Concise Thermodynamics: Principles and Applications in Physical Science and Engineering

By Jeremy Dunning-Davies

This one-semester course text introduces basic principles of thermodynamics and considers a variety of applications in science and engineering. The modern coverage is compact yet self-contained and holistic, with adequate material in a concise and economically-priced book for advanced undergraduates and postgraduates reading for first and higher degrees, and for professionals in research and industry. The mathematical prerequisite is an understanding of partial differentiation.

• Introduces basic principles of thermodynamics and considers a variety of applications in science and engineering
• The modern coverage is compact yet self-contained and holistic, with adequate and concise material

• Language: English
• Publisher: Elsevier Science
• Release date: Jan 1, 2008
• ISBN: 9780857099389

Jeremy Dunning-Davies

Jeremy Dunning-Davies, University of Hull, UK

Book preview

Concise Thermodynamics

Principles and Applications in Physical Science and Engineering

Second Edition

Jeremy Dunning-Davies, BSc, PhD

Department of Physics, University of Hull Institute for Basic Research, Palm Harbor, Florida, USA

Woodhead Publishing Limited

Oxford Cambridge Philadelphia New Delhi

Table of Contents

Cover image

Title page

Copyright page

Dedication

Author’s Preface

1: Introduction

2: The Zeroth Law

Exercises A

3: The First Law

Some Applications of the First Law

Exercises B

4: The Second Law

Exercises C

5: The Second Law and Non-static Processes.

6: The Third Law.

7: Extension to open and non-equilibrium systems.

8: Thermodynamic cycles.

Exercises D

9: Negative Temperatures and the Second Law.

10: Phase Transitions

11: Thermodynamic Equilibrium and Stability

12: Concavity of the Entropy and Negative Heat Capacities

13: Black Hole Entropy and an Alternative Model for a Black Hole

14: Energy Sources and the World’s Energy Requirements

Traditional sources of energy.

Nuclear power.

Conventional methods for the disposal of radioactive waste.

An alternative method for disposal of high-level radioactive waste.

15: Concluding Remarks

Appendix

Partial derivatives

The Chain Rule

Homogeneous Functions

Taylor’s Theorem for a Function of Several Variables

Extreme Values of Functions of Several Variables

Answers and Solutions to Exercises

Exercises A (p.8)

Exercises B (p. 21)

Exercises C (p.36)

Exercises D(p.57)

Glossary

List of symbols

References and suggestions for further reading

Index

Copyright

Published by Woodhead Publishing Limited,

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First edition published by Albion Publishing Limited, 1996

Second edition published by Horwood Publishing Limited, 2007

Reprinted by Woodhead Publishing Limited, 2011

© Horwood Publishing Limited, 2008; © Woodhead Publishing Limited, 2010

The author has asserted his moral rights

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials. Neither the author nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book.

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British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 978-1-904275-31-2

Printed by Lightning Source.

Dedication

to

Faith, Jonathan and Bryony

who make it all worthwhile.

Author’s Preface

Jeremy Dunning-Davies, February 2007, University of Hull.

As its title indicates, this book is intended to be an introduction to the basic principles 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 enthusiasm and success of these students over a number of years provided a raison 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 mentioned course to fit into the new semester system and is proving of value in a course now given to physics undergraduates. The remaining chapters are concerned with research topics which have fascinated me recently. These could prove a source of material for a short postgraduate course, or may simply be of interest to research workers, particularly in physics and astrophysics. Chapter 14, which is concerned with the world’s energy resources and its energy needs in the not too distant future is included to indicate another increasingly important aspect of thermodynamics and one which seems appropriate to consider at the present time.

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 is a topic which may be appreciated by people drawn from a wide variety of backgrounds: it is of importance to the physicist and astrophysicist, as well as the chemist; it is of tremendous importance to much that interests the engineer. At the same time, everyone, both young and old, meets examples of thermodynamics each day in the normal course of events. Thermodynamics is concerned with heat. Notions of hot and cold, of one body being warmer than another, and the idea of the flow of heat are all central to the subject and, in science, all retain the meanings they have in our everyday lives. Initially, curiously enough, it is probably this latter point which is most difficult for many to accept but that is the absolute truth, thermodynamics is concerned with notions and concepts which are, in a non-scientific way, familiar to everyone. If this seemingly trivial point is borne in mind always, academic study of thermodynamics takes on a whole new perspective and is not a difficult subject to understand and appreciate.

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 thermodynamic equilibrium and stability are also discussed, before attention is shifted 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 of this later! Then follows a critical examination of black hole thermodynamics, and a suggestion for a possible alternative model for a black hole is advanced. This topic may be regarded by some as controversial since the view expressed disagrees with Hawking, - especially as far as the expression, associated with his name, for the entropy of a black hole is concerned. However, the arguments put forward are easily understandable to anyone who has followed the earlier chapters, and grown to accept the almost all-embracing power of the laws of thermodynamics. These two topics take the book outside the realm of a purely undergraduate text, yet all the material included is accessible to undergraduates while possibly being of some interest to people at all levels. As mentioned earlier, the text is completed with an examination of the position of the world’s energy resources and needs, now and in the not too distant future. Some of the conclusions of this chapter may be controversial but the basic facts are surely worthy of careful consideration

I started to learn about thermodynamics as a postgraduate student of Peter Landsberg, now of Southampton University, and have continued to benefit from his knowledge and experience. I must thank him also for the photographs of some of the famous founding fathers of thermodynamics, which appear at the front of this text. More recently, I have benefited tremendously from the friendship of, and collaboration with, Bernard Lavenda of the University of Camerino in Italy, and from the friendship and encouragement of George Cole here in Hull University. Also, I feel that, technically, I could not have produced this text without the help of Gordon McKinnon in resolving various word processing problems. The entire project only started because of the publishing enthusiasm of Mr. Ellis Horwood, to whom I owe thanks for initiating the book and guiding me through all the pitfalls so carefully. It has now been guided into a second edition by Miss Francesca Bonner, to whom I am most grateful. I hope this proves worthwhile. Finally, my grateful thanks to my wife, Faith, and children, Jonathan and Bryony, who have supported me at all times and have been ‘forced’ to listen to readings on various aspects of thermodynamics and black holes for quite some time.

I gratefully acknowledge the financial support of the EU Third Framework ‘Human Capital and Mobility Programme’ (contract number CHRX - CT92-0007) and of the University of Hull via the award of a research support grant.

1

Introduction

Thermodynamics is the branch of science which considers how changes of temperature affect the various properties of matter and of systems. The subject may be viewed on a microscopic level, in which case the interactions of atoms and molecules are studied as the temperature alters. For such a study, a specific model for the phenomenon under consideration is required. However, the truly unique status of classical thermodynamics becomes apparent when the subject is viewed macroscopically. In this case, only the behaviour of matter and radiation in bulk is considered: any internal structure they may possess is ignored. Hence, classical thermodynamics is concerned solely with relations between macroscopic observable quantities.

In many physical problems, details of the correct microscopic physics may not be known, but the thermodynamic approach may still provide answers about the macroscopic behaviour of the system - answers which are independent of the unknown detailed physics. In fact, thermodynamic arguments have absolute validity independent of the actual model used to explain any particular phenomenon.

It is remarkable to realise that these far-reaching statements may be made on the basis of the four laws of thermodynamics - the first two of which are arguably more important than the remainder. These laws themselves are remarkable also in that, in reality, they are no more than reasonable hypotheses formulated as a result of practical experience. Nevertheless, they prove to be of immense power, having been applied successfully to matter in extreme physical conditions;- such as matter in bulk at nuclear densities inside neutron stars and in the early stages of the hot big bang model of the Universe, as well as at very low temperatures in laboratory experiments. However, there is no way in which the laws of thermodynamics may