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Nicolas Léonard Sadi Carnot (June 1, 1796August 24, 1832) was a French physicist and military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics. (Note: He did not publish in a journal. He published it in the form of a small book in 1824.) Technically, he is the world's first thermodynamicist, being responsible for such concepts as Carnot efficiency, Carnot theorem, Carnot heat engine, and others.


Born in Paris, Sadi Carnot was the first son of the eminent military leader and geometer, Lazare Nicholas Marguerite Carnot, elder brother of Hippolyte Carnot, and uncle of Marie François Sadi Carnot (President of the French Republic (1887-1894), son of Hippolyte Carnot). His father named him for the Persian poet Sadi of Shiraz. (Carnot 1960, p. xi)

From age 16 (1812), he attended the École polytechnique where he and his contemporaries, Claude-Louis Navier and Gaspard-Gustave Coriolis, were taught by professors such 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, becoming the most celebrated of Fourier's contemporaries who were interested in the theory of heat. Since 1814, he served in the military. After the final defeat of Napoleon in 1815, his father went into exile. He later obtained permanent leave of absence from the French army. Subsequently, he spent time to write his book.

Reflections on the Motive Power of Fire


The historical context in which Carnot worked was that the scientific study of the steam engine hardly existed, but the engine was actually pretty far along in its development. It had attained a widely recognized economic and industrial importance. Newcomen had invented the first piston operated steam engine over a century before, in 1712. About 50 years after that, Watt made his celebrated improvements to greatly increase the efficiency and practicality of the engine. Compound engines, with more than one stage of expansion, had already been invented. There was even a crude form of an internal combustion engine, which Carnot was familiar with, and described in some detail in his book. (Carnot 1960, p. 56) Amazing progress on the practical side had been made, so at least some intuitive understanding of the engine's workings existed. The scientific basis of its operation, however, was almost nonexistent even after all this time. In 1824, the principle of conservation of energy was still immature and controversial, and an exact formulation of the first law of thermodynamics was yet over a decade away. The mechanical equivalent of heat was still two decades away. The prevalent theory of heat was the caloric theory which supposed that heat was a sort of weightless, invisible fluid that flowed when out of equilibrium.

Engineers of Carnot's time had tried various mechanical means, such as high pressure steam, or use of some fluid other than steam, to improve the efficiency of engines. The efficiency, the work generated from a given quantity of fuel, such as from burning a lump of coal, in these early stages of engine development was mere 3%.

The Carnot cycle

Main articles: Carnot heat engine and Carnot cycle

Carnot proposed to answer two questions about the operation of heat engines: "Is the potential work available from a heat source potentially unbounded?" and "Can heat engines be in principle improved by replacing the steam by 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. The equations were kept to a minimum and hardly called for anything beyond simple algebra and arithmetic, except occasionally in the footnotes, where he indulged in a few arguments involving a little calculus. He discussed the relative merits of air and steam as the working fluid, the merits of various points of steam engine design, and even threw out some ideas of his own on possible practical improvements. But, the most important part of the book was devoted to a quite abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are of general applicability to all heat engines, independent of the particular design choices that might be made.

Perhaps the most important contribution Carnot made to thermodynamics was the process of abstraction of the essential features of the steam engine as it was known in his day into a more general, 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 in the contemporary versions of the steam engine. By idealizing the engine, he could give clear answers to his original two questions that were impossible to dispute.

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

He saw very clearly, intuitively, that he could give very definite answers to the two questions set before the reader. 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 there is supposed to be no conduction of heat between parts of the engine at different temperatures. He knew that the mere conduction of heat between bodies at different temperatures is a wasteful, irreversible process and must be eliminated if the heat engine is to have the 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." By "motive power of heat," we would today use the term "efficiency of a reversible heat engine," and by "transfer of caloric," we would mean 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 then due in steam engines not to actual consumption of the caloric but to its transportation from a warm body to a cold body.

—Carnot 1960, p. 7


In the fall of caloric the 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

Towards the second law

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot however further postulated that some caloric is lost, not being converted to mechanical work. Hence no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.

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

Reception and later life

The impact of the Carnot cycle on the engineering development of the steam engine was probably pretty small. It has been remarked, in fact, that "the development of thermodynamics owes more to the steam engine, than the development of the steam engine owes to thermodynamics." The practical developments, as is so often the case in science, led the way.

Carnot’s book apparently received very little attention from his contemporaries at first. The only citation within a few years after his publication was a review of it in a periodical “Revue Encyclopédique,“ which was a journal that covered a wide range of topics in literature. The work only began to have a real impact when modernised by Émile Clapeyron, in 1834 and then further elaborated upon by Clausius and Kelvin, who together derived from it the notion of entropy and the second law of thermodynamics.


Carnot died in a cholera epidemic when he was only 36 in 1832. (Asimov 1982, p. 332) Because of the concern of cholera, a lot of his belongings and writings were buried together with him after his death. Thus only a handful of his scientific writings survived besides his book.

After the publication of his book in 1824, his book quickly went out of print and for some time his book was very difficult to obtain. For example, Kelvin had great difficulty in getting a copy of Carnot's book. Nowadays, his book in French can be downloaded electronically. An English translation of his book was published by Dover in 1960 and then reprinted by Peter Smith in 1977. Some of his posthumous manuscripts were also translated into English and included. (Please see reference.)

Carnot published his book in the days of steam engines. His theory explained why steam engines using superheated steam were better because of the higher temperature of the hot reservoir involved. Carnot's theory did not help to improve the efficiency of steam engines in the beginning; his theory only helped to explain why an existing practise was better. Only towards the end of the nineteenth century was Carnot's idea that the heat engine efficiency can be increased by increasing the temperature of the hot reservoir put into practice by, for example, Rudolf Diesel (1858-1913) who was quite fascinated by Carnot's theory and designed an engine (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 than a steam engine. (Reference: "The Diesel motor", Journal of the Franklin Institute, November 1901.) Thus eventually, Carnot's book had a real impact on the design of practical engines.


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)

* 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., "Sadi Carnot", Scientific American 245 (2): 102–114

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


* O'Connor, John J. & Robertson, Edmund F., "Nicolas Léonard Sadi Carnot", MacTutor History of Mathematics archive
* An animation of the Carnot cycle as a java applet
* Reflections on the Motive Power of Heat, English translation by R.H. Thurston
* "Sadi Carnot and the Second Law of Thermodynamics", J. Srinivasan, Resonance, November 2001, 42 (PDF file)

* Witten was mentioned in the comic Ex Machina.

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