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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 10 Issue 4 (2005) pp 248-249

A Close Look at Temperature during the Free Expansion of a Dilute Monatomic Ideal Gas

David Keeports

Department of Chemistry and Physics, Mills College, Oakland, CA 94613,
Received January 21, 2005. March 11, 2005.

Published online: 13 June 2005

Abstract. I present here an analysis of temperature for a very dilute monatomic ideal gas as the gas begins to expand into a vacuum. As the expansion begins, the Maxwell–Boltzmann distribution function describes the velocity x-component distribution of the bulk gas; however, the rate of passage of molecules with speeds between vx and vx + dvx across the expansion boundary is proportional not only to the Maxwell–Boltzmann function but also to vx. Because the vx distribution function for molecules initially passing the expansion boundary more heavily favors molecules with larger vx than does the Maxwell–Boltzmann distribution, the equilibrium temperature of the gas first crossing the boundary exceeds that of the bulk gas. I present here a derivation of the relation between these two temperatures. This derivation provides an interesting exercise appropriate for physical chemistry students who are familiar with the Maxwell–Boltzmann distribution function.

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

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Issue date: August 1, 2005

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