Comment on “The Gibbs paradox and the distinguishability of identical particles,” by M. A. M. Versteegh and D. Dieks [Am. J. Phys. 79, 741–746 (2011)]

Corti, David S.

doi:doi:10.1119/1.3657773

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American Journal of Physics -- February 2012 -- Volume 80, Issue 2, pp. 170

Comment on “The Gibbs paradox and the distinguishability of identical particles,” by M. A. M. Versteegh and D. Dieks [Am. J. Phys. 79, 741–746 (2011)]

David S. Corti

School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, Indiana 47907-2100

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Abstract

References (15)

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We revisit recent discussions concerning the Gibbs paradox—the apparent discrepancy between the entropy change upon mixing identical gases as evaluated from the statistical mechanics of classical distinguishable particles and macroscopic thermodynamics. Contrary to what is often stated, we show that thermodynamics does not require this entropy of mixing to be zero. A zero value follows from the implicit assumption that the identical gas particles are indistinguishable. If the identical particles are explicitly assumed to be distinguishable, thermodynamics yields the same entropy of mixing as classical statistical mechanics.

ACKNOWLEDGMENT

The author would like to thank Professor M. Uline for useful discussions and for bringing Ref. 5 to his attention, as well as useful comments by the anonymous reviewers, who brought Refs. 2, 3, and 12 to his attention.

Article Outline

INTRODUCTION
ENTROPY OF MIXING OF IDEAL GASES
CONCLUSIONS

EDITORIALLY RELATED

The Gibbs paradox and the distinguishability of identical particles
Marijn A. M. Versteegh et al.
Am. J. Phys. 79, 741 (2011)AJPIAS000079000007000741000001

KEYWORDS and PACS

Keywords

entropy, free energy, physics education, statistical mechanics, teaching

PACS

05.00.00

Statistical physics, thermodynamics, and nonlinear dynamical systems

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History

Received Jul 2011
Accepted Oct 2011

PUBLICATION DATA

ISSN

0002-9505 (print)

1943-2909 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1119/1.3657773

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Comment on “The Gibbs paradox and the distinguishability of identical particles,” by M. A. M. Versteegh and D. Dieks [Am. J. Phys. 79, 741–746 (2011)]