Statistical and Thermal Physics

An Introduction

Michael J.R. Hoch

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367464103
• eBook ISBN: 9781000389166
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Thermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems.

Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail.

Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi–Dirac and Bose–Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course.

Key Features:

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• Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems

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• Additional problem exercises with solutions provide further learning opportunities

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• Suitable for advanced undergraduate students in physics or applied physics.

Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.

Part I

Classical Thermal Physics

The Microcanonical Ensemble

Section IA

Introduction to Classical Thermal Physics Concepts

The First and Second Laws of Thermodynamics

1 Introduction

Basic Concepts

1.1 Statistical and Thermal Physics

The subject of statistical and thermal physics is concerned with the description of macroscopic systems made up of large numbers of particles of the order of Avogadro’s number N_A = 6.02 × 10²³ mol⁻¹. The particles may be atoms or molecules in gases, liquids, and solids or systems of subatomic particles such as electrons in metals and neutrons in neutron stars. A rich variety of phenomena are exhibited by many particle systems of this sort. The concepts and relationships that are established in thermal physics provide the basis for discussion of the properties of these systems and the processes in which they are involved. Applications cover a wide range of situations from basic science, in many important fields that include condensed matter physics, astrophysics, and physical chemistry, to practical devices in energy technology.

The origins of modern thermal physics may be traced to the analysis of heat engines in the nineteenth century. Following this early work, a number of researchers contributed to the development of the subject of thermodynamics with its famous laws. By the end of the nineteenth century, thermodynamics, classical mechanics, and electrodynamics provided the foundation for all of classical physics. Today, thermodynamics is a well-developed subject, with modern research focused on special topics such as nonequilibrium thermodynamics. Application of the methods of thermodynamics to complex systems far from equilibrium, which include living organisms, presents a major challenge.

The microscopic classical statistical description of systems of large numbers of particles began its development in the late nineteenth century, particularly through the work of Ludwig Boltzmann. This approach was transformed by the development of quantum mechanics in the 1920s, which then led to quantum statistics that is of fundamental importance in a great deal of modern research on bulk matter. Statistical techniques are used to obtain average values for properties exhibited by macroscopic systems. The microscopic approach on the basis of classical or quantum mechanics together with statistical results has given rise to the subject known as statistical mechanics or statistical physics. Bridge relationships between statistical physics and thermodynamics have been established and provide a unified subject.

Under conditions of high temperature and low density, we shall find that it does not matter whether classical or quantum mechanical descriptions are used for a system of particles. At high densities and low temperatures, this is no longer true because of the overlap of the particles’ wave functions, and quantum mechanics must be used, giving rise to quantum statistics. Under high-density, low-temperature conditions, the properties of a system depend in a crucial way on whether the particles that make up the system are fermions or bosons. Many fascinating phenomena occur in condensed matter as the temperature is lowered. Examples are ferromagnetism, superconductivity, and superfluidity. These important new properties appear fairly abruptly at phase transitions. Progress in the microscopic understanding and description of the behavior of these systems involves quantum mechanics and statistical physics ideas. Applications of quantum statistics are not confined to terrestrial systems and include astrophysical phenomena such as the microwave background radiation from the Big Bang and the mass–radius relationships for white dwarf stars and neutron stars. An important concept in thermal physics is that of entropy, which, as we shall see, increases with time as systems become more disordered. The increas...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Author
• Part I Classical Thermal Physics: The Microcanonical Ensemble
• Section IA Introduction to Classical Thermal Physics Concepts: The First and Second Laws of Thermodynamics
• Section IB Microstates and the Statistical Interpretation of Entropy
• Section IC Applications of Thermodynamics to Gases and Condensed Matter, Phase Transitions, and Critical Phenomena
• Part II Quantum Statistical Physics and Thermal Physics Applications
• Section IIA The Canonical and Grand Canonical Ensembles and Distributions
• Section IIB Quantum Distribution Functions, Fermi–Dirac and Bose–Einstein Statistics, Photons, and Phonons
• Section IIC The Classical Ideal Gas, Maxwell–Boltzmann Statistics, Nonideal Systems
• Section IID The Density Matrix, Reactions and Related Processes, and Introduction to Irreversible Thermodynamics
• Appendix A: Useful Mathematical Relationships
• Appendix B: The Binomial Distribution
• Appendix C: Elements of Quantum Mechanics
• Appendix D: The Legendre Transform in Thermodynamics
• Appendix E: Recommended Texts on Statistical and Thermal Physics
• Index