The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the functioning of the second law and also provided evidence for the existence of atoms at a time when many scientists (like Ernst Mach and Wilhelm Ostwald) were skeptical.1
REFERENCES
1.
An accessible account of the history of Boltzmann's work is given in David Lindley, Boltzmann's Atom (The Free Press, New York, 2001).
2.
Ralph
Baierlein
, “Entropy and the second law: A pedagogical alternative
,” Am. J. Phys.
62
, 15
–26
(Jan. 1994
);Marcelo
Alonso
and Edward J.
Finn
, “An integrated approach to thermodynamics in the introductory physics course
,” Phys. Teach.
33
, 296
–310
(May 1995
);Thomas A.
Moore
and Daniel V.
Schroeder
, “A different approach to introducing statistical mechanics
,” Am. J. Phys.
65
, 26
–36
(Jan. 1997
);David C.
Schoepf
, “A statistical development of entropy for the introductory physics course
,” Am. J. Phys.
70
, 128
–136
(Feb. 2002
).3.
The analogy between entropy and disorder can be misleading. See
D. F.
Styer
, “Insight into entropy
,” Am. J. Phys.
68
, 1090
–1096
(Dec. 2000
) for a discussion and a better analogy.4.
The simulations were created using Easy Java Simulations (EJS) by Francisco Esquembre (see www.um.es/fem/Ejs/). Parts of the simulations are based on the MultipleCoinToss and PartitionedBox EJS models by Wolfgang Christian and Mario Belloni. See www.compadre.org/osp/ for these and other EJS models.
5.
A package containing all of the simulations is available at www.compadre.org/osp/items/detail.cfm?ID= 10161. Worksheets for the activity are available as supplemental documents on the same page.
6.
This model is equivalent to the double‐urn model first introduced by Paul and Tatiana Ehrenfest and presented as the dog‐flea model in
V.
Ambegaokar
and A. A.
Clerk
, “Entropy and time
,” Am. J. Phys.
67
, 1068
–1073
(Dec. 1999
).7.
The activity uses dimensionless units with kB = 1, so that S = lnΩ.
8.
These dice are used in role‐playing games and can be found at hobby stores.
9.
For a detailed discussion of entropy and irreversibility in an ideal gas, see
R. H.
Swendsen
, “Explaining irreversibility
,” Am. J. Phys.
76
, 643
–648
(July 2008
).10.
H. S.
Leff
, “Thermodynamic entropy: The spreading and sharing of energy
,” Am. J. Phys.
64
, 1261
–1271
(Oct. 1996
).11.
William F. Magie, A Source Book in Physics (McGraw‐Hill, New York, 1935), p. 263.
12.
For an extensive list of references on Maxwell's Demon, see
H. S.
Leff
and A. F.
Rex
, “Resource Letter MD‐1: Maxwell's Demon
,” Am. J. Phys.
58
, 201
–209
(March 1990
).13.
Harvey S.
Leff
, “Maxwell's demon, power, and time
,” Am. J. Phys.
58
, 135
–142
(Feb. 1990
).
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