Figure 1. Sensitivity of life-cycle cost analysis to gasoline prices. Carnot, Nicolas Léonard Sadi (1796–1832)
Sadi Carnot, French physicist and engineer, was born in Paris during the French Revolution. He was the eldest son of Lazare Carnot, a military engineer known for writings on mathematics, mechanics, military strategy and politics. Lazare was a major government official under the First Republic that had begun in 1789, and often was described as the "Organizer of Victory" for his training and equipping of the raw recruits called to arms to defend France. Lazare had a great interest in the theory and building of machines of all kinds, an interest he passed on to his son.
Sadi Carnot's early education in mathematics, physics, languages and music was provided at home by his father. In 1812 he entered the prestigious Ecole Polytechnique, a college intended mainly for future military officers, and received a rigorous training in mathematics and science. In 1813 Carnot petitioned Napoleon to allow the Polytechnique students to help defend France against their European attackers. Napoleon granted this request and in March 1814 Carnot and his comrades from the Polytechnique fought in vain to keep the attacking armies out of Paris. Later that year Carnot graduated tenth in his class of sixty-five from the Polytechnique. He then studied military engineering at the Artillery College in Metz, and from 1816 to 1818 served as a second lieutenant in charge of planning fortifications.
Carnot soon realized that he did not have the temperament of a soldier and in 1818 left the army. After leaving the army Carnot took up residence in his father's former Paris apartment, and was presumably supported by his family whiile he attended classes at Sorbonne, the College de France, and the Conservatoire des Arts et Metiers. He also frequently visited factories and workshops, both to see steam engines actually in use, and to learn more about the economics of such industrial use of energy. There were rumors that he did at least on a few occasions receive some consultant's fees for his advise, but there was no clear documentary evidence of this. In 1827 he returned to active military service with the rank of captain, but this lasted only a little more than a year. He resigned in 1828 and died of cholera four years later in Paris.
Sadi Carnot has been called "the founder of the science of thermodynamics." In 1824, when he was twenty-eight, he first became interested in steam engines. All that time, Great Britain led the world in the design and improvement of such engines for industrial purposes. Always the French patriot, Carnot wanted his country to surpass the British, who had spawned the Industrial Revolution. He thought that a more scientific discussion of steam engines based on sound physical principles might reveal more about such engines than had the highly practical, engineering-type approach of the British pioneers.
Carnot developed the concept of an ideal "Carnot engine" (i.e., one in which all physical processes were completely reversible) to study engine efficiency and to apply his results to practical steam engines. Carnot demonstrated that this idealized engine would be more efficient than any practical steam engine ever built or that could be built. Carnot's engine consisted of a gas in a cylinder fitted with a frictionless piston. He imagined a "cycle," in which the gas absorbed heat from a hot source at temperature TH, expanded and did work by pushing the piston outward, gave up heat to a colder condenser at temperature TC, and then contracted, returning to exactly the same state as at the beginning of the cycle. This cycle later came to be called a "Carnot" cycle by researchers in the fields of heat and thermodynamics.
From his study of this cycle, Carnot concluded that the engine efficiency was independent of the working substance (e.g., steam or air). He also found that the maximum possible efficiency of an ideal engine (i.e., the ratio of the work done to the heat delivered from the hot source) was in every case 
There is a problem with Carnot's analysis, however, since at that time almost all physicists (including Carnot) thought heat consisted of a substance called "caloric," which could not be created or destroyed. As a result, the amount of heat taken from the hot source at temperature TH would have to be the same as that delivered to the cold reservoir at temperature TC. Because no heat was converted into work, the efficiency of such an engine would be zero.
It is noteworthy, however, that some of Carnot's notes that were published together with his classic treatise Réflexions sur la puissance motrice de feu (Reflections on the Motive Power of Fire), written in 1824 but only formally published in 1878, contain the following sentences: "When a hypothesis no longer suffices to explain phenomena, it should be abandoned. This was the situation with caloric, which physicists regarded as matter, as a subtle fluid." He goes on to say that Count Rumford's experiments (1798) had shown that heat is produced by motion, for example, by the rubbing of two objects together, which increases the molecular motion in the objects. When this concept of heat was introduced into Carnot's 1824 manuscript, there emerged a lucid statement of the conservation of energy principle—what became the first law of thermodynamics.
Carnot's research also made a major contribution to the second law of thermodynamics. Since the maximum efficiency of a Carnot engine is given by 1 -TC/TH, if the engine is to be 100 percent efficient (i.e., emax = 1), TC must equal zero. This led William Thomson (Lord Kelvin) to propose in 1848 that TC must be the absolute zero of the temperature scale later known as the "absolute scale" or "Kelvin scale."
Because Carnot's 1824 manuscript remained unpublished at the time of his death in 1832, it was left to Kelvin and Rudolf Clausius to show how the second law of thermodynamics was implicit in Carnot's work. For this reason Kelvin once referred to Carnot as "the profoundest thinker in thermodynamic philosophy in the first thirty years of the nineteenth century."
Bibliography
Challey, J. F. (1971). "Carnot, Nicolas Léonard Sadi". In Dictionary of Scientific Biography, Vol. 3, ed. Charles Coulston Gillispie. New York: Scribner.
Gillispie, C. C. (1971). Lazare Carnot Savant. Princeton: Princeton University Press.
Harismendy, P. (1995). Sadi Carnot: L'ingénieur de la Républic. Paris: Perrin.
Kuhn, T. S. (1955). "Carnot's Version of Carnot's Cycle." American Journal of Physics 23:91–95.
Kuhn, T. S. (1977). "Energy Conservation as an Example of Simultaneous Discovery." In Kuhn: The Essential Tension, pp. 66–104. Chicago: University of Chicago Press.
Mendoza, E., ed. (1960). Reflections on the Motive Power of Fire by Sadi Carnot and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. New York: Dover Publications, Inc.
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