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Sadi Carnot
was the eldest son of Lazare Carnot and he was born in the Palais du Petit-Luxembourg.
His younger brother was Hippolyte Carnot. At the time of Sadi's birth,
his father was a member of the Directory, the French Revolutionary government
which lasted four years from November 1795 to November 1799. Sadi was
given named after a medieval Persian poet and philosopher called Sadi
of Shiraz. Sadi Carnot was born at a time of unrest and political turmoil
in France and, due the position of his father, whose fortunes changed
dramatically many times, he was brought up in a totally unstable environment
of interacting politics and science. His father was appointed to the high
office of Napoleon's minister of war in 1799. Lazare Carnot resigned in
1807 and devoted himself to the education of his two sons. Sadi had a
fine teacher in his father, who taught him mathematics and science as
well as languages and music.
Under his father's tuition, Sadi Carnot showed great promise and was sent
to the Lycée Charlemagne in Paris to prepare him for the examinations
to the Ecole Polytechnique in Paris. In 1812, at age 16 the minimum age
possible, Carnot entered the Ecole Polytechnique where Poisson Ampére
and Arago were among his teachers. Chasles was in the same class as Carnot
and their friendship lasted throughout Carnot's life. Carnot graduated
from the Ecole Polytechnique in 1814 but, before he graduated, Carnot
and other students from the Ecole Polytechnique fought unsuccessfully
with Napoleon to defend Vincennes. This skirmish against the Allies was
fought just outside Paris, to the east of the city. After graduating,
Carnot went to the Ecole du Génie at Metz to take the two year
course in military engineering. In 1815 Napoleon returned from exile for
his famed Hundred Days rule. Carnot's father was appointed minister of
the interior and Sadi Carnot was put in a somewhat difficult position
in the military academy with his father in such a prominent position.
In October 1815 after the defeat of Napoleon, Carnot's father was exiled
and he went to Germany never to return to France. It is probable that
a military career was not the easiest one for Carnot with his father in
exile. Carnot was moved from place to place, given jobs of inspecting
fortifications, drawing up plans and writing reports. However, it seems
that he was not well treated and his recommendations were ignored. Unhappy
at his lack of promotion and the refusal to give him a job which allowed
him to make use of his training, in 1819, he sat and passed the examinations
to join the recently formed General Staff Corps in Paris. Almost immediately
he took leave on half pay, living in Paris in his father's former apartment,
but he remained on call for army duty. Carnot began to attend courses
at various institutions in Paris, including the Sorbonne and the Collège
de France. At this time he became interested in industrial problems and,
in particular, began to study the theory of gases. His interests were
wide [1]:-
He made frequent visits to factories and workshops,
studied the latest theories of political economy, and left in his notes
detailed proposals on such current problems as tax reform. Beyond this,
his activity and ability embraced mathematics and the fine arts.
Carnot visited his father in 1821 in his exiled home in Magdeburg. Hippolyte
Carnot, his brother, was living with his father at this time. It is clear
that there were many discussions about steam engines. The first steam
engine had come to Magdeburg three years earlier and had interested Lazare
Carnot and Sadi Carnot left Magdeburg filled with enthusiasm to develop
a theory for steam engines. After returning to Paris, Carnot began the
work which led to the mathematical theory of heat and helped start the
modern theory of thermodynamics. E Mendoza explains in [2] the background:-
The problem occupying Carnot was how to design good
steam engines. Steam power already had many uses - draining water from
mines, excavating ports and rivers, forging iron, grinding grain, and
spinning and weaving cloth - but it was inefficient. The import into France
of advanced engines after the war with Britain showed Carnot how far French
design had fallen behind. It irked him particularly that the British had
progressed so far through the genius of a few engineers who lacked formal
scientific education. British engineers had also accumulated and published
reliable data about the efficiency of many types of engines under actual
running conditions; and they vigorously argued the merits of low- and
high-pressure engines and of single-cylinder and multi-cylinder engines.
The first of Carnot's major works was a paper which he wrote in 1822-23.
This paper attempted to find a mathematical expression for the work produced
by one kilogram of steam. The paper is similar in its aims and also in
its methods to several other papers which appeared around this time by
Hachette, Navier and Petit However [1]:-
Carnot's work is distinguished for his careful, clear
analysis of the units and concepts employed and for his use of both an
adiabatic working stage and an isothermal stage in which work is consumed.
From its style and detailed descriptions the paper was clearly intended
for publication but Carnot never published it and its existence was only
discovered in manuscript form in 1966.
When Lazare Carnot died in August 1823, Hippolyte Carnot returned to Paris
and there he helped Sadi Carnot to make the book on steam engines that
he was working on at the time more understandable to the general public.
In 1824 Carnot published this work, the only one he published during his
lifetime, Réflexions sur la puissance motrice du feu et sur les
machines propres à développer cette puissance which includes
his description of the "Carnot cycle". This book only became
well known after Clapéyron published an analytic reformulation
of it in 1834. Carnot's ideas were later incorporated into the thermodynamic
theory of Clausius and Thomson
Carnot continued with his research after the publication of his book and
although nothing of this was published, notes that Carnot made as his
ideas developed have survived. In 1827, however, the General Staff Corps
in Paris was reorganised and he was recalled to full time duties. He served
for rather less than one year as a military engineer, being posted first
to Lyon and then to Auxonne. Still unhappy with his career, Carnot retired
permanently and returned to live in Paris where he aimed to continue with
his research into the theory of heat.
Following his father's political views, Carnot was strongly republican
so he was pleased with the direction France seemed to be going with the
July 1830 Revolution. Around this time he became interested in public
life, in particular he was interested in improving public education. He
was suggested for a government position, but he declined and, after the
monarchy was restored, he returned to his scientific work. In June 1832
he took ill and had not fully regained his strength when the cholera epidemic
of 1832 hit Paris. Although only 36 years of age, he died within a day
of contracting cholera.
That Carnot's important book Réflexions sur la puissance motrice
du feu et sur les machines propres à développer cette puissance
should have been neglected at the time of its publication is certainly
not because it went unnoticed. It was published on 12 June 1824 and on
26 July of that year Pierre Girard gave a long review of it to the Académie
des Sciences in Paris. 'Pierre Girard's review was a very positive one
and was published in the Revue encyclopédique. Perhaps the problem
with the review was that although it stated the theorems and the conclusions
of Carnot's work fully, it did not comment on the highly original reasoning
which Carnot had employed to achieve his results.
It is possible that Carnot's personality played a role in the lack of
enthusiasm for his work in his lifetime. He is described in [2] as follows:-
Friends described him as reserved, almost taciturn, but insatiably curious
about science and technical processes.
In [1] he is described in similar terms:-
Although sensitive and perceptive, he appeared extremely introverted,
even aloof, to all but a few close friends ...
The Réflexions was an attempt by Carnot to answer two fundamental
questions, firstly whether there was a upper limit to the power of heat,
and secondly whether there was a better means than steam to produce this
power. His attack on these question was to produce a much more general
theory than had previously been attempted based not on heat as random
motion of atoms, as Hooke and Boyle had done, but by the concept of heat
as a weightless fluid called caloric. He introduced the concept of the
"Carnot engine", an ideal heat engine. He showed that the efficiency
of the "Carnot engine" depends only on the temperature difference
within the engine and not on the substance such as steam that drives the
mechanism. He also introduced the important concept of reversibility,
namely that motive power can be used to produce the temperature difference
in the engine.
Notes which Carnot made between 1824 and 1826 show that he was moving
away from the caloric theory. He set out in his notes details of experiments
which he intended to carry out to study the temperature effects of friction
in fluids. Some of these proposed experiments were identical with those
actually performed by Joule twenty years later. It is likely that Carnot
would have made many more significant scientific contributions had his
life not been so tragically short.
Article by: Dr. J.J. O'Connor and E. F. Robertson, Pure Maths Area,
School of Mathematics and Statistics, North Haugh St. Andrews, Scotland
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