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

TCE

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, dave@mills.edu
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 v_x and v_x + dv_x across the expansion boundary is proportional not only to the Maxwell–Boltzmann function but also to v_x. Because the v_x distribution function for molecules initially passing the expansion boundary more heavily favors molecules with larger v_x 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

(*) Corresponding author. (E-mail: dave@mills.edu)

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