Front Cover

Contents

Appendices

List of books, films and film loops, slides and apparatus

Index

Nuffield Advance Physics team and special advisers

Joint organizers

Dr P. J. Black, Reader in Crystal Physics, University of Birmingham

Jon Ogborn, Worcester College of Education; formerly of Roan School, London SE3

Team members

W. Bolton, formerly of High Wycombe College of Technology and Art

R. W. Fairbrother, Centre for Science Education, Chelsea College; formerly of Hinckley Grammar School

G. E. Foxcroft, Rugby School

Martin Harrap, formerly of Whitgift School, Croydon

Dr John Harris, Centre for Science Education, Chelsea College; formerly of Harvard Project Physics

Dr A. L. Mansell, Centre for Science Education, Chelsea College; formerly of Hatfield College of Technology

A. W. Trotter, North London Science Centre; formerly of Elliott School, Putney

Evaluation

P. R. Lawton, Garnett College, London

Acknowledgements

The Organizers wish to express their gratitude to the many people who gave help with the development of this Unit.

Professor R. G. Chambers, Professor P. T. Landsberg, Professor P. T. Matthews, Professor D. J. Millen, Professor M. Woolfson, and Dr J. W. Warren formed a working party which met to discuss the proposals for the Unit.

The development of the computer-constructed films which play a large part in this Unit would have been impossible without the willing help of Dr F. R. A. Hopgood of the Atlas Computer Laboratory, Chilton, Berkshire, who was responsible for the actual production of the films. We are also grateful to Dr P. Davies for help with mathematical statistics, and to Dr G. G. S. Miller for help at an earlier stage with computer programming.

We wish also to acknowledge our debt to the Nuffield Advanced Chemistry and Physical Science Projects.

We have also been influenced by H. A. Bent's valuable book, The Second Law.

Consultative Committee

  • Professor Sir Nevill Mott, F.R.S. (Chairman)
  • Professor Sir Ronald Nyholm, F.R.S. (Vice-Chairman)
  • Professor J. T. Allanson
  • Dr P. J. Black
  • N. Booth, H.M.I.
  • Dr C. C. Butler, F.R.S.
  • Professor E. H. Coulson
  • D. C. Firth
  • Dr J. R. Garrood
  • Dr A. D. C. Grassie
  • Professor H. F. Halliwell
  • Miss S. J. Hill
  • Miss D. M. Kett
  • Professor K. W. Keohane
  • Professor J. Lewis
  • J. L. Lewis
  • A. J. Mee
  • Professor D. J. Millen
  • J. M. Ogborn
  • E. Shire
  • Dr J. E. Spice
  • Dr P. Sykes
  • E. W. Tapper
  • C. L. Williams, H.M.I.

Foreword

It is almost a decade since the Trustees of the Nuffield Foundation decided to sponsor curriculum development programmes in science. Over the past few years a succession of materials and aids appropriate to teaching and learning over a wide variety of age and ability ranges has been published. We hope that they may have made a small contribution to the renewal of the science curriculum which is currently so evident in the schools.

The strength of the development has unquestionably lain in the most valuable part that has been played in the work by practising teachers and the guidance and help that have been received from the consultative committees to each Project.

The stage has now been reached for the publication of materials suitable for Advanced courses in the sciences. In many ways the task has been a more difficult one to accomplish. The sixth form has received more than its fair share of study in recent years and there is now an increasing acceptance that an attempt should be made to preserve breadth in studies in the 16-19 year age range. This is no easy task in a system which by virtue of its pattern of tertiary education requires standards for the sixth form which in many other countries might well be found in first year university courses.

Advanced courses are therefore at once both a difficult and an interesting venture. They have been designed to be of value to teacher and student, be they in sixth forms or other forms of education in a similar age range. Furthermore, it is expected that teachers in universities, polytechnics, and colleges of education may find some of the ideas of value in their own work.

If this Advanced Physics course meets with the success and appreciation I believe it deserves, it will be in no small measure due to a very large number of people, in the team so ably led by Jon Ogborn and Dr Paul Black, in the consultative committee, and in the schools in which trials have been held. The programme could not have been brought to a successful conclusion without their help and that of the examination boards, local authorities, the universities, and the professional associations of science teachers.

Finally, the Project materials could not have reached successful publication without the expert assistance that has been received from William Anderson and his editorial staff in the Nuffield Science Publications Unit and from the editorial and production teams of Penguin Education.

K. W. Keohane

Co-ordinator of the Nuffield Foundation Science Teaching Project

The diagrams in this document have been redrawn from the original black and white ones.

Introduction

It seems to us to be worth a good deal of effort to make the ideas behind the Second Law of Thermodynamics intelligible to students at school. The approach in this book is through the statistics of molecular chaos, because we not only feel that this is the best way for a first insight into what entropy is, but also because the growing importance of statistical thinking in physics, chemistry, and in biology, not to mention sociology, economics, and education, makes it especially desirable to provide opportunities for students to think about the difficult concepts involved.

In addition, much that is new and powerful here emerges from a very few fundamental ideas: given quanta and atoms, one emerges with the Boltzmann factor, Kelvin temperature, entropy, and the Second Law.

The Unit contains a good deal more than an average class will wish to or will be able to follow. The first three Parts are simple introductory material. Part One is a brief introduction to the notion of an irreversible process, largely employing films shown forwards and in reverse. Part Two, helping to signal the practical importance of the ideas being developed, considers whether or not it matters that the fossil fuel reserves of the Earth are being used up. Part Three starts the statistical thinking off in the simplest of contexts: that of diffusion. Its purpose is to introduce a way of thinking, especially the use of dice-throwing games, so as to ease later and harder work on similar lines.

Part Four will complete the Unit for many students, apart from a brief glance at one or two applications from Part Six. It contains a study of thermal equilibrium in an Einstein solid. This problem is studied by means of random simulation, both with dice on the bench and with films constructed by computer. By this means, detailed statistical arguments can be avoided: in particular no knowledge of factorials or of permutations and combinations need be assumed. The outcome is an exponential (Boltzmann) distribution. After seeing that the direction of heat flow is governed by the steepness of this distribution, the Kelvin temperature is given a definition in terms of the slope of the distribution. This definition is less fundamental than one produced later, in Part Five, but we feel that it still represents a worthwhile achievement. The molar heat capacity of an Einstein solid at high temperatures follows at once, being 3Lk, so that the Boltzmann constant k can be measured, using observations of the molar heat capacities of a variety of solid elements. (L is the Avogadro constant.) The Boltzmann constant k is introduced in a fundamental way, as a scale constant which fixes the size of the Kelvin degree.

Students who pursue the theoretical arguments no further will still be able to appreciate some of the examples, given in Part Six, of the uses of the ideas, particularly those examples which use the Boltzmann factor to discuss the temperature dependence of rate of reaction, vapour pressure of water, or current in a semiconductor. The work described so far is to be regarded as the normal amount for an ordinary class taking Nuffield Advanced Physics, even though it occupies little more than half the whole book.

The further work in Parts Five and Six has been included for several reasons.

Part Five contains theoretical arguments, of no great complexity, which nevertheless take the ideas a large step forward. The Boltzmann distribution met in Part Four is seen to arise from changes to the number of ways W of arranging quanta among atoms, when quanta enter or leave the system. Heat flow is seen as taking the direction which increases W; the Kelvin temperature is given a fundamental statistical definition and entropy S = k ln W is introduced. This Part should not be too difficult for a proportion of students: those who can appreciate it will gain a great deal.

We have also included the work of Part Five because of the need for students in other subjects and at other levels, to have a simple, intelligible, but basically truthful introduction to entropy and the Boltzmann factor, and we think our material has something novel to offer for this purpose.

The ideas suggested in Part Six are a conscious attempt to bridge the gap between physics and chemistry. It has been a matter of regret among the members of the Advanced Physics, Chemistry, and Physical Science Projects, that the development of teaching proposals in this difficult area was so slow and arduous that the three Projects had too little time to integrate their various proposals before publication. For this reason, we have included in Part Six some preliminary attempts at bringing together ideas from physics and chemistry, even though these extend the work in this Unit beyond what is practicable in the short teaching time available to a physics course. However, we hope that this material may be of particular value where ideas from this Unit are used or adapted for courses which go beyond the limits of a sixth form physics course.

The kinetic theory of gases does not appear in this work to any great extent. It ought not to be missed out of a student's school course, and discussion of it should be substituted for part of the work offered here, with students who have taken an O-level course which does not include the theory.

Aims of the teaching

We think it better to succeed in achieving modest aims rather than to fail to achieve grandiose ones. This Unit is not likely to make a student a competent thermodynamicist. Those who stop at Part Four will not even explicitly meet the concept of entropy. But we do think the Unit can achieve some things of value. We hope students will recognize - albeit informally - the distinction between reversible and irreversible processes. We hope they will understand that the key to the problem of the natural direction of a process is statistical, and in particular, that heat flows from hot to cold by chance. We hope that they will appreciate what a statistical equilibrium is like, through becoming acquainted with it in various forms. We hope that they will understand that temperature - the clue to the direction of heat flow - is related to the chances for or against flow in a particular direction. We hope also that the work in Part Two and Part Six will show them that these ideas are of the greatest practical importance.

Difficulties

Many will feel this Unit to be a daunting prospect. Thermodynamics is widely acknowledged to be difficult, and statistical mechanics has no reputation for being an easy subject. Not a few expert physicists acknowledge their own inadequacy in this field. Yet in a sense, it is all very easy. What happens is what happens in many ways, expresses just about the sum total of the basic ideas underlying the subject.

Experience suggests that the problem is mainly one of confidence. Once one has begun to use the ideas, confidence comes quite quickly, because every problem is essentially the same problem: a process will only occur if the number of ways W or the entropy S = k ln W do not decrease as a result. We ourselves have found Bent's The Second Law a particularly helpful book, and we urge all who are concerned about their ability to cope with the material in this Unit to obtain a copy. Its particular merit lies in the large number of simple but penetrating questions, with answers given, which it contains. Because one of the teacher's worries is the need to be able to answer students' questions, this is a very valuable feature of the book.

We hope also that the material in Part Six will help teachers, even if it is not used with students. Examples 5, 6, and 8 may be particularly valuable for this purpose. Example 6 makes play with entropy values for various materials. (It is a peculiar deficiency of many courses in thermodynamics for physicists that one can emerge from them without having encountered a single numerical value for an entropy or an entropy change, and without having any idea of what order of magnitude to expect.) Example 7 deals with physical and chemical equilibrium, the area in which thermodynamics finds its largest practical applications. Example 8 discusses the special case of electrochemical cells, a natural link between physics and chemistry.

A book for teachers and students

In the absence of suitable textbooks, we have written this book so that it can be used by both teachers and students. In it, material intended particularly for teachers is printed in ruled boxes. Much use is made of questions incorporated into the text. Each question needs to be answered before proceeding. Answers are given on in the Answers part.

In the list at the end, details are given of books referred to in the text.

Time

In the Advanced Physics Course, four weeks have been allowed for work on this Unit. As suggested above, this will confine the work done with many classes to that offered in Parts One to Four, with a little from Part Six. However, we hope that work in this area in physics lessons will not be seen as divorced from similar work in chemistry. It may well provide an opportunity to join forces and this might make it a good deal easier to find time for the work of Parts Five and Six.