Nicolas Léonard Sadi Carnot

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Sadi Carnot
Sadi Carnot.jpeg
Nicolas Léonard Sadi Carnot (1796-1832) in the traditional uniform of a student of the École Polytechnique.
Born (1796-06-01)1 June 1796
Palais du Petit-Luxembourg, Paris, France
Died 24 August, 1832 (age 36)
Paris, France
Nationality  French
Alma mater École Polytechnique</br>École Royale du Génie</br>Sorbonne</br>Collège de France
Known for Carnot cycle</br>Carnot efficiency</br>Carnot theorem</br>Carnot heat engine
Scientific career
Fields Physicist and engineer
Institutions French army
Academic advisors Siméon Denis Poisson</br>André-Marie Ampère</br>François Arago
Influenced Benoît Paul Émile Clapeyron</br>Rudolf Julius Emmanuel Clausius
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 (1 June 1796 — 24 August 1832) was a French military engineer who, in his 1824 book Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle; his book also laid the foundations for the second law of thermodynamics. He is often described as the "Father of thermodynamics", being responsible for such concepts as Carnot efficiency, Carnot theorem, the Carnot heat engine, and others.

Life

Sadi Carnot was born in Paris, and was the first son of the eminent military leader and geometer, Lazare Nicholas Marguerite Carnot. Lazare was the elder brother of Hippolyte Carnot, and uncle of Marie François Sadi Carnot (President of the French Republic 1887-1894). His father named him after the Persian poet Sadi of Shiraz, and he was always known by this third given name.

From the age of 16, he lived in Paris and attended the École polytechnique where he and his contemporaries, Claude-Louis Navier and Gaspard-Gustave Coriolis, were taught by such notable professors as Joseph Louis Gay-Lussac, Siméon Denis Poisson and André-Marie Ampère. After graduation he became an officer in the French army before committing himself to scientific research; Carnot's research went to make him one of the most celebrated of Fourier's contemporaries who were interested in the theory of heat. He served in the military until 1814; following the defeat of Napoleon in 1815, his father went into exile, and he later obtained permanent leave of absence from the French army. It was during his military leave that he spent time to write his book Reflections on the Motive Power of Fire.

Reflections on the Motive Power of Fire

Background

When Carnot began working on his book the use of steam engines was relatively developed; notwithstanding this, there had been no real scientific study concerning steam engines. Steam engines had, however, risen to a widely recognized economic and industrial importance. 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 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, which Carnot was familiar with and which he described in some detail in his book. Significant progress had been made concerning engines, so there existed at the time some intuitive understanding of the workings of engines. Despite this, the scientific basis of 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; what's more is that the mechanical equivalent of heat had not been identified and would remain unknown for another two decades. The prevalent theory of heat at the time 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 burnt — was a mere 3%.

The Carnot Cycle

Carnot sought 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 28 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 he 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 improvements of the practical nature. The most important part of the book was devoted to 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 (T1T2)T1</var>, 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 the transfer of caloric takes place." 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 heat." He 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 1960, p. 7

and

In the fall of caloric, motive power evidently 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 1960, p. 15

The Second Law of Thermodynamics

In Carnot's idealized model, the caloric heat converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Nevertheless, Carnot further postulated that some caloric is lost and isn't converted into mechanical work. Hence, no real heat engine could realize the Carnot cycle's reversibility, and would consequently be less efficient.

Though formulated in terms of caloric, rather than entropy, this was an early rendition of the second law of thermodynamics.

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.

Death

Carnot died during a cholera epidemic in 1832, at the age of only 36. (Asimov 1982, p. 332) Because of the contagious nature of cholera, many of Carnot's belongings and writings were buried together with him after his death. As consequence, only a handful of his scientific writings survived.

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 in getting a copy of Carnot's book. In 1890 an English translation 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, who was fascinated[citation needed] by Carnot's theories, went on 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.


See also

References

The text of part of an earlier version of this article was taken from the public domain resource A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908)

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  • John Birkinbine and W.M. Wahl, "The Diesel motor", Journal of the Franklin Institute, vol. 152, no. 5 (November 1901), pp. 371-382.
  • The Diesel motor", Journal of the Franklin Institute, November 1901

External links