CHAPTER 4 THE SECOND LAW
4.3 CONCEPTSDEVELOPED WITHCARNOTENGINES 106
BIOGRAPHICAL SKETCH
Sadi Carnot (1796–1832)Sadi Carnot was the eldest son of Lazare
Carnot, a famous French anti-royalist politi-
cian, one of Napoleon’s generals with a great
interest in mathematics. As a boy Sadi was
shy and sensitive. He studied at theEcole ́
Polytechnique, a training school for army en-
gineers, and became an army officer.
Carnot is renowned for the one book he
wrote: a treatise of 118 pages entitledReflec-
tions on the Motive Power of Fire and on Ma-
chines Fitted to Develop that Power. This was
published in 1824, when he was 28 and had
retired from the army on half pay.
The book was written in a nontechnical
style and went virtually unnoticed. Its purpose
was to show how the efficiency of a steam en-
gine could be improved, a very practical matter
since French power technology lagged behind
that of Britain at the time:a
Notwithstanding the work of all kinds done by
steam-engines, notwithstanding the satisfactory
condition to which they have been brought today,
their theory is very little understood, and the at-
tempts to improve them are still directed almost
by chance.... We can easily conceive a multitude of ma-
chines fitted to develop the motive power of heat
through the use of elastic fluids; but in whatever
way we look at it, we should not lose sight of the
following principles:
(1) The temperature of the fluid should be
made as high as possible, in order to obtain a
great fall of caloric, and consequently a large
production of motive power.
(2) For the same reason the cooling should be
carried as far as possible.
(3) It should be so arranged that the passage
of the elastic fluid from the highest to the lowest
temperature should be due to increase of volume;
that is, it should be so arranged that the cooling
of the gas should occur spontaneously as the re-
sult of rarefaction [i.e., adiabatic expansion].
Carnot derived these principles from the ab-
stract reversible cycle now called the Carnot
cycle. He assumed the validity of the caloric
theory (heat as an indestructible substance),
which requires that the net heat in the cycle be
zero, whereas today we would say that it is the
net entropy change that is zero.
Despite the flaw of assuming that heat is
conserved, a view which there is evidence he
was beginning to doubt, his conclusion was
valid that the efficiency of a reversible cycle
operating between two fixed temperatures is
independent of the working substance. He
based his reasoning on the impossibility of the
perpetual motion which would result by com-
bining the cycle with the reverse of a more ef-
ficient cycle. Regarding Carnot’s accomplish-
ment, William Thomson (later Lord Kelvin)
wrote:
Nothing in the whole range of Natural Philoso-
phy is more remarkable than the establishment
of general laws by such a process of reasoning.
A biographer described Carnot’s personal-
ity as follows:b
He was reserved, almost taciturn, with a hatred
of any form of publicity.... his friends all spoke
of his underlying warmth and humanity. Pas-
sionately fond of music, he was an excellent vi-
olinist who preferred the classical Lully to the
“moderns” of the time; he was devoted to litera-
ture and all the arts.
Carnot came down with scarlet fever and,
while convalescing, died—probably of the
cholera epidemic then raging. He was only 36.
Two years later his work was brought to
public attention in a paper written byEmile ́
Clapeyron (page 217 ), who used indicator dia-
grams to explain Carnot’s ideas.aRef. [ 27 ]. bRef. [ 115 ], page x.