States of Matter

by Goodstein, David L.

• ISBN13: 9780486495064
• ISBN10: 048649506X
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: Dover Publications

Summary

Overview covers thermodynamics and statistical mechanics; gases, solids, and liquids; perfect gases; electronics in metals; and the Bose condensation. Also: structure of a fluid, potential energy, interacting gases and liquids, Weiss molecular field theory, van der Waals equation, and other pertinent aspects of phase transitions. 154 figures .1975 edition.

Table of Contents

Preface	xi
Thermodynamics and Statistical Mechanics	1	(97)
Introduction: Thermodynamics and Statistical Mechanics of the Perfect Gas	1	(9)
Thermodynamics	10	(31)
The Laws of Thermodynamics	10	(3)
Thermodynamic Quantities	13	(6)
Magnetic Variables in Thermodynamics	19	(4)
Variational Principles in Thermodynamics	23	(2)
Examples of the Use of Variational Principles	25	(4)
Thermodynamic Derivatives	29	(5)
Some Applications to Matter	34	(7)
Statistical Mechanics	41	(42)
Reformulating the Problem	43	(6)
Some Comments	49	(4)
Some Properties of Z and J	53	(2)
Distinguishable States: Application to the Perfect Gas	55	(6)
Doing Sums over States as Integrals	61	(10)
Fluctuations	71	(12)
Remarks on the Foundations of Statistical Mechanics	83	(15)
Quantum and Thermodynamic Uncertainties	83	(4)
Status of the Equal Probabilities Postulate	87	(2)
Ensembles	89	(1)
Appendix A. Thermodynamic Mnemonic	90	(8)
Perfect Gases	98	(44)
Introduction	98	(1)
The Ideal Gas	99	(6)
Bose-Einstein and Fermi-Dirac Statistics	105	(5)
Slightly Degenerate Perfect Gases	110	(4)
The Very Degenerate Fermi Gas: Electrons in Metals	114	(13)
The Bose Condensation: A First Order Phase Transition	127	(15)
Solids	142	(85)
Introduction	142	(2)
The Heat Capacity Dilemma	144	(16)
The Einstein Model	147	(5)
Long Wavelength Compressional Modes	152	(2)
The Debye Model	154	(6)
Normal Modes	160	(15)
Crystal Structures	175	(8)
Crystal Space: Phonons, Photons, and the Reciprocal Lattice	183	(12)
Diffraction of X rays	185	(1)
The Reciprocal Lattice and Brillouin Zones	186	(5)
Umklapp Processes	191	(3)
Some Orders of Magnitude	194	(1)
Electrons in Crystals	195	(32)
A Semiqualitative Discussion	195	(7)
The Kronig-Penney Model	202	(10)
The Fermi Surface: Metal or Nonmetal?	212	(15)
Liquids and Interacting Gases	227	(93)
Introduction	227	(4)
The Structure of a Fluid	231	(17)
Measuring the Structure	232	(5)
The Statistical Mechanics of Structure	237	(9)
Applicability of This Approach	246	(2)
The Potential Energy	248	(12)
The Pair Potential	250	(2)
The Approximation of Pairwise Additivity	252	(8)
Interacting Gases	260	(23)
Cluster Expansions and the Dilute Gas	260	(3)
Behavior and Structure of a Dilute Gas	263	(3)
The Liquefaction of Gases and the Joule-Thomson Process	266	(5)
Higher Densities	271	(12)
Liquids	283	(37)
The Yvon-Born-Green Equation	284	(4)
The Hypernetted Chain and Percus-Yevick Equations	288	(14)
Comments and Comparisons	302	(18)
Some Special States	320	(116)
Introduction	320	(1)
Superfluidity	321	(50)
Properties of Liquid Helium	321	(6)
The Bose Gas as a Model for Superfluidity	327	(8)
Two-Fluid Hydrodynamics	335	(7)
Phonons and Rotons	342	(6)
The Feynman Theory	348	(12)
A Few Loose Ends	360	(11)
Superconductivity	371	(40)
Introduction	371	(4)
Some Thermodynamic Arguments	375	(11)
Electron Pairs	386	(6)
The BCS Ground State	392	(12)
The Superconducting State	404	(7)
Magnetism	411	(25)
Introduction	411	(1)
Magnetic Moments	412	(7)
Paramagnetism	419	(2)
Ferromagnetism	421	(15)
Critical Phenomena and Phase Transitions	436	(58)
Introduction	436	(2)
Weiss Molecular Field Theory	438	(5)
The van der Waals Equation of State	443	(10)
Analogies Between Phase Transitions	453	(4)
The Generalized Theory	457	(16)
Equilibrium Behavior	459	(4)
Fluctuations	463	(10)
Critical Point Exponents	473	(5)
Scaling Laws: Physics Discovers Dimensional Analysis	478	(6)
Evaluation and Summary: Testing the Scaling Laws	484	(10)
Index	494