Chemical Education Today
Letters A Simple Derivation of the Boltzmann Distribution—A Comment The derivation of Boltzmann’s distribution that McDowell (1) presented in his recent note is very similar to the derivation provided by Henry Bent in The Second Law (2), his excellent introductory text on classical and statistical thermodynamics, which was published in 1965. I have been using this derivation in my teaching for almost 30 years. Perhaps, because Bent’s book was published 35 years ago, it is no longer read by chemical educators. If this is the case it is unfortunate, because The Second Law is a lively, marvelously clear, and insightful treatment of thermodynamics and its chemical applications. It has guided my presentation of thermodynamics to undergraduates throughout my teaching career. Literature Cited 1. McDowell, S. A. C. J. Chem. Educ. 1999, 76, 1393. 2. Bent, H. A. The Second Law; Oxford University Press: New York, 1965; pp 163–165. Frank Rioux Department of Chemistry College of St. Benedict, St. John’s University St. Joseph, MN 56374
The author replies: I am grateful to Professor Rioux for bringing to my attention the derivation given in Harry Bent’s book. I have been teaching statistical thermodynamics at the undergraduate level for the last 3 years and I found that students had difficulty with the derivation of the Boltzmann distribution using Lagrange’s method of undetermined multipliers. This is the route taken by a large number of textbooks of recent vintage. Some time ago I happened on an article in JCE by Douglas Russell (which is cited in my article, J. Chem. Educ. 1996, 73, 299) that presents a simplified version of the derivation, obviating the need for the Lagrange method and linking the statistical formulation directly to classical thermodynamics via the point of minimum Helmholtz energy. It occurred to me to try a similar derivation but using the more fundamental thermodynamic parameter, entropy, rather than the Helmholtz energy. This seemed like a rather logical and natural thing to do. In fact, Boltzmann’s famous equation S = k ln W implies such a direct and straightforward connection. It is unfortunate that I was not aware of Bent’s treatment, but this is not surprising considering that our small library has a limited stock of books and is not likely to carry many of the older or even latest texts. The three referees who reviewed the paper apparently were also unaware of the content of Bent’s text. Rioux’s comments seem to indicate that Bent’s book is invaluable, and so it is indeed unfortunate that it has not been reprinted in 35 years. Sean McDowell Department of Biological and Chemical Sciences The University of the West Indies Bridgetown, Barbados, West Indies
JChemEd.chem.wisc.edu • Vol. 77 No. 12 December 2000 • Journal of Chemical Education
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