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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 9 Issue 2 (2004) pp 74-79

Understanding Entropy with the Boltzmann Formula

Finn Hynne

Department of Chemistry and CATS, H.C.Orsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark,
Received August 8, 2003. Accepted October 14, 2003.

Published online: 2 February 2004

Abstract. We show how a chemical reaction can be used to suggest the relation between spontaneity and growth of the number of microstates for an isolated system (Boltzmannís principle) and to motivate the interpretation of entropy via the Boltzmann formula in a chemically relevant way. Using elementary arguments, we obtain an explicit expression for the entropy of a real chemical system as a function of the extent of reaction for a progressing chemical reaction taking place in solution. Enlightened by the insight provided by the chemical-reaction example, we explain how the Boltzmann formula can more generally play a valuable role in classical thermodynamics as a tool to understand the concepts and relations. We use it to explain the peculiar thermodynamic definition of entropy and concepts like temperature and pressure in mechanical terms, thus, connecting the statistical and thermodynamic descriptions.

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

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Issue date: April 1, 2004

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