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).
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.
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.)
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