An Introduction to Thermodynamics and Statistical Mechanics

Goals
The subject of thermodynamics was being developed on a postulatory basis long
before we understood the nature or behavior of the elementary constituents of
matter. As we becamemorefamiliar with these constituents, we were still slow to
place our trust in the “new” fieldofquantummechanics,whichwastellingusthat
their behaviors could be described correctly and accurately using probabilities
and statistics.
The influence of this historical sequence has lingered in our traditional ther
modynamics curriculum. Until recently, we continued to teach an introductory
course using the more formal and abstract postulatory approach. Now, however,
there is a growing feeling that the statistical approach is more effective. It demon
strates the firm physical and statistical basis of thermodynamics by showing how
the properties of macroscopic systems are direct consequences of the behaviors
of their elementary constituents. An added advantage of this approach is that it is
easily extended to include some statistical mechanics in an introductory course.
It gives the student a broader spectrum of skills as well as a better understanding
of the physical bases.
This book is intended for use in the standard junior or senior undergraduate
course in thermodynamics, and it assumes no previous knowledge of the subject.
I try to introduce the subject as simply and succinctly as possible, with enough
applications to indicate the relevance of the results but not so many as might risk
losing the student in details. There are many advanced books of high quality that
can help the interested student probe more deeply into the subject and its more
specialized applications.
I try to tie everything straight to fundamental concepts, and I avoid “slick
tricks” and the “pyramiding” of results. I remain focused on the basic ideas and
physical causes, because I believe this will help students better understand, retain,
and apply the tools and results that we develop.
Active learning
I think that real learning must be an active process. It is important for the student
to applynewknowledgetospecificproblemsassoonaspossible.Thisshouldbea
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Preface
dailyactivity, andproblemsshouldbeattemptedwhiletheknowledgeisstillfresh.
Aroutine of frequent, timely, and short problem-solving sessions is far superior
to afewinfrequentproblem-solvingmarathons.Forthisreason,attheendofeach
chapter the text includes a very large number of suggested homework problems,
which are organized by section. Solutions to the odd-numbered problems are at
the end of the book for instant feedback.
Active learning can also be encouraged by streamlining the more passive
components. The sooner the student understands the text material, the sooner he
or she can apply it. For this reason, I have put the topics in what I believe to be the
most learning-efficient order, and I explain the concepts as simply and clearly as
possible. Summaries are frequent and are included within the chapters wherever
I think would be helpful to a first-time student wrestling with the concepts. They
are also shaded for easy identification. Hopefully, this streamlining of the passive
aspects might allow more time for active problem solving.
Changes in the second edition
The entire book has been rewritten. My primary objective for the second edition
has been to explore more topics, more thoroughly, more clearly, and with fewer
words.ToaccomplishthisIhavewrittenmoreconcisely,combinedrelatedtopics,
and reduced repetition. The result is a modest reduction in text, in spite of the
broadened coverage of topics.
InadditionIwantedtocorrectwhatIconsideredtobethetwobiggestproblems
with the first edition: the large number of uncorrected typos and an incomplete
description of the chemical potential. A further objective was to increase the
number and quality of homework problems that are available for the instructor
or student to select from. These range in difficulty from warm-ups to challenges.
In this edition the number of homework problems has nearly doubled, averaging
around 40 per chapter. In addition, solutions (and occasional hints) to the odd
numberedproblemsaregivenatthebackofthebook.Myexperiencewithstudents
at this level has beenthatsolutionsgivequickandefficientfeedback,encouraging
those who are doing things correctly and helping to guide those who stumble.
The following list expands upon the more important new initiatives and fea
tures in this edition in order of their appearance, with the chapters and sections
indicated in parentheses.
Fluctuations in observables, such as energy, temperature, volume, number of particles,
etc. (Sections 3A, 3C, 7C, 9B, 19A)
Improved discussion and illustrations of the chemical potential (Sections 5C, 8A, 9E,
14A)
The explicit dependence of the number of accessible states on the system’s internal
energy, volume, and number of particles (Chapter 6)
Behaviors near absolute zero (Sections 9H, 24A, 24B)
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ix
Entropy and the third law (Section 8D)
Anewchapter on interdependence among thermodynamic variables (Chapter 11)
Thermal conduction, and the heat equation (Section 12E)
Amore extensive treatment of engines, including performance analysis (Section 13F),
modelcycles, a description of several of the more common internal combustion engines
(Section 13H), and vapor cycles (Section 13I)
Anewchapter on diffusive interactions, including such topics as diffusive equilibrium,
osmosis, chemical equilibrium, and phase transitions (Chapter 14)
Properties of solutions (colligative properties, vapor pressure, osmosis, etc.)
(Section 14B)
Chemical equilibrium and reaction rates (Section 14C)
Amore thorough treatment of phase transitions (Section 14D)
Binary mixtures, solubility gap, phase transitions in minerals and alloys, etc.
(Section 14E)
Conserved properties (Section 16E)
Calculating the chemical potential for quantum systems (Section 19E)
Chemical potential and internal energy for quantum gases (Section 20D)
Entropy and adiabatic processes in photon gases (Section 21E)
Thermal noise (Section 21F)
Electrical properties of materials, including band structure, conductors, intrinsic and
doped semiconductors, and p–n junctions (Chapter 23)
Update of recent advances in cooling methods (Section 24A)
Update of recent advances in Bose–Einstein condensation (Section 24B)
Stellar collapse (Section 24C)
Organization
Thebookhasbeenorganizedtogivetheinstructorasmuchflexibilityaspossible.
Some early chapters are essential for the understanding of later topics. Many
chapters, however, could be skipped at a first reading or their order rearranged as
the instructor sees fit. To help the instructor or student with these choices, I give
the following summary followed by more detailed information.
Summary of organization
Part I Introduction
Chapter1 essentialifthestudentshavenotyethadacourseinquantummechan
ics. Summarizes important quantum effects
Part II Small systems
Chapter 2 and Chapter 3 insightful, but not needed for succeeding chapters
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Preface
Part III Energy and the first law
Chapter 4, Chapter 5 and Chapter 6 essential
Part IV States and the second law
Chapter 6, Chapter 7 and Chapter 8 essential
Part V Constraints
Chapter 9 essential
Chapter 10, Chapter 11, Chapter 12, Chapter 13 and Chapter 14 any order, and
any can be skipped
Part VI Classical statistics
Chapter 15 essential
Chapter 16, Chapter 17 and Chapter 18 any order, and any can be skipped
Part VII Quantum statistics
Chapter 19, Chapter 20 A, B essential
Chapter 21, Chapter 22, Chapter 23 and Chapter 24 any order, and any can be
skipped
More details
Part I– Introduction Chapter 1 is included for the benefit of those students
who have not yet had a course in quantum mechanics. It summarizes important
quantum effects that are used in examples throughout the book.
Part II– Small systems Chapters 2 and 3 study systems with only a few ele
ments. By studying small systems first the student develops both a better appre
ciation and also a better understanding of the powerful tools that we will need for
large systems in subsequent chapters. However, these two chapters are not essen
tial for understanding the rest of the book and may be skipped if the instructor
wishes.
Part III– Energy and the first law Chapters 4 and 5 are intended to give the
student anintuitive physical picture of whatgoesonwithininteractingsystemson
a microscopic scale. Although the mathematical rigor comes later, this physical
understanding is essential to the rest of the book so these two chapters should not
be skipped.
Part IV– States and the second law Chapters 6, 7, and 8 are the most impor
tant in the book. They develop the statistical basis for much of thermodynamics.
Part V– Constraints Chapter 9 derives the universal consequences of the fun
damental ideas of the preceding three chapters. So this chapter shows why things
mustbehaveastheydo,andwhyour“commonsense”iswhatitis.Chapters10–14
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all describe the application of constraints to more specific systems. None of these
topicsisessential, althoughsomemodelsinChapter10wouldbehelpfulinunder
standing examples used later in the book; if Chapters 11 and 12 are covered, they
should bedoneinnumericalorder.Topicsinthesefivechaptersincludeequations
of state and models, the choice and manipulation of variables, isobaric, isother
mal, and adiabatic processes, reversibility, important nonequilibrium processes,
engines, diffusion, solutions, chemical equilibrium, phase transitions, and binary
mixtures.
Part VI– Classical statistics Chapter 15 develops the basis for both classi
cal “Boltzmann” and quantum statistics. So even if you go straight to quantum
statistics, this chapter should be covered first. Chapters 16, 17, and 18 are appli
cations of classical statistics, each of which has no impact on any other material
in the book. So they may be skipped or presented in any order with no effect on
subsequent material.
Part VII– Quantum statistics Chapter 19 introduces quantum statistics, and
the first two sections of Chapter 20 introduce quantum gases. These provide the
underpinnings for the subsequent chapters and therefore must be covered first.
The remaining four (Chapters 21–24 ) are each independent and may be skipped
or presented in any order, as the instructor chooses.
Acknowledgments
I wish to thank my students for their ideas, encouragement, and corrections,
and my colleagues Joe Boone and Rich Saenz for their careful scrutiny and
thoughtfulsuggestions.IalsoappreciatethesuggestionsreceivedfromProfessors
Robert Dickerson and David Hafemeister (California Polytechnic State Univer
sity), Albert Petschek (New Mexico Institute of Mining and Technology), Ralph
Baierlein (Wesleyan University), Dan Wilkins (University of Nebraska, Omaha),
Henry White (University of Missouri), and I apologize to the many whose names
I forgot to record