Nicolas Léonard Sadi Carnot

For the President of France and nephew of Nicolas Léonard, see Marie François Sadi Carnot.

Nicolas Léonard Sadi Carnot
Carnot aged 17 in the uniform of a cadet of the École Polytechnique. Portrait by Louis-Léopold Boilly (1813).
Born	(1796-06-01)1 June 1796 Petit-Luxembourg, Paris, France
Died	24 August 1832 (aged 36) Ivry-sur-Seine, France
Resting place	Old cemetery of Ivry-sur-Seine
Nationality	France
Alma mater	École Polytechnique École d'application de l'artillerie et du génie
Known for	Carnot cycle Thermal efficiency Carnot theorem Carnot heat engine Second law of thermodynamics
Scientific career
Fields	Physics, military engineering
Institutions	French Army
Signature
Notes
He was the brother of Hippolyte Carnot, his father was the mathematician Lazare Carnot, and his nephews were Marie François Sadi Carnot and Marie Adolphe Carnot.

Nicolas Léonard Sadi Carnot (French pronunciation: [nikɔla leɔnaʁ sadi kaʁno]; 1 June 1796 – 24 August 1832) was a French military engineer and physicist. A graduate of the École Polytechnique, Carnot served as an officer in the Engineering Arm (le Génie) of the French Army. He also pursued scientific studies and in June of 1824 published an essay titled Reflections on the Motive Power of Fire. In that book, which would be his only publication, Carnot developed the first successful theory of the maximum efficiency of heat engines. That work attracted little attention during Carnot's lifetime, but in 1834 it became the object of a detailed commentary and explication by Émile Clapeyron. Clapeyron's commentary in turn attracted the attention of both Lord Kelvin and Rudolf Clausius, who built upon Carnot's analysis in order to formalize what then came to be known as the "second law of thermodynamics" and to define the concept of entropy.

Sadi was the son of Lazare Carnot, an eminent mathematician, engineer, and commander of the French Revolutionary Army and later of the Napoleonic army. Some of the difficulties that Sadi faced in his own career might have been connected to the persecution of his family by the restored Bourbon monarchy after 1815. Carnot died in relative obscurity at the age of 36, but today he is often characterized as the "father of thermodynamics".

Life

Sadi Carnot was born in Paris on the 1st of June 1796, at the Petit Luxembourg palace, where his father Lazare resided as one of the five members of the Directory, the highest governing body of the French First Republic in the immediate aftermath of the Thermidorian Reaction. His mother, Sophie née Dupont (1764-1813), came from a wealthy family based in Saint-Omer. Sadi was the elder brother of statesman Hippolyte Carnot and the uncle of Marie François Sadi Carnot, who served as President of France from 1887 to 1894.

Sadi was named by his father Lazare after the 13th-century Persian poet Sadi of Shiraz. An older brother, also named Sadi, had been born in 1794 but died in infancy the following year. "Sadi" is the only given name that appears in the second-born's civil birth certificate, dated 14 prairial, year IV in the French Republican calendar. On 11 July 1796 the child was baptized in the Catholic church of Saint-Louis-d'Antin as "Nicolas-Léonard Dupont". The principal witness at that baptism was his maternal grandfather, Jacques-Antoine-Léonard Dupont. The father is wrongly identified in the baptismal record as Jacques-Léonard-Joseph-Auguste Dupont (who was, in fact, the child's maternal uncle). Following the biographical notice published long after his death by his brother Hippolyte, most sources now give his full name as "Nicolas Léonard Sadi", but there is no evidence that he ever used any name other than "Sadi".

The young Sadi Carnot was educated first at home by his father and later at the Lycée Charlemagne, in Paris, where he prepared for the examinations required to enter the École Polytechnique, which his father had helped to establish. In 1811, at the age of 16 (the minimum allowed) Sadi Carnot became a cadet of the École Polytechnique, where his classmates included the future mathematician Michel Chasles. Among his professors were André-Marie Ampère, Siméon Denis Poisson, François Arago, and Gaspard-Gustave Coriolis. Thus, the school had become renowned for its instruction in mathematics and physics.

After graduating in 1814, Sadi went on to more specialized training at the École d'application de l'artillerie et du génie ("School of Applied Artillery and Military Engineering") in Metz, completing a two-year course. Sadi then became an officer in the French army's corps of engineers. His father Lazare had served as Napoleon's minister of the interior during the "Hundred Days", and, after Napoleon's final defeat in 1815, Lazare was forced into exile in the German city of Magdeburg. Sadi's position in the army, under the restored Bourbon monarchy of King Louis XVIII, became increasingly difficult.

Sadi Carnot was posted to different locations, where he inspected fortifications, tracked plans, and wrote many reports. It appeared that his recommendations were ignored and his career was stagnating. On 15 September 1818 he took a six-month leave to prepare for the entrance examination of Royal Corps of Staff and School of Application for the Service of the General Staff.

In 1819, Sadi transferred to the newly formed General Staff in Paris. He remained on call for military duty, but from then on he dedicated most of his attention to private intellectual pursuits and received only two-thirds pay. Carnot befriended Nicolas Clément and Charles-Bernard Desormes and attended lectures on physics and chemistry. He became interested in understanding the limitation to improving the performance of steam engines, which led him to the investigations that became his Reflections on the Motive Power of Fire, published in 1824.

Carnot retired from the army in 1828, without right to a pension. On 3 August, 1832 he was interned in a private sanatorium run by psychiatrist Jean-Étienne Esquirol and located in Ivry, just south of Paris. According to the hospital records, he was cured from "mania" but then died of cholera on 24 August. Carnot is buried in the old cemetery of Ivry, close to the Mairie d'Ivry station.

Reflections on the Motive Power of Fire

Background

When Carnot began working on his book, steam engines had achieved widely recognized economic and industrial importance, but there had been no real scientific study of them. Newcomen had invented the first piston-operated steam engine over a century before, in 1712; some 50 years after that, James Watt made his celebrated improvements, which were responsible for greatly increasing the efficiency and practicality of steam engines. Compound engines (engines with more than one stage of expansion) had already been invented, and there was even a crude form of internal-combustion engine, with which Carnot was familiar and which he described in some detail in his book. Although there existed some intuitive understanding of the workings of engines, scientific theory for their operation was almost nonexistent. In 1824 the principle of conservation of energy was still poorly developed and controversial, and an exact formulation of the first law of thermodynamics was still more than a decade away; the mechanical equivalence of heat would not be formulated for another two decades. The prevalent theory of heat was the caloric theory, which regarded heat as a sort of weightless and invisible fluid that flowed when out of equilibrium.

Engineers in Carnot's time had tried, by means such as highly pressurized steam and the use of fluids, to improve the efficiency of engines. In these early stages of engine development, the efficiency of a typical engine—the useful work it was able to do when a given quantity of fuel was burned—was only 3%.

Carnot cycle

Main articles: Carnot heat engine and Carnot cycle

Carnot wanted to answer two questions about the operation of heat engines: "Is the work available from a heat source potentially unbounded?" and "Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?" He attempted to answer these in a memoir, published as a popular work in 1824 when he was only 27 years old. It was entitled Réflexions sur la Puissance Motrice du Feu ("Reflections on the Motive Power of Fire"). The book was plainly intended to cover a rather wide range of topics about heat engines in a rather popular fashion; equations were kept to a minimum and called for little more than simple algebra and arithmetic, except occasionally in the footnotes, where Carnot indulged in a few arguments involving some calculus. He discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam-engine design, and even included some ideas of his own regarding possible practical improvements. The most important part of the book concentrated on an abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are generally applied to all heat engines, independent of their design.

Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine, as they were known in his day, into a more general and idealized heat engine. This resulted in a model thermodynamic system upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam-engine. By idealizing the engine, he could arrive at clear and indisputable answers to his original two questions.

He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T₁−T₂)/T₁, where T₁ is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin.) No thermal engine operating any other cycle can be more efficient, given the same operating temperatures.

The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. Carnot knew that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be eliminated if the heat engine is to achieve maximum efficiency.

Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid. He stated this for emphasis as a general proposition:

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

— Carnot 1890, p. 68

For his "motive power of heat", we would today say "the efficiency of a reversible heat engine"; and rather than "transfer of caloric" we would say "the reversible transfer of entropy ∆S" or "the reversible transfer of heat at a given temperature Q/T". Carnot knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be.

He concluded:

The production of motive power is therefore due in steam engines not to actual consumption of caloric but to its transportation from a warm body to a cold body.

— Carnot 1890, p. 46

and

In the fall of caloric, motive power undoubtedly increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.

— Carnot 1890, p. 61

In an idealized model, the caloric transported from a hot to a cold body by a frictionless heat engine that lacks conductive heat flow, driven by a difference of temperature, yielding work, could also be used to transport the caloric back to the hot body by reversing the motion of the engine consuming the same amount of work, a concept subsequently known as thermodynamic reversibility. Carnot further postulated that no caloric is lost during the operation of his idealized engine. The process being completely reversible executed by this kind of heat engine is the most efficient possible process. The assumption that heat conduction not driven by a temperature difference can exist, so that no caloric is lost by the engine, guided him to design the Carnot-cycle to be operated by his idealized engine. The cycle is consequently composed of adiabatic processes where no heat/caloric ∆S = 0 flows and isothermal processes where heat is transferred ∆S > 0 but no temperature difference ∆T = 0 exists. The proof of the existence of a maximum efficiency for heat engines is as follows:

As the cycle named after Carnot doesn't waste caloric, the reversible engine has to use this cycle. Imagine now two large bodies, a hot and a cold one. He postulates now the existence of a heat machine with a greater efficiency. We couple now two idealized machines —but of different efficiencies— and connect them to the same hot and the same cold body. The first and less efficient one lets a constant amount of entropy ∆S = Q/T flow from hot to cold during each cycle, yielding an amount of work denoted W. If we use now this work to power the other —more efficient— machine, it would, using the amount of work W gained during each cycle by the first machine, make an amount of entropy ∆S' > ∆S flow from the cold to the hot body. The net effect is a flow of ∆S' − ∆S ≠ 0 of entropy from the cold to the hot body, while no net work is done. Consequently, the cold body is cooled down and the hot body rises in temperature. As the difference of temperature rises, now the yielding of work by the first is greater in the successive cycles and due to the second engine difference in temperature of the two bodies stretches by each cycle even more. In the end this set of machines would be a perpetuum mobile that cannot exist. This proves that the assumption of the existence of a more efficient engine was wrong, so that a heat engine that operates the Carnot cycle must be the most efficient one. This means that a frictionless heat engine that lacks conductive heat flow driven by a difference of temperature shows maximum possible efficiency.

Carnot concludes further that the choice of the working fluid, its density or the volume occupied by it cannot change this maximum efficiency. Using the equivalence of any working gas used in heat engines, he deduced that the difference in the specific heat of a gas measured at constant pressure and that measured at constant volume must be constant for all gases. By comparing the operation of his hypothetical heat-engines for two different volumes occupied by the same amount of working gas he correctly deduces the relation between entropy and volume for an isothermal process:

$\Delta S\propto \ln {\frac {V}{V_{0}}}.$

Reception and later life

Carnot's book received very little attention from his contemporaries. The only reference to it within a few years after its publication was in a review in the periodical Revue Encyclopédique, which was a journal that covered a wide range of topics in literature. The impact of the work had only become apparent once it was modernized by Émile Clapeyron in 1834 and then further elaborated upon by Clausius and Kelvin, who together derived from it the concept of entropy and the second law of thermodynamics. Rankine, who introduced the term potential energy in 1853, was later made aware that an equivalent phrase, "in its purely mechanical sense, had been anticipated by Carnot", who had employed the term force vive virtuelle.

On Carnot's religious views, he was a Philosophical theist. He believed in divine causality, stating that "what to an ignorant man is chance, cannot be chance to one better instructed," but he did not believe in divine punishment. He criticized established religion, though at the same time spoke in favor of "the belief in an all-powerful Being, who loves us and watches over us."

He was a reader of Blaise Pascal, Molière and Jean de La Fontaine.

Death and posterity

Sadi Carnot died in 1832 in Dr. Esquirol's mental hospital in the Parisian suburb of Ivry-sur-Seine, reportedly of cholera. Sadi's younger brother Hippolyte obscured the details of Sadi's death and destroyed most of his personal papers. Much later, in 1878, when Carnot's essay had come to be widely recognized as a founding document of the new science of thermodynamics, Hippolyte sponsored the publication of a new edition that included a "Biographical notice on Sadi Carnot" written by Hippolyte and some "Excerpts from unpublished notes by Sadi on mathematics, physics and other subjects". These are almost the only sources of information on most aspects of Sadi's life and thought. In the opinion of historian of science Arthur Birembaut, the "smokescreen" that Hippolyte drew over his brother's life makes it impossible now to reconstruct the details of Sadi's career, his relationship with other physicists and engineers, and the circumstances of his death.

After the publication of Reflections on the Motive Power of Fire, the book quickly went out of print and for some time was very difficult to obtain. Kelvin, for one, had a difficult time getting a copy of Carnot's book. In 1890 an English translation of the book was published by R. H. Thurston; this version has been reprinted in recent decades by Dover and by Peter Smith, most recently by Dover in 2005. Some of Carnot's posthumous manuscripts have also been translated into English.

Carnot published his book in the heyday of steam engines. His theory explained why steam engines using superheated steam were better because of the higher temperature of the consequent hot reservoir. Carnot's theories and efforts did not immediately help improve the efficiency of steam engines; his theories only helped to explain why one existing practice was superior to others. It was only towards the end of the nineteenth century that Carnot's ideas, namely that a heat engine can be made more efficient if the temperature of its hot reservoir is increased, were put into practice. Carnot's book did, however, eventually have a real impact on the design of practical engines. Rudolf Diesel, for example, used Carnot's theories to design the diesel engine, in which the temperature of the hot reservoir is much higher than that of a steam engine, resulting in an engine which is more efficient.

Works

• Reflections on the Motive Power of Fire (1824)

See also

• History of the internal combustion engine

Bibliography

• Asimov, Isaac (1982), Asimov's Biographical Encyclopedia of Science and Technology (2nd rev. ed.), Doubleday
• Carnot, Sadi (1960), Reflection on the Motive Power of Fire, Dover
• Carnot, Sadi (1977), Mendoza, E. (ed.), Reflection on the Motive Power of Fire and other papers translated into English, Gloucester, Massachusetts: Peter Smith
• Wilson, S. S. (August 1981), "Sadi Carnot", Scientific American, 245 (2): 102–114, Bibcode:1981SciAm.245b.134W, doi:10.1038/scientificamerican0881-134
• Birkinbine, John; Wahl, W.M. (November 1901), "The Diesel motor", Journal of the Franklin Institute, 152 (5): 371–382, doi:10.1016/s0016-0032(01)90202-9
• Carnot, Sadi (1890). Reflections on the Motive Power of Heat. Thurston, Robert Henry (editor and translator). New York: J. Wiley & Sons.
• (full text of 1897 ed.) (Archived February 4, 2012, at the Wayback Machine)
• Chisholm, Hugh, ed. (1911). "Carnot, Sadi Nicolas Léonhard" . Encyclopædia Britannica. Vol. 5 (11th ed.). Cambridge University Press.

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  1890 copy of "Reflections on the Motive Power of Heat"
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  Portrait of Carnot in a 1890 copy of "Reflections on the Motive Power of Heat"
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  Title page of a 1890 copy of "Reflections on the Motive Power of Heat"
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  First page of the table of contents for a 1890 copy of "Reflections on the Motive Power of Heat"

External links

• Media related to Nicolas Léonard Sadi Carnot at Wikimedia Commons

• Texts on Wikisource:
  • Reflections on the Motive Power of Heat
• O'Connor, John J.; Robertson, Edmund F., "Nicolas Léonard Sadi Carnot", MacTutor History of Mathematics Archive, University of St Andrews
• Reflections on the Motive Power of Heat (1890), English translation by R. H. Thurston (at Internet Archive)
• Sadi Carnot and the Second Law of Thermodynamics, J. Srinivasan, Resonance, November 2001, 42 (PDF file)
• Reflections on the Motive Power of Heat (1824), analysed on BibNum (click "À télécharger" for English analysis)