We identify an operative principle in Sadi Carnot’s only publication that is closely related to a distinct version of the second law of thermodynamics. Although Carnot did not propose the second law of thermodynamics, he assumed its equivalent in proving Carnot’s theorem. We show that, in the absence of the first law, Carnot’s assumption is equivalent to Clausius’ version of the second law. Both Carnot’s assumption and Clausius’ version, in the absence of the first law, are more restrictive than Kelvin’s statement of the second law.
REFERENCES
1.
See, for example,
C. J.
Adkins
, Thermodynamics
(McGraw-Hill
, London, 1978
), pp. 59
–61
.2.
3.
M. K.
Barnett
, “Sadi Carnot and the second law of thermodynamics
,” Osiris
13
, 333
–357
(1958
).4.
Joseph
Kestin
, The Second Law of Thermodynamics
(Dowden, Hutchinson and Ross
, Stroudsburg, PA, 1967
), p. 12
.5.
Rudolph
Clausius
, “On the motive power of heat, and on the laws which can be deduced from it for the theory of heat
,” found in Reflections on the Motive Power of Fire
, edited by E.
Mendoza
and translated by W. F.
Magie
(Dover
, New York, 1960
), pp. 107
–152
.6.
W.
Thomson
, “On the dynamical theory of heat, with numerical results deduced from Mr. Joule’s equivalent of a thermal unit, and M. Regnault’s observations on steam
,” excerpted in Ref. 4, pp. 110
–111
.7.
See Ref. 4.
8.
Sadi
Carnot
, Reflections on the Motive Power of Fire
, edited by E.
Mendoza
and translated by R. H.
Thurston
(Dover
, New York, 1960
), pp. 1
–59
.9.
The view that Carnot employed the caloric theory of heat in the “Reflections” has been adopted by most expositors and contested by a few. For an extended discussion and further references see
T. S.
Kuhn
, “La Mer’s version of ‘Carnot’s cycle’
,” Am. J. Phys.
23
, 387
–389
(1955
);T. S.
Kuhn
, “Carnot’s version of ‘Carnot’s cycle’
,” Am. J. Phys.
23
, 91
–95
(1955
);V. K.
La Mer
, “Some current misinterpretations of N. L. Sadi Carnot’s memoir and cycle II
,” Am. J. Phys.
23
, 95
–102
(1955
); andV. K.
La Mer
, “Some current misinterpretations of N. L. Sadi Carnot’s memoir and cycle
,” Am. J. Phys.
22
, 20
–27
(1954
).10.
Carnot’s posthumously published notes reveal that Carnot came to believe, within a few years following the publication of the “Reflections,” that energy rather than caloric was conserved. See Ref. 8, pp.
60
–69
.11.
Caratheodory’s axiomatization of thermodynamics is one example of an ahistorical presentation of thermodynamics; Callen’s postulational approach is another. For the former see
C. J.
Adkins
, Thermodynamics
(McGraw-Hill
, London, 1978
), pp. 93
–104
;12.
The concept of “a space of possible ideas” that shapes our thinking about a subject is borrowed from
Ian
Hacking
, The Emergence of Probability
(Cambridge U. P.
, Cambridge, 1975
), p. 9
.13.
See
H.
Schamp
, “Independence of the first and second laws of thermodynamics
,” Am. J. Phys.
30
, 825
–829
(1962
).14.
Qualitatively heat can be defined as that which changes the state of a thermodynamic system without work interactions or mass transfer.
15.
Reference 8, p.
6
.16.
18.
Reference 8, p.
12
.19.
J. T.
Vanderslice
, H. W.
Schamp
, and E. A.
Mason
adopt this version of the second law in their text Thermodynamics
(Prentice Hall
, Englewood Cliffs, NJ, 1966
), p. 29
, and loosely, but we believe misleadingly, characterize it as “similar to the statement given by William Thomson in 1851–1852.”20.
That Thomson proposed his statement of the second law independently of Clausius’s statement of the second law has been disputed by
Levi
Tansjo
in “Comment on the discovery of the second law
,” Am. J. Phys.
56
, 179
–182
(1988
). Whether or not Thomson’s discovery was independent of Clausius’s discovery, the Thomson statement of the second law is verbally and logically distinct from the Clausius statement.21.
22.
Seventy years ago the Nobel Laureate Percy Bridgman observed, “There have been nearly as many formulations of the second law as there have been discussions of it.…[and] not all these formulations can be exactly equivalent, but it is possible to distinguish stronger and weaker forms.” See
Percy
Bridgman
, The Nature of Thermodynamics
(Harvard U. P.
, Cambridge, MA, 1941
), p. 116
. Bridgman adds, in the ellipsis of this quotation, the seemingly adventitious remark, “I question whether such an examination would be of great physical interest.” We disagree.23.
Thermodynamics texts always assume that some cyclic processes are possible in the course of proving that others are impossible. See, for instance, Ref. 2, Fermi, pp. 31, 34–35, and Ref. 1, Adkins, pp.
56
–57
. We do the same in assuming that a heat engine and a refrigerator are possible with some combination of values , , and .24.
There is some unknown relation (for example, energy or caloric conservation or some other relation) among , , and that, given any two quantities, determines the third. This unknown relation precludes us from making more than one adjustment. In general adjustments of heat or work can be made among quantities describing engines. See Ref. 2, Fermi, p.
37
.25.
These deductions are assigned as Problem 3 of Chap. 5 in Ref. 19, and
E. A.
Mason
, Thermodynamics
(Prentice Hall
, Englewood Cliffs, NJ, 1966
), p. 47
.© 2008 American Association of Physics Teachers.
2008
American Association of Physics Teachers
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