Table Of ContentCONCISE THERMODYNAMICS
Principles and Applications in Physical
Science and Engineering
Second Edition
ABOUT OUR AUTHOR
Jeremy Dunning-Davies was born in South Wales and attended Barry Boys'
Grammar School, Glamorganshire. He entered Liverpool University as a Derby
Open Scholar in Mathematics in 1959, graduated in 1962 and obtained a
Postgraduate Certificate in Education in 1963. He then undertook postgraduate
study in statistical thermodynamics at the University of Wales in Cardiff under
ProfessorPeterLandsberg.Itisnottoosurprising,therefore,that,whilethere,he
developed a deep and lasting interest in thermodynamics. He was awarded his
Ph.D. for a thesis entitled 'The Ideal Relativistic Quantum Gas' in 1966, in
which year he took up an appointment as an Assistant Lecturer in Applied
Mathematicsat the University ofHull. He becamea fullLecturer in 1968and a
Senior Lecturer in 1981. He moved as a Senior Lecturer to the Physics
DepartmentatHullUniversityin2002.
On moving to Hull, he continued his collaboration with Peter Landsberg and
producedseveralarticlesinboththermodynamicsitselfandonfurther aspectsof
the ideal relativistic quantum gases. In 1987, he met Bernard Lavenda from
Camerino at a conference and another highly successful research collaboration
ensuedintotheprobabilisticfoundationsofthermodynamics.Thisledthemonto
investigate, and question, some of the results associated with the
thermodynamics of black holes. In 1996, at a conference in London, he met
Ruggero Santilli from Florida and a new interest in newclean energies and the
safedisposalofnuclearwastesurfaced.
Inhiscareer, JeremyDunning-Davies has produced wellin excess of a hundred
academic articles as well as three books: Mathematical Methods for
Mathematicians, Physical Scientists and Engineers (1982); Concise
Thermodynamics (First Edition) (1996) and Exploding A Myth (2007). His
interestshaverangedfrom thermodynamicsto properties of the idealrelativistic
quantum gases which, in tum, led him to an interest in white dwarf stars and,
eventually, astrophysics and cosmology. His more recent interest in new clean
energiesandthedisposal of nuclearwastehas beenoccasioned alsoby hisbasic
interest in, and love for, thermodynamics - that truly fundamental topic which
pervades all areas of physics. Additionally, through friendship with Bill
Stephenson, a member of the Electronic Engineering Department at Hull at the
time,hehasmadecontributionstothetheoryoffiltercircuits. Also,he hasbeen
deeply involved with, and interested in, educational issues, something which is
not too surprising for someone whose father was an eminently successful
primaryschoolheadmasterin SouthWales andwhosemother and wifewere/are
bothteachers.
CONCISE THERMODYNAMICS
Principles and Applications in Physical
Science and Engineering
Second Edition
Jeremy Dunning-Davies, BSc, PhD
DepartmentofPhysics, University ofHull
Institutefor Basic Research, PalmHarbor,Florida, USA
WP
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v
to
Faith, Jonathan and Bryony
whomake itall worthwhile.
vi
vii
Contents
Author'sPreface (ix)
1. Introduction 1
2. TheZeroth Law 5
ExercisesA 8
3. The First Law 11
ExercisesB 21
4. The SecondLaw 25
ExercisesC 36
5. The Second Law and Non-staticProcesses 39
6. TheThird Law 43
7. ExtensiontoOpen and Non-equilibriumSystems 45
8. ThermodynamicCycles 51
ExercisesD 57
9. NegativeTemperaturesand theSecond Law 59
10. Phase Transitions 63
11. ThermodynamicEquilibriumand Stability 71
12. ConcavityoftheEntropyand NegativeHeatCapacities 75
13. Black Hole EntropyandanAlternativeModel foraBlackHole 81
14. Energy Sourcesand theWorld'sEnergy Requirements 85
15. ConcludingRemarks 95
Appendix 99
Answers and SolutionstoExercises 109
Glossary 131
List ofSymbols 134
Bibliography 135
Index 137
viii
ix
Author's Preface
As its title indicates, this book is intended to be an introduction to the basicprinciples
of thermodynamics. The material of the first eight chapters formed a one-term course
given to final year mathematics' undergraduates here at Hull University. Indeed, the
enthusiasmand successofthese students over a numberofyearsprovided araison d'etre
for writing the book. The addition of chapters on phase transitions and questions of
thermodynamic equilibrium and stability seem the natural way of extending the
mentionedcourse to fitinto the new semester system and is proving of valuein acourse
now given to physics undergraduates. The remaining chapters are concerned with
research topicswhichhavefascinatedmerecently.Thesecouldproveasourceofmaterial
for a short postgraduate course, or may simply be of interest to research workers,
particularly inphysics and astrophysics. Chapter 14,whichisconcerned withthe world's
energy resources and itsenergy needs inthe not too distant future isincluded to indicate
another increasingly important aspect of thermodynamics and one which seems
appropriate toconsideratthepresenttime.
Thermodynamics is the branch of science concerned with the ways in which the
properties of matter and of systems change with alterations in temperature. It is a
remarkable subject since it may be studied on both the microscopic and macroscopic
levels; it applies to matter in all manner of extreme physical conditions; and yet, when
examined in detail, is found to depend on ''Laws'' which are really only "facts of
experience". Again, it isa topic whichmaybe appreciated bypeople drawn from a wide
variety ofbackgrounds: it isof importance to the physicist and astrophysicist, aswell as
the chemist; it is of tremendous importance to much that interests the engineer. At the
sametime,everyone, bothyoungandold,meetsexamplesofthermodynamicseachdayin
the normal course of events. Thermodynamics is concerned with heat. Notions of "hot"
and"cold", ofonebodybeingwarmerthananother,andtheideaofthe''flow ofheat" are
allcentraltothesubject and,inscience,all retainthemeaningstheyhaveinoureveryday
lives.Initially,curiously enough,it isprobably thislatter point whichismostdifficultfor
many to accept but that is the absolute truth, thermodynamicsisconcerned with notions
and concepts which are, in a non-scientific way, familiar to everyone. Ifthis seemingly
trivialpointisborne inmindalways,academic studyofthermodynamicstakesonawhole
newperspective andisnotadifficultsubjecttounderstandandappreciate.
The major part of this book is devoted to an examination of the basic laws and
principles of thermodynamics. Topics such as phase transitions and questions of
thermodynamicequilibrium and stability are also discussed, before attention isshifted to
one or two topics which have concerned me personally over recent years. The latter
involve looking at the mathematical property of concavity of the entropy; where the
entropy is a function quite fundamental to the subject and is introduced via the Second
Law of Thermodynamics - but more ofthis later! Then follows a critical examination of
blackhole thermodynamics,and a suggestion for apossible alternative modelforablack
hole is advanced. This topic may be regarded by some as controversial since the view
