MACMILLAN COLLEGE WORK OUT SERIES

Heat and Thermodynamics

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MACMILLAN COLLEGE WORK OUT SERIES

HeatandThermodynamicsMichael Sprackling

150th YEAR

MMACMILLAN

© Michael Sprackling 1993

All rights reserved. No reproduction, copy or transmission ofthis publication may be made without written permission.

No paragraph of this publication may be reproduced, copied ortransmitted save with written permission or in accordance withthe provisions of the Copyright, Designs and Patents Act 1988,or under the terms of any licence permitting limited copyingissued by the Copyright Licensing Agency, 90 Tottenham CourtRoad, London W1P 9HE.

Any person who does any unauthorised act in relation to thispublication may be liable to criminal prosecution and civilclaims for damages.

First published 1993 byTHE MACMILLAN PRESS LTDHoundmills, Basingstoke, Hampshire RG21 2XSand LondonCompanies and representativesthroughout the world

ISBN 978-0-333-56513-1 ISBN 978-1-349-12690-3 (eBook)DOI 10.1007/978-1-349-12690-3

A catalogue record for this book is availablefrom the British Library

Contents

Preface

1 Basic Concepts in Thermodynamics 1.1 Introduction 1.2 Some Definitions 1.3 The First Stages in Problem-Solving With Closed Systems 1.4 Worked Example

2 Work 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

Definition of Work Problem-Solving Electrical Work Worked Examples on Electrical Work Work to Change the Volume of a Closed Hydrostatic System Worked Examples on Pressure-Volume Work Work to Change the Length of an Elastic Rod Worked Examples on Work and Elastic Deformation Exercises

3 Gases and the Ideal Gas Scale of Temperature 3.1 Boyle's Law 3.2 Ideal Gases 3.3 Problem-Solving 3.4 Worked Examples on Boyle's Law 3.5 The Ideal Gas Scale of Temperature and the Ideal Gas Equation 3.6 Worked Examples on the Ideal Gas Equation 3. 7 Exercises

4 The First Law of Thermodynamics 4.1 Internal Energy 4.2 The First Law of Thermodynamics 4.3 Problem-Solving 4.4 Worked Examples on the First Law of Thermodynamics 4.5 Reversible Processes 4.6 Worked Examples on Reversible Processes 4. 7 Heat Capacities 4.8 Worked Examples on Heat Capacities 4.9 Exercises

5 The Second Law of Thermodynamics 5.1 The Clausius Statement of the Second Law 5.2 Heat Engines 5.3 Worked Examples on Heat Engines 5.4 Kelvin's Statement of The Second Law

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1 1 3 4

5 6 6 6 8 8

12 12 14

15 16 16 16 20 21 25

26 27 27 27 29 30 31 33 42

43 43 44 48

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5.5 Carnot's Theorem and its Corollary 5.6 Universal Temperatures 5.7 Thermodynamic Temperature 5.8 Worked Examples on Heat Engines and Thermodynamic Temperature 5.9 Celsius Temperature 5.10 Problem-Solving 5.11 Worked Examples on Heat Engines and the Second Law of Thermodynamics 5 .12 Exercises

6 Entropy 6.1 The Inequality of Clausius 6.2 Entropy 6.3 Worked Examples on Entropy 6.4 Entropy and Work 6.5 Worked Examples on Entropy and Work 6.6 The Entropy Form of the First Law 6.7 Worked Examples on the Entropy Form of the First Law 6.8 Entropy and Irreversible Processes 6.9 Worked Examples on the Law of the Increase of Entropy 6.10 Maxwell's Relations 6.11 Some Useful Mathematical Relations 6.12 Problem-Solving 6.13 Worked Examples on Entropy 6.14 Exercises

7 Thermodynamic Potential Functions 7.1 The Helmholtz Function (Helmholtz Free Energy) 7.2 Worked Examples on the Helmholtz Function 7.3 The Gibbs Function (Gibbs Free Energy) 7.4 Worked Examples on the Gibbs Function 7.5 Useful Work and Availability 7.6 Worked Examples on Availability 7. 7 Exercises

8 Some Simple Thermodynamic Systems 8.1 Closed Hydrostatic Systems 8.2 Worked Examples on Closed Hydrostatic Systems 8.3 Ideal Gases 8.4 Worked Examples on Ideal Gases 8.5 Perfectly Elastic Solids 8.6 Worked Examples on Perfectly Elastic Solids 8.7 Voltaic Cells 8.8 Worked Example on Voltaic Cells 8.9 Exercises

9 Heat Capacities and Equations of State 9.1 Introduction 9.2 Heat Capacities 9.3 Worked Examples on Heat Capacities 9.4 Equations of State 9.5 Worked Examples on Equations of State 9.6 Exercises

10 Phase Changes

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10.1 The Enthalpy of a Phase Change (Latent Heat) 10.2 Worked Examples on the Enthalpy of a Phase Change 10.3 The Clapeyron-Clausius Equation

48 49 49 50 53 53 53 60

61 61 62 66 67 68 69 71 71 75 75 75 76 81

82 83 86 87 90 91

100

101 102 111 112 119 120 126 127 128

130 130 131 139 141 145

147 148 153

10.4 Worked Examples on the Clapeyron-Clausius Equation 154 10.5 The Equation of Clausius 157 10.6 Worked Example on the Equation of Clausius 158 10.7 Exercises 159

11 The Third Law of Thermodynamics 11.1 The Third Law of Thermodynamics 161 11.2 Worked Examples on the Third Law 161 11.3 Planck's and Simon's Versions of the Third Law 164 11.4 Worked Example on Absolute Entropy 165 11.5 Allotropic Transformations 165 11.6 Worked Example on Allotropic Transformations 166 11.7 Exercises 167

12 Irreversible Processes 12.1 Irreversible Processes and Thermodynamics 168 12.2 The Joule Process 168 12.3 Worked Examples on the Joule Process 169 12.4 The Joule-Thomson Process 173 12.5 Worked Examples on the Joule-Thomson Process 174 12.6 Exercises 182

13 A Simple Kinetic Theory of Gases 13.1 A Simple Kinetic Theory of Gases 183 13.2 Worked Examples on a Kinetic Theory of Gases 185 13.3 Exercises 190

14 Heat Transfer 14.1 Introduction 191 14.2 Heat Conduction 191 14.3 A General Approach to Solving Heat Conduction Problems 192 14.4 Worked Examples on Heat Conduction 193 14.5 Heat Convection 197 14.6 Worked Examples on Heat Convection 198 14.7 Thermal Radiation 202 14.8 Worked Examples on Thermal Radiation 204 14.9 Exercises 208

Recommended Reading 210 Index 211

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Preface

Thermodynamics is one of the major subjects of classical phenomenological physics, a subject of great power and beauty. Nevertheless, it is, for many students, a difficult subject and one that they do not understand on a first (and often, only) reading. To them the subject seems to be a collection of subtle concepts, linked by countless equations with no underlying framework.

Despite its forbidding nature, thermodynamics is a subject with a wide range of applications and is a vital component in the education of physical scientists. However, the lack of understanding so often encountered leaves the student with a gap between wanting to able to use the theory and being able to do so. One way of promoting understanding and bridging this gap is through problem-based learning. The aim of this approach is to make students 'doers of the word, not hearers only' by providing detailed solutions to a carefully selected range of problems, showing how principles and concepts may be applied to particular situations, and then offering the student situations that differ slightly but which can be tackled by an extension of the approaches that have been used in the solved problems.

Learning how to use the theory of thermodynamics through problem-solving is the approach followed in this book, which is aimed at undergraduates in the physical sciences and in engineering taking a first course in thermodynamics or thermal physics. The book starts with a summary of the important basic concepts in thermodynamics and establishes the basic vocabulary and outlook. The core topics in classical thermodynamics are then examined in a series of chapters that include a brief introduction to each topic, where important results are stated and, sometimes, derived, followed by a number of examples worked out in detail.

One of the powerful features of classical thermodynamics is that it provides rela­tionships between the properties of a system. Consequently, only a small number of properties need to be 'explained' at the atomic level. In the simplest treatments this is done under the heading of kinetic theory and this book contains a chapter on a simple kinetic theory of gases. Also important is the rate of energy transfer between a system and its surroundings, so the final chapter deals with the very practical topic of heat transfer.

The book assumes a knowledge of elementary calculus, including partial differentia­tion, and SI units are used throughout.

Michael Sprackling January 1993