An Experimental Approach to Teaching and Learning Elementary Statistical Mechanics

1

From
the
Letters

page of the Journal of Chemical Education

for September 2008

with

modifications in blue
(
J. Chem. Educ.
2008
,
85
, 1191.)



An Experimental Approach to Teaching and Learning E
lementary

Statistical Mechanics



Frank and David Ellis devised a
n 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 equilibri
um, including the role of entropy in equilibrium
(1)
.
However, the article’s discussion of entropy change was based on an older classical
d
escription

of entropy.



Entropy change as a measure of the dispersion of energy in a process has been
advocated by
Frank Lambert since 2002
(2)
. A 2007 article 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)
.



Consequen
tly, this letter is written to show that the apparatus supports the modern
view of entropy change. In the upper part of Figure 5 of the article, 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

(or volume in a 3
-
D chamber)
.

Obviously, if the power to the apparatus is
shut off
–

to illustrate matter
without

kinetic energy
–

there will not be any “dispersal of
matter”
(
3a, 3b
)
.



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

(
i.e., a greater
spreading out
)

of energy among the particles, an entropy increase. (In addition, this is a
visual analogy for an increased amount 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
,
49
, 187
-
192.














http://www.entropysite.com/cracked_crutch.html/

(accessed Feb 2008)
;
J.Chem.



2



Educ.

2002
,
49,

1241
-
1246
.

http://www.entropysite.com/entropy_is_si
mple/index/




(accessed Feb 2008)
.


3
.

Lambert, F
.

L.,
(a)
J
.

Chem
.

Educ
.

2007
,

84
,

1548
-
1550.












http://www.entropysite.com/ConFigEntPublicat.pdf.
(accessed

Feb 20
08);

(b)







scroll to December 2005, #10
-
13 in
http://www.entropysite.com/#whatsnew





(accessed Feb 2008).






Frank B. Ellis























Department of Chemistry and Environmental Science











New Jersey Institute of Technology

















Newark, NJ 07012

























frank.b.ellis@njit.edu



David C. Ellis























Westfield, NJ 07090



Frank L. Lambert
























Occidental College




Los Angeles, CA 90041




flambert@att.net





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