Table Of ContentERRATA
On p. 22, the exponent in equation (4) should be divided by the number
2—lost in the foregoing derivation by a careless approximation.
On p. 87 line 4 slightly underestimates the total number of rotational
quantum states.
Copyright
Copyright © 1965, 1966, 1974 by Leonard K. Nash
All rights reserved.
Bibliographical Note
This Dover edition, first published in 2006, is an unabridged republication
of the 1974 second edition of the work originally published in 1965 by
Addison-Wesley Publishing Company, Inc., Reading, Massachusetts.
International Standard Book Number:
9780486137469
Manufactured in the United States by Courier Corporation
44978502
www.doverpublications.com
Preface
Macroscopic thermodynamics is here reexamined from the perspective of
atomic-molecular theory. The thermodynamic concepts of entropy and
equilibrium are thus invested with new meaning and implication, and one
comes to see how thermodynamic magnitudes (e.g., gaseous heat capacities
and equilibrium constants) can be calculated from spectroscopic data.
Chapter 1 introduces and develops a statistical analysis of the concept of
distribution—culminating in a very simple derivation of the Boltzmann
distribution law and a demonstration of the relation of statistical and
thermodynamic entropies. Chapters 2, 3, and 4 then treat in turn the
formulation, the evaluation, and the application of partition functions.
Compared with the first edition, the present second edition offers in its
opening chapter an analysis that is both much simpler and more decisive.
This chapter also provides a brief but convincing demonstration of one
crucial point merely announced in the first edition, namely: the enormous
odds by which some distributions are favored over others. The remaining
chapters reflect complete reorganization and extensive rewriting of the
corresponding material in the first edition, and further incorporate several
major additions. These include some illuminating interpretations of
partition functions and statistical entropies, a brief but substantial
development of the statistics of indistinguishable units, an exploration of
the “dilute-gas condition” under which these statistics reduce to a limiting
form equivalent to “corrected” Boltzmann statistics, and a derivation of the
Maxwell-Boltzmann molecular-speed distribution law in three dimensions.
Enlarged by 70%, the set of problems should both challenge and reward the
reader.
This text has been designed to convey its message at either of two levels.
First: if systematically supported by a series of exegetical lectures, the book
may be used in strong introductory college chemistry courses. Years of
experience in teaching such a course convince me that, wherever classical
thermodynamics can be taught successfully, this much statistical
thermodynamics can be taught at least as successfully—and with striking
reflexive improvement in student understanding of classical
thermodynamics. Second: the book lends itself to essentially independent
study by more advanced students who seek a view of the subject that is less
formal, and far less compressed, than that afforded by undergraduate
physical-chemistry texts.
Irrespective of background, the reader will find need for just three small
bodies of prior knowledge.
1. A rudimentary knowledge of the calculus, such as is acquired by my
own freshmen in the first two-thirds of an introductory course in college
mathematics.
2. An elementary understanding of macroscopic thermodynamics, on
which we draw for a few simple relations like dE = T dS – P dV. Many
current texts for the introductory college chemistry course offer a quite
sufficient foundation in this area.
3. A slight acquaintance with the energy-quantization conditions that
permit calculation of molecular parameters from spectroscopic
measurements. The inclusion of some abbreviated didactic material lends
the present book a minimal self-sufficiency in this department, but one may
well prefer the more ample background afforded, for example, by pp. 1-80
of G. M. Barrow’s Structure of Molecules (Benjamin, 1962).
The argument constructed on these modest foundations comprises
essentially all the statistical mechanics that appears in even the most
sophisticated of undergraduate physical – chemistry textbooks. I have
neglected internal rotation, and I have not pursued the argument into the
realm of kinetics—where it readily yields some powerful new insights.
More significant than these easily remediable omissions is one notable
limitation: applying to assemblies of effectively independent units, the
results here obtained from analysis of microcanonical ensembles cannot at
once be extended to assemblies of strongly interacting units. Given a
sufficiently enlarged background, one may easily approach these important
assemblies by way of Gibbsian analyses (of canonical and ground canonical
ensembles) that fully display both the great power and the great beauty of
statistical mechanics.
Among the many equations appearing herein, some are marked by letters
to facilitate back-references in the immediately succeeding text, or in a
problem. On the other hand, apart from facilitating such back-references,
the numbers attached to thirty-odd equations signal a call for particular
attention. As they proceed, readers would be well advised to compile their
own lists of these numbered equations, each of which expresses an
important idea and/or represents a useful computational tool.
Cambridge, Massachusetts
L.K.N.
August 1973.
Table of Contents
Title Page
Copyright Page
Preface
Acknowledgments
1 - The Statistical Viewpoint
2 - The Partition Function
3 - Evaluation of Partition Functions
4 - Applications
Problems
Index
Acknowledgments
I am obliged to the publishers cited below for permission to reproduce a
number of figures taken from copyrighted works. As identified by the
numbers assigned them in this book, the figures in question are:
Figure 7, taken from p. 55 of J. D. Fast’s Entropy (Eindhoven, Holland:
Philips Technical Library, 1962);
Figure 16, from p. 68 of G. W. Castellan’s Physical Chemistry, 2nd ed.
(Reading, Mass.: Addison-Wesley Publishing Co., 1971);
Figure 19, from an article by R. K. Fitzgerel and F. H. Verhoek, Journal of
Chemical Education 37, 547 (1960);
Figure 22, from p. 142 of Malcolm Dole’s Introduction to Statistical
Thermodynamics (Englewood Cliffs, N.J.: Prentice-Hall, 1954);
Figures 23 and 24, from pp. 203 and 257 respectively of Statistical
Thermodynamics by J. F. Lee, F. W. Sears, and D. L. Turcotte (Reading,
Mass.: Addison-Wesley Publishing Co., 1963); and
Figure 25, from p. 102 of Statistical Thermodynamics by R. H. Fowler and
E. A. Guggenheim (Cambridge: University Press, 1939).
I am happy to acknowledge that my first 18 pages have been developed
on a pattern suggested by reading of the late Ronald W. Gurney’s ingenious
introductory text. The arguments on pp. 49 – 53 and 61 – 62 owe some of
their shape to constructive criticisms of the first edition forwarded to me by
William C. Child, Jr., who has kindly supplied several more comments on a
draft of this second edition. For a multitude of additional suggestions I am
much indebted to Francis T. Bonner, Peter C. Jordan, and Lawrence C.
Krisher. To Walter Kauzmann, the author of a splendid alternative to the
present text, I am deeply grateful for his generous willingness to indicate
