9780137792085

Classical and Statistical Thermodynamics

by
  • ISBN13:

    9780137792085

  • ISBN10:

    0137792085

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2000-05-09
  • Publisher: Pearson

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Summary

This book provides a solid introduction to the classical and statistical theories of thermodynamics while assuming no background beyond general physics and advanced calculus. Though an acquaintance with probability and statistics is helpful, it is not necessary. Providing a thorough, yet concise treatment of the phenomenological basis of thermal physics followed by a presentation of the statistical theory, this book presupposes no exposure to statistics or quantum mechanics. It covers several important topics, including a mathematically sound presentation of classical thermodynamics; the kinetic theory of gases including transport processes; and thorough, modern treatment of the thermodynamics of magnetism. It includes up-to-date examples of applications of the statistical theory, such as Bose-Einstein condensation, population inversions, and white dwarf stars. And, it also includes a chapter on the connection between thermodynamics and information theory. Standard International units are used throughout. An important reference book for every professional whose work requires and understanding of thermodynamics: from engineers to industrial designers. y

Table of Contents

Preface xiv
The Nature of Thermodynamics
1(18)
What is thermodynamics?
3(2)
Definitions
5(1)
The kilomole
6(1)
Limits of the continuum
6(1)
More definitions
7(2)
Units
9(1)
Temperature and the zeroth law of thermodynamics
10(2)
Temperature scales
12(7)
Problems
16(3)
Equations of State
19(16)
Introduction
21(1)
Equation of state of an ideal gas
22(1)
Van der Waals' equation for a real gas
23(2)
P-v-T surfaces for real substances
25(2)
Expansivity and compressibility
27(2)
An application
29(6)
Problems
31(4)
The First Law of Thermodynamics
35(16)
Configuration work
37(3)
Dissipative work
40(1)
Adiabatic work and internal energy
41(2)
Heat
43(2)
Units of heat
45(1)
The mechanical equivalent of heat
46(1)
Summary of the first law
46(1)
Some calculations of work
47(4)
Problems
48(3)
Applications of the First Law
51(16)
Heat capacity
53(1)
Mayer's equation
54(3)
Enthalpy and heats of transformation
57(2)
Relationships involving enthalpy
59(2)
Comparison of u and h
61(1)
Work done in an adiabatic process
61(6)
Problems
64(3)
Consequences of the First Law
67(18)
The Gay-Lussac-Joule experiment
69(3)
The Joule-Thomson experiment
72(2)
Heat engines and the Carnot cycle
74(11)
Problems
80(5)
The Second Law of Thermodynamics
85(22)
Introduction
87(1)
The mathematical concept of entropy
88(1)
Irreversible processes
89(2)
Carnot's theorem
91(3)
The Clausius inequality and the second law
94(3)
Entropy and available energy
97(1)
Absolute temperature
98(5)
Combined first and second laws
103(4)
Problems
104(3)
Applications of the Second Law
107(20)
Entropy changes in reversible processes
109(1)
Temperature-entropy diagrams
110(1)
Entropy change of the surroundings for a reversible process
111(1)
Entropy change for an ideal gas
112(1)
The Tds equations
113(5)
Entropy change in irreversible processes
118(3)
Free expansion of an ideal gas
121(1)
Entropy change for a liquid or solid
122(5)
Problems
123(4)
Thermodynamic Potentials
127(22)
Introduction
129(1)
The Legendre transformation
130(2)
Definition of the thermodynamic potentials
132(2)
The Maxwell relations
134(1)
The Helmholtz function
134(2)
The Gibbs function
136(1)
Application of the Gibbs function to phase transitions
137(5)
An application of the Maxwell relations
142(1)
Conditions of stable equilibrium
143(6)
Problems
146(3)
The Chemical Potential and Open Systems
149(20)
The chemical potential
151(4)
Phase equilibrium
155(2)
The Gibbs phase rule
157(3)
Chemical reactions
160(2)
Mixing processes
162(7)
Problems
166(3)
The Third Law of Thermodynamics
169(12)
Statements of the third law
171(3)
Methods of cooling
174(1)
Equivalence of the statements
175(3)
Consequences of the third law
178(3)
Problems
179(2)
The Kinetic Theory of Gases
181(32)
Basic assumptions
183(3)
Molecular flux
186(2)
Gas pressure and the ideal gas law
188(2)
Equipartition of energy
190(1)
Specific heat capacity of an ideal gas
191(2)
Distribution of molecular speeds
193(5)
Mean free path and collision frequency
198(3)
Effusion
201(2)
Transport processes
203(10)
Problems
208(5)
Statistical Thermodynamics
213(20)
Introduction
215(1)
Coin-tossing experiment
216(5)
Assembly of distinguishable particles
221(2)
Thermodynamic probability and entropy
223(2)
Quantum states and energy levels
225(4)
Density of quantum states
229(4)
Problems
231(2)
Classical and Quantum Statistics
233(28)
Boltzmann statistics
235(1)
The method of Lagrange multipliers
236(2)
The Boltzmann distribution
238(4)
The Fermi-Dirac distribution
242(2)
The Bose-Einstein distribution
244(2)
Dilute gases and the Maxwell-Boltzmann distribution
246(2)
The connection between classical and statistical thermodynamics
248(5)
Comparison of the distributions
253(1)
Alternative statistical models
254(7)
Problems
257(4)
The Classical Statistical Treatment of an Ideal Gas
261(16)
Thermodynamic properties from the partition function
263(2)
Partition function for a gas
265(1)
Properties of a monatomic ideal gas
266(2)
Applicability of the Maxwell-Boltzmann distribution
268(1)
Distribution of molecular speeds
269(1)
Equipartition of energy
270(1)
Entropy change of mixing revisited
271(2)
Maxwell's demon
273(4)
Problems
275(2)
The Heat Capacity of a Diatomic Gas
277(14)
Introduction
279(1)
The quantized linear oscillator
279(3)
Vibrational modes of diatomic molecules
282(2)
Rotational modes of diatomic molecules
284(3)
Electronic excitation
287(1)
The total heat capacity
288(3)
Problems
289(2)
The Heat Capacity of a Solid
291(14)
Introduction
293(1)
Einstein's theory of the heat capacity of a solid
293(3)
Debye's theory of the heat capacity of a solid
296(9)
Problems
301(4)
The Thermodynamics of Magnetism
305(26)
Introduction
307(1)
Paramagnetism
308(7)
Properties of a spin-1/2 paramagnet
315(3)
Adiabatic demagnetization
318(3)
Negative temperature
321(4)
Ferromagnetism
325(6)
Problems
328(3)
Bose-Einstein Gases
331(22)
Blackbody radiation
333(5)
Properties of a photon gas
338(2)
Bose-Einstein condensation
340(5)
Properties of a boson gas
345(2)
Application to liquid helium
347(6)
Problems
349(4)
Fermi-Dirac Gases
353(20)
The Fermi energy
355(2)
The calculation of μ(T)
357(4)
Free electrons in a metal
361(3)
Properties of a fermion gas
364(3)
Application to white dwarf stars
367(6)
Problems
370(3)
Information Theory
373(40)
Introduction
375(1)
Uncertainty and information
375(4)
Unit of information
379(2)
Maximum entropy
381(3)
The connection to statistical thermodynamics
384(2)
Information theory and the laws of thermodynamics
386(1)
Maxwell's demon exorcised
387(4)
Problems
388(3)
Appendices
A. Review of Partial Differentiation
391(10)
A.1 Partial derivatives
391(2)
A.2 Exact and inexact differentials
393(6)
Problems
399(2)
B. Stirling's Approximation
401(2)
C. Alternative Approach To Finding the Boltzmann Distribution
403(4)
D. Various Integrals
407(6)
Bibliography 413(4)
Classical thermodynamics
413(1)
Kinetic theory of gases
414(1)
Statistical mechanics
414(1)
Special topics
415(2)
Answers to selected problems 417(8)
Index 425

Excerpts

Preface This book is intended as a text for a one-semester undergraduate course in thermal physics. Its objective is to provide third- or fourth-year physics students with a solid introduction to the classical and statistical theories of thermodynamics. No preparation is assumed beyond college-level general physics and advanced calculus. An acquaintance with probability and statistics is helpful but is by no means necessary. The current practice in many colleges is to offer a course in classical thermodynamics with little or no mention of the statistical theory--or vice versa. The argument is that it is impossible to do justice to both in a one-semester course. On the basis of my own teaching experience, I strongly disagree. The standard treatment of temperature, work, heat, entropy, etc. often seems to the student like an endless collection of partial derivatives that shed only limited light on the underlying physics and can be abbreviated. The fundamental concepts of classical thermodynamics can easily be grasped in little more than half a semester, leaving ample time to gain a reasonably thorough understanding of the statistical method. Since statistical thermodynamics subsumes the classical results, why not structure the entire course around the statistical approach? There are good reasons not to do so. The classical theory is general, simple, and direct, providing a kind of visceral, intuitive comprehension of thermal processes. The physics student not confronted with this remarkable phenomenological conception is definitely deprived. To be sure, the inadequacies of classical thermodynamics become apparent upon close scrutiny and invite inquiry about a more fundamental description. This, of course, exactly reflects the historical development of the subject. If only the statistical picture is presented, however, it is my observation that the student fails to appreciate fully its more abstract concepts, given no exposure to the related classical ideas first. Not only do classical and statistical thermodynamics in this sense complement each other, they also beautifully illustrate the physicist's perpetual striving for descriptions of greater power, elegance, universality, and freedom from ambiguity. Chapters 1 through 10 represent a fairly traditional introduction to the classical theory. Early on emphasis is placed on the advantages of expressing the fundamental laws in terms of state variables, quantities whose differentials are exact. Accordingly, the search for integrating factors for the differentials of work and heat is discussed. The elaboration of the first law is followed by chapters on applications and consequences. Entropy is presented both as a useful mathematical variable and as a phenomenological construct necessary to explain why there are processes permitted by the first law that do not occur in nature. Calculations are then given of the change in entropy for various reversible and irreversible processes. The thermodynamic potentials are broached via the Legendre transformation following elucidation of the rationale for having precisely four such quantities. The conditions for stable equilibrium are examined in a section that rarely appears in undergraduate texts. Modifications of fundamental relations to deal with open systems are treated in Chapter 9 and the third law is given its due in Chapter 10. The kinetic theory of gases, treated in Chapter 11, is concerned with the molecular basis of such thermodynamic properties of gases as the temperature, pressure, and thermal energy. It represents, both logically and historically, the transition between classical thermodynamics and the statistical theory. The underlying principles of equilibrium statistical thermodynamics are introduced in Chapter 12 through consideration of a simple coin-tossing experiment. The basic concepts are then defined. The statistical interpretation of a system containing many molecu

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