Concepts in Thermal Physics

“In the beginning was the Word…”
“Consider sunbeams. When the sun’s rays let in
Pass through the darkness of a shuttered room,
You will see a multitude of tiny bodies
All mingling in a multitude of ways
Inside the sunbeam, moving in the void,
Seeming to be engaged in endless strife,
Battle, and warfare, troop attacking troop,
And never a respite, harried constantly,
With meetings and with partings everywhere.
From this you can imagine what it is
For atoms to be tossed perpetually
In endless motion through the mighty void.”
(John 1:1, 1st century AD)
(On the Nature of Things, Lucretius, 1st century BC)
“… (we) have borne the burden of the work and the heat of the day.”
(Matthew 20:12, 1st century AD)
Thermal physics forms a key part of any undergraduate physics course.
It includes the fundamentals of classical thermodynamics (which was
founded largely in the nineteenth century and motivated by a desire to
understand the conversion of heat into work using engines) and also sta
tistical mechanics (which was founded by Boltzmann and Gibbs, and is
concerned with the statistical behaviour of the underlying microstates of
the system). Students often find these topics hard, and this problem is
not helped by a lack of familiarity with basic concepts in mathematics,
particularly in probability and statistics. Moreover, the traditional focus
of thermodynamics on steam engines seems remote and largely irrelevant
to a twenty-first century student. This is unfortunate since an under
standing of thermal physics is crucial to almost all modern physics and
to the important technological challenges which face us in this century.
The aim of this book is to provide an introduction to the key con
cepts in thermal physics, fleshed out with plenty of modern examples
from astrophysics, atmospheric physics, laser physics, condensed matter
physics and information theory. The important mathematical princi
ples, particularly concerning probability and statistics, are expounded
in some detail. This aims to make up for the material which can no
longer be automatically assumed to have been covered in every school
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mathematics course. In addition, the appendices contain useful math
ematics, such as various integrals, mathematical results and identities.
There is unfortunately no shortcut to mastering the necessary mathe
matics in studying thermal physics, but the material in the appendix
provides a useful aide-m´emoire.
Many courses on this subject are taught historically: the kinetic the
ory of gases, then classical thermodynamics are taught first, with sta
tistical mechanics taught last. In other courses, one starts with the
principles of classical thermodynamics, followed then by statistical me
chanics and kinetic theory is saved until the end. Although there is
merit in both approaches, we have aimed at a more integrated treat
ment. For example, we introduce temperature using a straightforward
statistical mechanical argument, rather than on the basis of a somewhat
abstract Carnot engine. However, we do postpone detailed considera
tion of the partition function and statistical mechanics until after we
have introduced the functions of state which manipulation of the parti
tion function so conveniently produces. We present the kinetic theory
of gases fairly early on, since it provides a simple, well-defined arena in
which to practise simple concepts in probability distributions. This has
worked well in the course given in Oxford, but since kinetic theory is
only studied at a later stage in courses in other places, we have designed
the book so that the kinetic theory chapters can be omitted without
causing problems; see Fig. 1.5 on page 10 for details. In addition, some
parts of the book contain material which is much more advanced (of
ten placed in boxes, or in the final part of the book), and these can be
skipped at first reading.
The book is arranged in a series of short, easily digestible chapters,
each one introducing a new concept or illustrating an important appli
cation. Most people learn from examples, so plenty of worked examples
are given in order that the reader can gain familiarity with the concepts
as they are introduced. Exercises are provided at the end of each chapter
to allow the students to gain practice in each area.
In choosing which topics to include, and at what level, we have aimed
for a balance between pedagogy and rigour, providing a comprehensible
introduction with sufficient details to satisfy more advanced readers. We
have also tried to balance fundamental principles with practical appli
cations. However, this book does not treat real engines in any engineer
ing depth, nor does it venture into the deep waters of ergodic theory.
Nevertheless, we hope that there is enough in this book for a thorough
grounding in thermal physics and the recommended further reading gives
pointers for additional material. An important theme running through
this book is the concept of information, and its connection with entropy.
The black hole shown at the start of this preface, with its surface cov
ered in ‘bits’ of information, is a helpful picture of the deep connection
between information, thermodynamics, radiation and the Universe.
The history of thermal physics is a fascinating one, and we have pro
vided a selection of short biographical sketches of some of the key pio
neers in thermal physics. To qualify for inclusion, the person had to have
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made a particularly important contribution and/or had a particularly
interesting life– and be dead! Therefore one should not conclude from
the list of people we have chosen that the subject of thermal physics is
in any sense finished, it is just harder to write with the same perspective
about current work in this subject. The biographical sketches are nec
essarily brief, giving only a glimpse of the life-story, so the Bibliography
should be consulted for a list of more comprehensive biographies. How
ever, the sketches are designed to provide some light relief in the main
narrative and demonstrate that science is a human endeavour.
It is a great pleasure to record our gratitude to those who taught us the
subject while we were undergraduates in Cambridge, particularly Owen
Saxton and Peter Scheuer, and to our friends in Oxford: we have bene
f
itted from many enlightening discussions with colleagues in the physics
department, from the intelligent questioning of our Oxford students and
from the stimulating environments provided by both Mansfield College
and St John’s College. In the writing of this book, we have enjoyed the
steadfast encouragement of S¨ onke Adlung and his colleagues at OUP,
and in particular Julie Harris’ black-belt LATEX support.
Anumber of friends and colleagues in Oxford and elsewhere have been
kind enough to give their time and read drafts of chapters of this book;
they have made numerous helpful comments which have greatly im
proved the final result: Fathallah Alouani Bibi, James Analytis, David
Andrews, Arzhang Ardavan, Tony Beasley, Michael Bowler, Peter Duffy,
Paul Goddard, Stephen Justham, Michael Mackey, Philipp Podsiad
lowski, Linda Schmidtobreick, John Singleton and Katrien Steenbrugge.
Particular thanks are due to Tom Lancaster, who twice read the entire
manuscript at early stages and made many constructive and imaginative
suggestions, and to Harvey Brown, whose insights were always stimulat
ing and whose encouragement was always constant. To all these friends,
our warmest thanks are due. Errors which we discover after going to
press will be posted on the book’s website, which may be found at:
http://users.ox.ac.uk/∼sjb/ctp
It is our earnest hope that this book will make the study of thermal
physics enjoyable and fascinating and that we have managed to commu
nicate something of the enthusiasm we feel for this subject. Moreover,
understanding the concepts of thermal physics is vital for humanity’s
future; the impending energy crisis and the potential consequences of
climate change mandate creative, scientific and technological innova
tions at the highest levels. This means that thermal physics is a field
which some of tomorrow’s best minds need to master today