Chemical Education Today
Letters An Experimental Approach To Teaching and Learning Elementary Statistical Mechanics Frank and David Ellis devised an apparatus where energized bouncing beads with a distribution of energies can be in one of two states with different areas or with different kinetic energies. The apparatus provides powerful visual support of elementary concepts in kinetics and equilibrium, including the role of entropy in equilibrium (1). However, the article’s discussion of entropy change was based on an older classical description of entropy. Entropy change as a measure of the dispersion of energy in a process has been advocated by Frank Lambert since 2002 (2). In a 2007 article, Lambert dealt with the misleading concept of “positional entropy” in a few general chemistry texts because of its focus on “matter dispersal” without any explicit involvement of molecular energy (3a, 3b). Consequently, this letter is written to show that the apparatus supports the modern view of entropy change. In the upper part of Figure 5 of Ellis and Ellis’s article (reproduced here), two states are shown, one with a small area over which the beads bounce and one with a large area. This is an analogy to isothermal expansion wherein the state with the larger area has
the greater entropy because the same molecular (bead) energy is spread out over a larger area. Obviously, if the power to the apparatus is shut off—to illustrate matter without kinetic energy —there will not be any “dispersal of matter” (2a, 2b). In the lower part of Figure 5, two states are shown as an analogy to thermal entropy increase, one where the bead energies are all small and one where a larger quantity of energy supplied to a system results in a much larger distribution of energy among the particles, an entropy increase. (In addition, this is a visual analogy for an increased quantity of energy in a system’s particles resulting in increased occupancy of higher energy levels.) Literature Cited 1. Ellis, F. B.; Ellis, D. C. J. Chem. Educ. 2008, 85, 78–82. 2. Lambert, F. L. J. Chem. Educ. 2002, 79, 187–192. http://www. entropysite.com/cracked_crutch.html (accessed May 2008). Lambert, F. L. J. Chem. Educ. 2002, 79, 1241–1246. http://www. entropysite.com/entropy_is_simple/index (accessed May 2008). 3. (a) Lambert, F. L. J. Chem. Educ. 2007, 84, 1548–1550. http:// www.entropysite.com/ConFigEntPublicat.pdf (accessed May 2008). (b) scroll to December 2005, #10–13 in http://www.entropysite. com/#whatsnew (accessed May 2008).
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Sep/abs1191.html Abstract and keywords positional entropy
Full text (HTML and PDF) Links to cited URLs and JCE articles Frank B. Ellis
small area
large area thermal entropy
Department of Chemistry and Environmental Science New Jersey Institute of Technology Newark, NJ 07012
[email protected] David C. Ellis Westfield, NJ 07090
low temperature high temperature Figure 5. Diagrammatic representation illustrating the two types of entropy. In each case, the state of greater disorder or entropy is shown on the right. Reprinted from ref 1.
Frank L. Lambert Occidental College Los Angeles, CA 90041
[email protected] © Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
1191
