Disorder—A Cracked Crutch for Supporting Entropy Discussions

Disorder—A Cracked Crutch for Supporting Entropy Discussions

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In the Classroom JChemEd.chem.wisc.edu Vol. 79 No. 2 February 2002 Journal of Chemical Education 187 This article decries the use of “disorder” in teaching beginning students about thermodynamic entropy. It is cautionary rather than proscriptive about “disorder” being used warily as a device for assessing entropy change in advanced work or among professionals. 1 Overview To help students visualize an increase in entropy, many elementary chemistry texts use artists’ before-and-after drawings of groups of “orderly” molecules that become “disorderly”. This has been an anachronism ever since the ideas of quantized energy levels were introduced in elementary chemistry. “Orderly– disorderly” seems to be an easy visual support, but it can be so grievously misleading as to be characterized as a failure- prone crutch rather than a truly reliable, sturdy aid. 2 After mentioning the origin of this visual device in the late 1800s and listing some errors in its use in modern texts, I will build on a recent article by Daniel F. Styer. It succinctly summarizes objections from statistical mechanics to charac- terizing higher entropy conditions as disorderly ( 1 ). Then, after citing many failures of “disorder” as a criterion for evalu- ating entropy—all educationally unsettling, a few serious, I urge the abandonment of order–disorder in introducing entropy to beginning students. Although it seems plausible, it is vague and potentially misleading, a non-fundamental description that does not point toward calculation or elabo- ration in elementary chemistry, and an anachronism since the introduction of portions of quantum mechanics in first-year textbooks. 3 Entropy’s nature is better taught by first describing entropy’s dependence on the dispersion of energy (in classic thermodynamics) and the distribution of energy among a large number of molecular motions relatable to quantized states, microstates (in molecular thermodynamics). 4 Increased amounts of energy dispersed among molecules result in increased entropy that can be interpreted as molecular oc- cupancy of more microstates. (High-level first-year texts could go further to a page or so of molecular thermodynamic entropy as described by the Boltzmann equation.) The History and Use of “Disorder” to Characterize Entropy As is well known, in 1865 Clausius gave the name “en- tropy” to a unique quotient for the process of a reversible change in thermal energy divided by the absolute temperature ( 2 ). He could properly focus only on the behavior of chemical systems as macro units because in that era there was consider- able doubt even about the reality of atoms. Thus, the behavior of molecules or molecular groups within a macro system was totally a matter of conjecture (as Rankine unfortunately demonstrated in postulating “molecular vortices”) ( 3 ). Later in the 19th century, but still prior to the development of quantum mechanics, the greater “disorder” of a gas at high temperature
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Disorder—A Cracked Crutch for Supporting Entropy Discussions

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