Thermal Physics

Citation

Baierlein, R. (1999). Thermal Physics. Cambridge University Press.

Chapter Summary

The book has sixteen chapters, an epilogue and four appendices. Its conceptual core, in the preface's words, is four linked elements: entropy and the second law of thermodynamics, the canonical probability distribution, the partition function and the chemical potential. Chapters 1 to 3 review material from introductory physics; entropy, conceived microscopically, arrives in Chapter 2; and the remaining chapters build on the four core elements. Every chapter ends with a summary of essential ideas and a set of problems.

Chapter 1: Background

A mostly review chapter that recapitulates basic ideas, definitions and relationships, beginning with heating and temperature. Thermal physics has subtle aspects, so the book starts by restating the basics.

Chapter 2: The Second Law of Thermodynamics

Examines how macroscopic systems evolve in time, which leads to the second law. To describe evolution quantitatively the chapter introduces and defines multiplicity and entropy, and relates them to temperature and energy input by heating.

Chapter 3: Entropy and Efficiency

Begins with the efficiency of heat engines and the Carnot cycle, which provide the basis of William Thomson's definition of absolute temperature (taken up in Chapter 4). It then develops a method for computing entropy change when a process occurs rapidly, with the Otto cycle as an extended example and a discussion of reversibility.

Chapter 4: Entropy in Quantum Theory

Has two goals: to develop the quantum version of multiplicity, which shows how entropy is expressed in quantum theory, and to give a general quantitative definition of temperature in which entropy plays the key role.

Chapter 5: The Canonical Probability Distribution

Asks how to estimate a system's energy, pressure, magnetic moment and molecular velocity distribution if its temperature and external parameters are known. It derives the canonical probability distribution, develops techniques for applying it efficiently, and works out two major examples.

Chapter 6: Photons and Phonons

A chapter on photons and phonons, placed directly after the canonical distribution.

Chapter 7: The Chemical Potential

Introduces the last of the four core elements, the chemical potential, with a typical application. It plays a significant role in most of the later chapters.

Chapters 8–9: The Quantum Ideal Gas; Fermions and Bosons at Low Temperature

Chapter 8 develops an effective technique for working with a quantum ideal gas and notes that its applications are numerous. Chapter 9 examines applications for fermions and bosons at low temperature; the publisher's description names Bose–Einstein condensation among the recent developments the book explains.

Chapters 10–12: The Free Energies; Chemical Equilibrium; Phase Equilibrium

Chapter 10 has several goals: to deepen understanding of the chemical potential, to describe how the basic laws change when particles may enter or leave the system, to study the Helmholtz free energy further, and to introduce the Gibbs free energy. Chapter 11 turns to chemical equilibrium. Chapter 12 is about the coexistence of solids, liquids and gases, ending with the van der Waals equation as the first equation of state to describe gas and liquid in coexistence.

Chapter 13: The Classical Limit

The classical theory of statistical mechanics. The preface says that it can be studied at any time after Chapter 5.

Chapters 14–16: Approaching Zero; Transport Processes; Critical Phenomena

Chapter 14 explores connections among entropy, temperature and energy transfer: a general expression for entropy in terms of probabilities, a classic method of reaching low temperatures, the third law, temperatures numerically below absolute zero, and reflections on temperature, heating and entropy. Chapter 15 treats the transport of energy and momentum when a system has spatial variations in temperature or velocity. Chapter 16 introduces critical phenomena through two experiments, the mathematical behavior of quantities near a critical point, the Ising model and methods of extracting predictions from it.

Epilogue and appendices

The epilogue steps back from the applications to the underlying theoretical structure. The appendices are physical and mathematical data, examples of estimating occupation numbers, the framework of probability theory, and qualitative perspectives on the van der Waals equation.

Key Concepts

Chapters 1–4: Entropy and the second law

• Multiplicity and entropy: the microscopic definition that reaches the second law in Chapter 2.
• Heat engines and the Carnot cycle: the classical setting for efficiency and absolute temperature.
• Quantum multiplicity: how entropy and temperature are defined in quantum theory.

Chapters 5–9: Distributions, the partition function and quantum gases

• Canonical probability distribution: predicting a system's properties from its temperature.
• Partition function: the third of the four core elements.
• Chemical potential: the fourth core element, central to later chapters.
• Photons, phonons and quantum ideal gases: applications of the canonical and chemical-potential machinery.

Chapters 10–16: Free energies, equilibrium and further topics

• Helmholtz and Gibbs free energies: the quantities that govern chemical and phase equilibrium.
• Van der Waals equation: the first equation of state to describe gas–liquid coexistence.
• Third law and temperatures below absolute zero: topics of Chapter 14.
• Ising model: the model through which critical phenomena are developed.

Critical Analysis

Strengths

• A stated order of difficulty. The preface says the goal was to build from the familiar to the abstract and still reach entropy, conceived microscopically, in the second chapter. The book presumes only elementary classical mechanics and a few rudimentary quantum ideas, such as the de Broglie relation and energy eigenstates.
• A short, focused core. The preface describes the aim of keeping the book crisp and lean, with succinct derivations and topics essential for physics and astronomy, because a semester is short and few undergraduate curricula give more than one to thermal physics.
• Modularity. The preface says instructors' tastes vary, and the logical structure is displayed in a figure; the classical theory in Chapter 13 can be studied at any time after Chapter 5.
• Course aids. Each chapter contains a summary of essential ideas and an extensive set of problems of varying difficulty, key equations are highlighted, and a free solutions manual is available for instructors.
• Reviews. H. Eugene Stanley (Boston University) calls it a superb introduction to the key concepts of statistical mechanics, and S. C. Tegler (Northern Arizona University) describes it as conceptually clear yet mathematically rigorous, moving from the familiar to the abstract, with initial chapters that review freshman thermodynamics and bridge to the rest.

Limitations

• Compact by design. The preface sets the goal of keeping the book lean and limited to topics essential for physics and astronomy, so it is not a comprehensive reference; a graduate course would want a fuller text.
• Solutions for instructors. The solutions manual is offered to instructors, so students working independently have fewer ways to check problems.

Where It Fits in the Course

Within this thermodynamics and statistical mechanics list, Baierlein sits at the undergraduate level, between the gentlest introductions and the graduate text. Lemons's A Student's Guide to Entropy is a short guide to the single concept that links thermodynamics, statistical mechanics and information theory, and Rex and Finn's Finn's Thermal Physics is a concise introduction starting from classical thermodynamics. Schroeder's An Introduction to Thermal Physics and Blundell and Blundell's Concepts in Thermal Physics cover similar ground, defining temperature and entropy through counting of microstates and building up to quantum gases and applications; they are alternatives or companions for problems and examples. Pathria and Beale's Statistical Mechanics is the graduate-level treatment to read afterwards.

Baierlein's distinct features are the early microscopic entropy, the emphasis on the chemical potential as a core idea, and the freedom to move the classical limit later.

How to Use This Book

The book is for upper-level undergraduates in physics and astronomy with elementary classical mechanics and a little quantum theory, and it suits both a one-semester course and self-study.

A practical plan:

• Core path: Chapters 1 to 5, then 7, 8 and 9 for chemical potential and quantum gases; Chapters 2 and 4 are the heart of the entropy story.
• Quick start: Chapter 1 is described as mostly review, and much of Chapters 2 and 3 will also be familiar to readers with a good general physics course, so these can be skimmed before the entropy material takes hold.
• Applications: Chapter 6 on photons and phonons, Chapters 10 to 12 on free energies and equilibrium, and Chapters 15 and 16 on transport and critical phenomena, chosen to suit the course.
• Flexible placement: read the classical theory in Chapter 13 whenever it fits after Chapter 5.
• Finishing: read the epilogue to see the theoretical structure that links the applications, and use the end-of-chapter summaries to check understanding before attempting the problems.