An Introduction to Statistical Thermodynamics

190 Pages·1995·24.271 MB·English

by  R. P. H. Gasser, W. G. Richards

AN INTRODUCTION TO
STATISTICAL
THERMODYNAMICS

AN INTRODUCTION TO
STATISTICAL
THERMODYNAMICS
Robert P H Gasser 8. W Graham Richards
Oxford University
orld Scientific
ingapore New Jersey. London Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P 0 Box 128, Fmer Road, Singapore 912805
USA ofice: Suite lB, 1060 Main Street, River Edge, NJ 07661
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Library of Congress Cataloging-in-Publication Data
Gasser, R. P. H. (Robert Paul Holland)
An introduction to statistical thermodynamics / Robert P.H. Gasser
& W. Graham Richards.
p. cm.
ISBN 9810222432
ISBN 9810223722 (pbk)
1. Statistical thermodynamics. I. Richards, W. G. (William
Graham) 111. Title.
QC311.S.G63 1995
536'.7--dc20 95-20097
CIP
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
First published 1995
Reprinted 2001
Copyright 0 1995 by World Scientific Publishing Co. Re. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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Printed in Singapore by Uto-Print
PREFACE
As College Tutors we find that a major difficulty in teaching statisti-
cal thermodynamics to chemistry students is that (somewhat surprisingly)
when they first encounter this subject they often find the underlying phys-
ical principles more difficult to grasp than the mathematical formalism.
Thus the question ‘What is a partition function?’ is usually met with
blank incomprehension, even though the equation defining this function is
well-known and its derivation can be reproduced on request. A number of
existing textbooks provide excellent coverage of the more formal aspects of
the subject and examine the philosophical foundations on which it rests.
In this book, however, one of our principle aims is to make clear to the be-
ginner the physical basis of the relation between the observable behaviour
of systems of atoms or molecules and the properties of the individual par-
ticles. Some acquaintance with elementary calculus and quantum theory
is assumed, as is a familiarity with the basic ideas of classical thermo-
dynamics.
In pursuing our aim we have occasionally sacrificed rigour for the sake
of clarity and we have thought it especially important to introduce at the
earliest possible moment the world of experiment. This we regard as the
best way to an understanding of the subject. We have chosen therefore to
illustrate the principles by including reference to some modern experimental
subjects such as lasers, spectroscopy, and superconductivity. It is our hope
that, with this approach, even the student new to the subject will be enabled
V
to see the immediate relevance of statistical thermodynamics to a number
of subjects, which he will quickly recognize as being of general scientific
interest and importance. We also hope that this attempt to provide a more
widely scientifically cultured approach than is usual in elementary books
will offer some insight into the powerful and exciting pervasiveness of the
ideas of entropy and energy levels in atomic and molecular systems. The
book does not attempt to provide a comprehensive coverage of the subject
and, in particular, we have thought it wise to exclude a full account of the
statistical mechanics of solutions and of polymers. Solutions are treated
briefly but any worthwhile discussion of polymers would have required a
considerable expansion to do justice to their importance. In our view this
would have been undesirable. Our preference for a compact book is also
reflected in the choice and number of problems. Those we have put in
are intended more to illustrate and extend the discussion in the text, and
thereby to increase the student’s ‘feeling‘ for the subject, than to test his
ability to do numerical calculations.
The first chapters provide a basic outline of the subject and illustrate
the influence of quantum effects. The ideas are then applied to a number of
subjects, in which we hope that the reader will share our interest. Finally,
we have allowed ourselves to range outside the more conventional bounds
of the subject into areas of human endeavour where the applicability of
statistical ideas is not yet fully established-and perhaps never will be.
This may be thought a trifle over-ambitious in an elementary book, but it
is part of our second important aim in writing this book, which has been to
stimulate interest; even where, in so doing, the discussion may offend the
purist.
We wish to express our thanks to our colleagues in the Physical Chem-
istry Laboratory with whom we have had many discussions about the con-
tents of this book. These discussions have always been stimulating, often
controversial, and usually enlightening.
Since first published in 1974 as ‘Entropy and Energy Levels’, the book
has been very popular with students and we hope that this revised and
updated version will serve the same needs.
Oxford 1995
vi
ACKNOWLEDGEMENTS
We acknowledge gratefully permission to reproduce material from the
following sources:
FIG. 5.3(a): H. Wise, J. Phys. Chem. 58, 389 (1954). FIG. 5.3(b):
R. N. Doescher, J. Chem. Physics, 20, 331 (1952). FIG. 5.4: R. F. Barrow
and J. G. Stamper, Trans. Famday SOC.,5 4, 1592 (1958). Appendices
1, 2, and 3: J. E. Mayer and M. G. Mayer, Statistical Mechanics, Wiley,
New York, 1940.
vii

CONTENTS
PREFACE V
ACKNOWLEDGEMENTS vii
1. THE LAWS OF THERMODYNAMICS 1
The first law of thermodynamics. The second law of
thermodynamics. The third law of thermodynamics. Some
useful results from classical thermodynamics.
2. DISTRIBUTION LAWS 9
Energy levels. Boltzmann distribution law. Fermi-Dirac
statistics. BoseEinstein statistics. Chemical statistics.
3. DISTRIBUTIONS AND THERMODYNAMICS 23
Entropy and distribution. The constants a and ,8 in the
distribution law. The partition function Q. The relation of
the partition function to the thermodynamic functions.
4. DETERMINATION OF PARTITION FUNCTIONS 33
Localized and non-localized systems. Separation of the partition
function. Translational partition function. The Sackur-Tetrode
equation. Rotational partition function. Vibrational partition
function. Electronic partition functions. The hydrogen atom.
ix