Classical and Statistical Thermodynamics / Edition 1

by Ashley Carter

Overview

For a one-semester upper-level undergraduate course in Thermal Physics or Thermodynamics.

This book provides a solid introduction to the classical and statistical theories of thermodynamics.

Product Details

ISBN-13:	9780137792085
Publisher:	Pearson Education
Publication date:	05/09/2000
Edition description:	New Edition
Pages:	456
Product dimensions:	6.00(w) x 9.00(h) x 1.30(d)

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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 molecules is observed to require a knowledge of the properties of the individual molecules making up the system. This information is furnished by the quantum mechanical notions of energy levels, quantum states, and intermolecular forces. In Chapter 13, the explication of classical and quantum statistics and the derivation of the particle distribution functions is based on the method of Lagrange multipliers. A discussion of the connection between classical and statistical thermodynamics completes the development of the mathematical formulation of the statistical theory. Chapter 14 is devoted to the statistics of an ideal gas. Chapters 15 through 19 present important examples of the application of the statistical method. The last chapter introduces the student to the basic ideas of information theory and offers the intriguing thought that statistical thermodynamics is but a special case of some deeper, more far-reaching set of physical principles.

Throughout the book a serious attempt has been made to keep the level of the chapters as uniform as possible. On the other hand, the problems are intended to vary somewhat more widely in difficulty.

In preparing the text, my greatest debt is to my students, whose response has provided a practical filter for the refinement of the material presented herein.

ACKNOWLEDGMENTS

In addition to my students at Drew University, I owe thanks to two colleagues and friends, Professors Robert Fenstermacher and John Ollom, who have encouraged me at every turn during the writing of this book. I am indebted to Professor Mark Raizin of the University of Texas at Austin, who reviewed the manuscript and used it as the text in his thermal physics course; his comments were invaluable.

I am especially grateful to Professor Roy S. Rubins of the University of Texas at Arlington for his thoughtful and thorough critique. I also received useful feedback from other reviewers, whose suggestions contributed substantially to an improved text. They are Anjum Ansari, University of Illinois at Chicago; John Jaszczak, Michigan Technological University; David Monts, Mississippi State University; Hugh Scott, Oklahoma State University; Harold Spector, Illinois Institute of Technology at Chicago; Zlatko Tesanovic, John Hopkins University.

I thank my editor Alison Reeves and her assistants, Gillian Buonanno and Christian Botting, for their support, guidance, and patience. Production editors Richard Saunders and Patrick Burt of WestWords Inc. were particularly helpful. Finally, I am extremely grateful to Heather Ferguson, who turned my lecture notes into a first draft, and to Lori Carucci and her daughters Amanda and Brigette, who prepared the final manuscript.

Without all of these people, the book would never have seen the light of day.

A.H.C.
Drew University

Table of Contents

(NOTE: Each chapter concludes with Problems.)
1. The Nature of Thermodynamics.

What Is Thermodynamics? Definitions. The Kilomile. Limits of the Continuum. More Definitions. Units. Temperature and the Zeroth Law of Thermodynamics. Temperature Scales.

2. Equations of State.

Introduction. Equation of State of an Ideal Gas. Van der Waals' Equation for a Real Gas. P-v-T Surfaces for Real Substances. Expansivity and Compressibility. An Application.

3. The First Law of Thermodynamics.

Configuration Work. Dissipative Work. Adiabatic Work and Internal Energy. Heat. Units of Heat. The Mechanical Equivalent of Heat. Summary of the First Law. Some Calculations of Work.

4. Applications of the First Law.

Heat Capacity. Mayer's Equation. Enthalpy and hats of Transformation. Relationships Involving Enthalpy. Comparison of u and h. Work Done in an Adiabatic Process.

5. Consequences of the First Law.

The Gay-Lussac-Joule Experiment. The Joule-Thomson Experiment. Heat Engines and the Carnot Cycle.

6. The Second Law of Thermodynamics.

Introduction. The Mathematical Concept of Entropy. Irreversible Processes. Carnot's Theorem. The Clausius Inequality and the Second Law. Entropy and Available Energy. Absolute Temperature. Combined First and Second Laws.

7. Applications of the Second Law.

Entropy Changes in Reversible Processes. Temperature-Entropy Diagrams. Entropy Change of the Surroundings for a Reversible Process. Entropy Change for an Ideal Gas. The Tds Equations. Entropy Change in Irreversible Processes. Free Expansion of an Ideal Gas. Entropy Change for a Liquid or Solid.

8. Thermodynamic Potentials.

Introduction. The Legendre Transformation. Definition of the Thermodynamic Potentials. The Maxwell Relations. The Helmholtz Function. The Gibbs Function. Application of the Gibbs Function to Phase Transitions. An Application of the Maxwell Relations. Conditions of Stable Equilibrium.

9. The Chemical Potential and Open Systems.

The Chemical Potential. Phase Equilibrium. The Gibbs Phase Rule. Chemical Recessions. Mixing Processes.

10. The Third Law of Thermodynamics.

Statements of the Third Law. Methods of Cooling. Equivalence of the Statements. Consequences of the Third Law.

11. The Kinetic Theory of Gases.

Basic Assumptions. Molecular Flux. Gas Pressure and the Ideal Gas Law. Equipartition of Energy. Specific Heat Capacity of an Ideal Gas. Distribution of Molecular Speeds. Mean Free Path and Collision Frequency. Effusion. Transport Processes.

12. Statistical Thermodynamics.

Introduction. Coin-Tossing Experiment. Assembly of Distinguishable Particles. Thermodynamic Probability and Entropy. Quantum States and Energy Levels. Density of Quantum States.

13. Classical and Quantum Statistics.

Bloltzmann Statistics. The Method of Lagrange Multipliers. The Boltzmann Distribution. The Fermi-Dirac Distribution. The Bose-Einstein Distribution. Dilute Gases and the Maxwell-Boltzmann Distribution. The Connection between Classical and Statistical Thermodynamics. Comparison of the Distributions. Alternative Statistical Models.

14. The Classical Statistical Treatment of an Ideal Gas.

Thermodynamic Properties from the Partition Function. Partition Function for a Gas. Properties of a Monatomic Ideal Gas. Applicability of the Maxwell-Boltzmann Distribution. Distribution of Molecular Speeds. Equipartition of Energy. Entropy Change of Mixing Revisited. Maxwell's Demon.

15. The Heat Capacity of a Diatomic Gas.

Introduction. The Quantified Linear Oscillator. Vibrational Modes of Diatomic Molecules. Rotational Modes of Diatomic Molecules. Electronic Excitation. The Total Heat Capacity.

16. The Heat Capacity of a Solid.

Introduction. Einstein's Theory of the Heat Capacity of a Solid. Debye's Theory of the Heat Capacity of a Solid.

17. The Thermodynamics of Magnetism.

Introduction. Paramagnetism. Properties of a Spin-1/2 Paramagnet. Adiabatic Demagnetization. NegativeTemperature. Ferromagnetism.

18. Bose-Einstein Gases.

Blackbody Radiation. Properties of a Photon Gas. Bose-Einstein Condensation. Properties of a Boson Gas. Application to Liquid Helium.

19. Fermi-Dirac Gases.

The Fermi Energy. The Calculation of ...m(T). Free Electrons in a Metal. Properties of a Fermion Gas. Application to White Dwarf Stars.

20. Information Theory.

Introduction. Uncertainty and Information. Unit of Information. Maximum Entropy. The Connection to Statistical Thermodynamics. Information Theory and the Laws of Thermodynamics. Maxwell's Demon Exorcised.

Appendix A. Review of Partial Differentiation.

Partial Derivatives. Exact and Inexact Differentials.

Appendix B. Stirling's Approximation.
Appendix C. Alternative Approach to Finding the Boltzmann Distribution.
Appendix D. Various Integrals.
Bibliography.
Answers to Selected Problems.
Index.

Preface

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 molecules is observed to require a knowledge of the properties of the individual molecules making up the system. This information is furnished by the quantum mechanical notions of energy levels, quantum states, and intermolecular forces. In Chapter 13, the explication of classical and quantum statistics and the derivation of the particle distribution functions is based on the method of Lagrange multipliers. A discussion of the connection between classical and statistical thermodynamics completes the development of the mathematical formulation of the statistical theory. Chapter 14 is devoted to the statistics of an ideal gas. Chapters 15 through 19 present important examples of the application of the statistical method. The last chapter introduces the student to the basic ideas of information theory and offers the intriguing thought that statistical thermodynamics is but a special case of some deeper, more far-reaching set of physical principles.

Throughout the book a serious attempt has been made to keep the level of the chapters as uniform as possible. On the other hand, the problems are intended to vary somewhat more widely in difficulty.

In preparing the text, my greatest debt is to my students, whose response has provided a practical filter for the refinement of the material presented herein.

ACKNOWLEDGMENTS

In addition to my students at Drew University, I owe thanks to two colleagues and friends, Professors Robert Fenstermacher and John Ollom, who have encouraged me at every turn during the writing of this book. I am indebted to Professor Mark Raizin of the University of Texas at Austin, who reviewed the manuscript and used it as the text in his thermal physics course; his comments were invaluable.

I am especially grateful to Professor Roy S. Rubins of the University of Texas at Arlington for his thoughtful and thorough critique. I also received useful feedback from other reviewers, whose suggestions contributed substantially to an improved text. They are Anjum Ansari, University of Illinois at Chicago; John Jaszczak, Michigan Technological University; David Monts, Mississippi State University; Hugh Scott, Oklahoma State University; Harold Spector, Illinois Institute of Technology at Chicago; Zlatko Tesanovic, John Hopkins University.

I thank my editor Alison Reeves and her assistants, Gillian Buonanno and Christian Botting, for their support, guidance, and patience. Production editors Richard Saunders and Patrick Burt of WestWords Inc. were particularly helpful. Finally, I am extremely grateful to Heather Ferguson, who turned my lecture notes into a first draft, and to Lori Carucci and her daughters Amanda and Brigette, who prepared the final manuscript.

Without all of these people, the book would never have seen the light of day.

A.H.C.
Drew University

Editorial Reviews

A textbook for a one-semester undergraduate course in thermal physics for physics students in their third or fourth year. Carter (Drew U.) assumes no background beyond college-level general physics and advanced calculus, though probability and statistics would be helpful as well. He disagrees with the notion that classical and statistical thermodynamics cannot both be adequately covered in a single semester, and designs the course to introduce the fundamental concepts of classical thermodynamics in the first half of the semester, then move to the statistical method. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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