Nicolas Léonard Sadi Carnot

For the president of France fom 1887-1894, see Marie François Sadi Carnot. Nicolas Léonard Sadi Carnot (June 1 1796 - August 24 1832) was a French physicist, mathematician and engineer who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics.

Life

Born in Paris, Sadi Carnot was the son of the eminent geometer Lazare Nicholas Marguerite Carnot and brother of Hippolyte Carnot. His father named him for Sadi of Shiraz (One of the most famous persian poets).

From age 16, 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.

He died in Paris of cholera.

Reflections on 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, 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%. Today, owing to Carnot's influence, efficiency of engine design is at best 40%.

The Carnot cycle

(For more details see Carnot heat engine) 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 be 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." 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.

External links

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)

1796 births | 1832 deaths | French mathematicians | 19th century mathematicians | Alumni of the École Polytechnique

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