but also an enormous number of worked examples andproblems to show students clearly how to apply the underlyingprinciples to realistic problems.Thermodynamics and Statistical Physics covers:Thermodynamics- basic definitions of thermodynamics, equilibrium, state variables- the first and second laws- phase transitions and chemical reactions- thermodynamic potentialsStatistical Mechanics- statistics of microscopic states and connection to the entropy- the microcanonical, canonical and grand canonical ensembles- applications of Boltzmann statisticsQuantum Statistics- the density operator- many-particle wave functions- ideal quantum systems- the ideal Bose gas and applications to blackbody radiation, Kirchhoff's law, and lattice vibrations- the ideal Fermi gas and applications to condensed-matter physics, astrophysics, and nuclear physics- relativistic Bose and Fermi gases and applications to particle physicsReal Gases and Phase Transitions- real gases and the virial expansion- classification of phase transitions and critical indices- the Ising and Heisenberg models

Table of Contents

Foreword	v
Preface	vii
I Thermodynamics	1	(120)
Equilibrium and State Quantities	3	(30)
Introduction	3	(1)
Systems, phases and state quantities	4	(2)
Equilibrium and temperature---the zeroth law of thermodynamics	6	(4)
Kinetic theory of the ideal gas	10	(3)
Pressure, work and chemical potential	13	(2)
Heat and heat capacity	15	(2)
The equation of state for a real gas	17	(3)
Specific heat	20	(3)
Changes of state---reversible and irreversible processes	23	(2)
Exact and inexact differentials, line integrals	25	(8)
The Laws of Thermodynamics	33	(29)
The first law	33	(4)
Carnot's process and entropy	37	(4)
Entropy and the second law	41	(2)
Insertion: Microscopic interpretation of entropy and of the second law	43	(8)
Global and local equilibrium	51	(1)
Thermodynamic engines	52	(6)
Euler's equation and the Gibbs-Duhem relation	58	(4)
Phase Transitions and Chemical Reactions	62	(22)
Gibbs' Phase Rule	62	(5)
Phase equilibrium and the Maxwell construction	67	(3)
The law of mass action	70	(10)
Application of the laws of thermodynamics	80	(4)
Thermodynamic Potentials	84	(37)
The principle of maximum entropy	84	(1)
Entropy and energy as thermodynamic potentials	85	(2)
The Legendre transformation	87	(4)
The free energy	91	(4)
The enthalpy	95	(6)
The free enthalpy	101	(6)
The grand potential	107	(1)
The transformation of all variables	108	(1)
The Maxwell relations	108	(7)
Jacobi transformations	115	(3)
Thermodynamic stability	118	(3)
II Statistical Mechanics	121	(134)
Number of Microstates Ω and Entropy S	123	(19)
Foundations	123	(1)
Phase space	124	(3)
Statistical definition of entropy	127	(5)
Gibbs' paradox	132	(3)
Pseudo quantum mechanical counting of Ω	135	(7)
Ensemble Theory and Microcanonical Ensemble	142	(17)
Phase-space density, ergodic hypothesis	142	(3)
Liouville's theorem	145	(2)
The microcanonical ensemble	147	(2)
Entropy as an ensemble average	149	(1)
The uncertainty function	150	(9)
The Canonical Ensemble	159	(49)
General foundation of the Gibbs correction factor	164	(6)
Systems of noninteracting particles	170	(7)
Calculation of observables as ensemble averages	177	(9)
Connection between microcanonical and canonical ensembles	186	(5)
Fluctuations	191	(3)
Virial theorem and equipartition theorem	194	(6)
For better understanding: canonical ensemble as the mean value of all possible distributions	200	(8)
Applications of Boltzmann Statistics	208	(32)
Quantum Systems in Boltzmann Statistics	208	(6)
Paramagnetism	214	(9)
Negative temperatures in two-level systems	223	(2)
Gases with internal degrees of freedom	225	(9)
Relativistic ideal gas	234	(6)
The Macrocanonical Ensemble	240	(15)
Fluctuations in the macrocanonical ensemble	248	(7)
III Quantum Statistics	255	(144)
Density Operators	257	(28)
Fundamentals	257	(4)
Pure and mixed states	261	(5)
Properties of the density matrix	266	(4)
The density operators of quantum statistics	270	(15)
The Symmetry Character of Many-Particle Wavefunctions	285	(12)
Grand Canonical Description of Ideal Quantum Systems	297	(17)
The Ideal Bose Gas	314	(27)
Ultrarelativistic Bose gas	325	(16)
Ideal Fermi Gas	341	(46)
The degenerate Fermi gas	347	(38)
Supplement: Natural units	385	(2)
Applications of Relativistic Bose and Fermi Gases	387	(12)
Quark-gluon plasma in the Big Bang and in heavy-ion collisions	387	(12)
IV. Real Gases and Phase Transitions	399	(58)
Real Gases	401	(15)
For absorption: Mayer's cluster expansion	404	(10)
Virial expansion	414	(2)
Classification of Phase Transitions	416	(20)
Theorem of corresponding states	422	(2)
Critical indices	424	(1)
Examples for phase transitions	425	(11)
The Models of Ising and Heisenberg	436	(21)
Index	457