Nicolas Léonard Sadi Carnot

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

<<THIS ARTICLE DOES NOT CITE ITS SOURCES.>>

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, Hippolyte, 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, 34).

The motive power of fire

Background

The steam engine was a late 18th century invention that had undergone important improvements during Carnot's lifetime. An understanding of the nature of heat was still lacking, however, as was an understanding of the manner in which heat is tranformed into work. The prevalent theory of heat was the caloric theory, which supposed that heat was a sort of weightless, invisible fluid that flowed from a hotter to a cooler body.

Engineers of Carnot's time determined that the efficiency of an operating steam engine, the work generated from a given quantity of fuel, such as from burning a lump of [[coal] was a mere 3 percent. Carnot would show that the maximum achievable efficiency was about 40 percent.

The Carnot cycle

See main: Carnot heat engine and Carnot cycle

Carnot wished to investigate the maximum efficiency possible in a steam engine. He broke the stages of a working engine into cycles that the substance used in the engine goes through to generate what he descriptively calls motive power. These stages are now referred to as the "Carnot cycle," and are the foundation of the study of thermodynamics. Carnot does use the steam engine as a guide and as an example. In his ground-breaking work entitled Reflections on the Motive Power of Fire, he observed that, in a heat engine of any kind (an engine that uses a heated substance to produce work), heat must be transferred from a hotter body to a cooler body. By analyzing the cycle in which this heat transfer occurs, he concluded that

1. there is a maximum motive power that can be obtained through a given difference in temperature.

2. The maximum quantity of motive power is independent of the substance (such as steam) used;

3. the motive power generated depends only on the initial and final temperatures of the bodies between which the heat transfer takes place, and is greater for a greater difference in temperature;

4. the qunatity of motive power developed between two temperatures is a maximum when the process is reversible.

Carnot argued that if there were a way to produce more motive power than through a reversible process, that it would be possible to produce perpetual motion.

"Such a creation, Carnot argued, "is entirely contrary to ideas now accepted, to the laws of mechanics and of sound physics. It is inadmissible. We should then conclude that the maximum of motive power resulting from the employment of steam is also the maximum of motive power realizable by any means whatever."

Although Carnot showed that the efficiency of a reversible heat engine is a function of the two temperatures of the reservoirs between which it operates, he did not give the exact form of the function. Based on some crude assumptions, he did attempt to evaluate the maximum efficiency of a heat engine and compare it to the best steam engines in operation at the time. He concluded that those engines operate at 1/20th of the maximum possible theoretical efficiency.

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 0405065841.
• 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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