Deriving the Boltzmann Energy Distribution: An Alternate Approach

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 12 Issue 4 (2007) pp 215-218

Deriving the Boltzmann Energy Distribution: An Alternate Approach

Larry Eno

Department of Chemistry, Clarkson University, Potsdam, NY 13699-5810, ko00@clarkson.edu
Received July 7, 2005. Accepted November 11, 2006.

Published online: 4 August 2007

Abstract. Deriving the Boltzmann energy distribution is commonly effected through maximizing distinguishable arrangements subject to constraints. In this process, the constraints are accounted for using the Lagrange method of undetermined multipliers. Unfortunately, many students lack the mathematical background necessary to properly appreciate the Lagrange method. It is here shown that maximizing distinguishable arrangements subject to constraints can be readily effected—although admittedly less elegantly—without involving the Lagrange method.

Key Words: In the Classroom; physical chemistry; thermodynamics; statistical mechanics

(*) Corresponding author. (E-mail: ko00@clarkson.edu)

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