Nicolas Léonard Sadi Carnot

For the president of France from 1887-1894 and nephew of Nicolas Léonard, see Marie François Sadi Carnot.

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Sadi Carnot in the dress uniform of a student of the École polytechnique.

Nicolas Léonard Sadi Carnot (June 1 1796 - August 24 1832) was a French physicist and military engineer who 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. Technically, he is the world's first thermodynamicist, being responsible for such concepts as Carnot efficiency, Carnot theorem, Carnot heat engine, and others.

Life

Born in Paris, Sadi Carnot was the son of the eminent military leader and geometer, Lazare Nicholas Marguerite Carnot, brother of Hippolyte Carnot, and uncle of Marie François Sadi Carnot. His father named him for the Persian poet Sadi of Shiraz.

In 1812, at the age of 16, Carnot 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 in 1814, he became an officer in the French army. Carnot's father, who had aligned himself with the empire under Napoleon, was exiled after the French monarchy was restored in 1815, making any career moves on his part difficult. He retired from the military in 1820, receiving a stipend of half his salary. He moved to Paris, where he took a strong interest in the Association Polytechique, formed by the Polytechnic's former students. He also interacted with figures in the industrial and scientific circles in which he took an interest. Carnot traveled throughout France and gathered as much information on the commercial and industrial state of the country as he could. He also attended lectures at the Sorbonne and and the Ecole des Mines.

On the basis of his experience, and perhaps with the impetus of his father, who had also written on the efficiency of machines, Carnot published in 1824 a pamphlet in which he investigated the process by which heat engines such as a steam engine, produce work. He concluded that there is a maximum efficiency that any sort of heat engine can achieve, and this efficiency is dependent on the high and low temperatures between which the engine operates. He demonstrated this fact by showing that if it were not true, that it would be possible to create energy from nothing.

The importance of his work was difficult to discern at the time. A friend, Pierre-Simon Girard, tried to circulate Carnot's pamphlet, but he failed to generate interest in it. Some of its contents appeared in Revue Encyclopedique. Some interest was finally generated in the engineering community.

In 1832, Carnot took ill and died from Cholera. An examination of his papers after his death indicates that he had jettisoned the prevailing theory of heat based on caloric, and had begun to explore the possibility of an equivalence of work and heat, the principles of which became evident 15 years after his death.

"From some ideas I have formed on the theory of heat," he wrote, "the production of one unit of motive power requires the distruction of 2.70 units of heat" (Caullery 1934, 99). A translation of this quantity to current units would have placed him within 12 percent of current determinations of the equivalence of work and heat accepted today.

These notes, preserved by Carnot's brother, Hyppoltye, and published in 1871, also includes an unambiguous statement regarding the equivalence of heat and work and of the conservation of energy.

"Heat is nothing more than motive power, or, in other words, the motion that has changed form. Wherever motive power is produced, there is always production of heat in a quantity precisely proprotional to the motive power destroyed. Conversely, there there is destruction of heat, there is production of motive power" (Bejan 1997, 35).

The motive power of fire

Background

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, James 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. 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%. Carnot showed that typically the efficiency of an engine design is always limited to about 40%.

The Carnot cycle

See main: 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 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 operates. 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. 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.

and

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.

Towards the second law

In his ideal model, the head 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

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." <<WHO SAID THIS? IF WE ARE TO USE THIS QUOTE, WE NEED TO CITE THE SOURCE. OTHERWISE, WE SHOULD ELIMINATE THE QUOTE AND REPHRASE THE MAIN POINT HERE.>> The practical developments, as is so often the case in science, led the way.

Carnot’s memoir 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 Encyclopedique,“ 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.

See also

• Heat
• Heat engine
• Thermodynamics

References

ISBN links support NWE through referral fees

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• Caullery, Maurice. 1934. French Science and Its Principal Discoveries Since the Seventeenth Century. Manchester, NH: Ayer Company Publishers. 96-99. ISBN: 0405065841illus
• Morus, Iwan Rhys. 2005. When Physics Became King. Chicago: University of Chicago Press. 128-131. ISBN 0226542017.
• Bejan, Adrian. 1997. Advanced Engineering Thermodynamics. New York: Wiley.

External links

• John J. O'Connor and Edmund F. Robertson. Nicolas Léonard Sadi Carnot at the MacTutor 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)

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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