Comment on “Quirks of Stirling’s Approximation”

Department or Administrative Unit

Chemistry

Document Type

Editorial

Author Copyright

Copyright © 2018 American Chemical Society and Division of Chemical Education, Inc.

Publication Date

2-19-2018

Journal

Journal of Chemical Education

Abstract

In the article “Quirks of Stirling’s Approximation” published in this Journal, Macrae and Allgeier appear to conclude erroneously that the exactness of Boltzmann’s entropy formula for the microcanonical ensemble depends on the ensemble size. This conclusion seems to originate from the adoption of an unnecessary approximation appearing in Physical Chemistry: A Molecular Approach by McQuarrie and Simon. This letter provides a simple derivation of the entropy of the microcanonical ensemble that leads to the exact Boltzmann expression. In addition, this letter aims to stress that the entropy of a system or an ensemble is truly maximized only when no constraint is imposed on the system or ensemble. In particular, when the entropy of a microcanonical ensemble is to be maximized, it is inappropriate to assume the most probable distribution of the systems in the ensemble because this assumption is an unnecessary and unjustified constraint.

Comments

This article was originally published in Journal of Chemical Education. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Link to Full Text
Contact Author

Share

COinS