Carnot's scientific work attracted little attention during his lifetime, but in 1834 it became the object of a detailed commentary and explanation by another French engineer,Émile Clapeyron. Clapeyron's commentary in turn attracted the attention ofWilliam Thomson (later Lord Kelvin) andRudolf Clausius. Thomson used Carnot's analysis to develop an absolutethermodynamic temperature scale, while Clausius used it to define the concept ofentropy, thus formalizing thesecond law of thermodynamics.
Sadi Carnot was the son ofLazare Carnot, an eminent mathematician, engineer, and commander of theFrench Revolutionary Army and later of theNapoleonic army. Some of the difficulties that Sadi faced in his own career might have been connected to the persecution of his family by therestored Bourbon monarchy after the fall of Napoleon in 1815. Sadi Carnot died in relative obscurity at the age of 36, but today he is often characterized as the "father ofthermodynamics".
Portrait of Sadi's father, Lazare Carnot (1753–1823) as aNapoleonic general, by an unknown artist,ca. 1815,Museum of French History, Versailles
Sadi Carnot was born in Paris on 1 June 1796, at thePetit Luxembourg palace, where his fatherLazare resided as one of the five members of theDirectory, the highest governing body of theFrench First Republic in the immediate aftermath of theThermidorian Reaction. His mother, Sophienée Dupont (1764-1813), came from a wealthy family based inSaint-Omer.
Sadi's father Lazare named him after the 13th-century Persian poetSadi of Shiraz. An elder brother, also named Sadi, had been born in 1794 but died in infancy the following year. "Sadi" is the only given name that appears in the second-born's civil birth certificate, dated 14prairial, year IV in theFrench Republican calendar.[1] On 11 July 1796, the child was baptized in the Catholic church ofSaint-Louis-d'Antin as "Nicolas-Léonard Dupont". The principal witness at that baptism was his maternal grandfather, Jacques-Antoine-Léonard Dupont. The father is wrongly identified in the baptismal record as Jacques-Léonard-Joseph-Auguste Dupont (who was, in fact, the child's maternal uncle).[2] Following the biographical notice published long after his death by his brother Hippolyte, most sources now give his full name as "Nicolas Léonard Sadi", but there is no evidence that he ever used any name other than "Sadi".[1]
Sadi had a younger brother,Hippolyte Carnot, who was born in 1801 in Saint-Omer and who would later become a prominent politician. Hippolyte's eldest sonMarie François Sadi Carnot served asPresident of France from 1887 to 1894. Another of Hippolyte's sons was the chemist, mining engineer and politicianAdolphe Carnot. Sadi himself would remain a bachelor and left no descendants.
Portrait of Sadi Carnot, aged 10, by Félie Carnot, 1806. Académie François Bourdon,Le Creusot, France
The young Sadi was educated first at home by his father and later at theLycée Charlemagne, in Paris, where he prepared for the examinations required to enter theÉcole polytechnique, which his father had helped to establish. In 1811, at the age of 16 (the minimum allowed) Sadi Carnot became a cadet of the École polytechnique, where his classmates included the future mathematicianMichel Chasles. Among his professors wereAndré-Marie Ampère,Siméon Denis Poisson,François Arago, andGaspard-Gustave Coriolis. Thus, the school had become renowned for its instruction in mathematics and physics.[3]
During theBattle of Paris in March of 1814, Carnot, Chasles, and other cadets of the École polytechnique participated in the defense ofVincennes. This appears to have been Carnot's only experience of battle. Carnot graduated in 1814 and was admitted at theÉcole d'application de l'artillerie et du génie ("School of Applied Artillery and Military Engineering") inMetz, where he completed a two-year course. Sadi then became an officer in theFrench army's corps of engineers.
Carnot's father Lazare served asNapoleon's minister of the interior during the "Hundred Days", and, afterNapoleon's final defeat in 1815, Lazare was forced into exile in the German city ofMagdeburg. Sadi's position in the army, under therestored Bourbon monarchy of KingLouis XVIII, became increasingly difficult.[4] Lazare never returned to France, dying in Magdeburg in 1823.
Sadi became acaptain in theGénie and was posted to various locations, where he inspectedfortifications, tracked plans, and wrote many reports. However, it appeared that his recommendations were ignored and that his career was stagnating.[4] On 15 September 1818, at the age of 22, he took a six-month leave to prepare for the entrance examination to the newly formedGeneral Staff in Paris. Carnot passed the exam and joined the General Staff in January 1819, with the lower rank oflieutenant.[4] He remained on call for military duty, but from then on he dedicated most of his attention to private intellectual pursuits and received only two-thirds pay.[4]
In Paris, Carnot befriendedNicolas Clément andCharles-Bernard Desormes and attended lectures on physics and chemistry at theSorbonne and theCollège de France. He also attended theConservatoire national des arts et métiers, where he followed the lectures on chemistry by Clément and those on economics byJean-Baptiste Say.[5] Carnot became interested in understanding the limits to improving the performance ofsteam engines, which led him to the investigations that became hisReflections on the Motive Power of Fire, published at his own expense in June 1824.
Carnot was finally promoted to his former rank of captain in September of 1827, but the following April he quit the army, having completed only fifteen months of active service and without right to a pension.[6] In a directory of alumni of the École polytechnique published by Ambroise Fourcy in 1828, Carnot is listed as "maker of steam engines". This and some other indications suggest that Carnot may have been involved in a practical scheme for the improvement of steam engines, but no patents or other concrete evidences of that work have emerged.[7]
Carnot initially welcomed theJuly Revolution of 1830, which ended the Bourbonic regime underCharles X and established a newconstitutional monarchy under "Citizen King"Louis Philippe.[10] According to his brother Hippolyte, there was some discussion among leaders of the new regime of incorporating Sadi to theChamber of Peers, as he could be considered to have inherited theImperial title of "Count Carnot" that Napoleon had bestowed on his father Lazare in 1815. Nothing came of this, however, perhaps because Sadi'srepublican convictions prevented him from accepting a hereditary distinction.[11]
According to recollections published long after Sadi's death by his brother Hippolyte, Sadi was an avid reader ofBlaise Pascal,Molière andJean de La Fontaine.[12] Hippolyte recalled that Sadi was aphilosophical theist who believed in divine causality but not in divine punishment. Carnot wrote in his private papers that "what to an ignorant man is chance, cannot be chance to one better instructed". He was critical of established religion, but spoke in favor of "the belief in an all-powerful Being, who loves us and watches over us".[13]
Hippolyte also described his brother as a talentedviolin player, interested principally in the music ofJean-Baptiste Lully andGiovanni Battista Viotti, who also cultivated gymnastics, fencing, swimming, dancing, and skating.[14] According to historian of science James F. Challey, "although sensitive and perceptive", Carnot "appeared extremely introverted, even aloof, to all but a few close friends".[15] This may help explain why Carnot's work failed to make any significant impression within either the scientific or the engineering community during his lifetime.
In the summer of 1832 Carnot apparently suffered from a severe bout ofscarlet fever. On 3 August he was interned in a private sanatorium run by psychiatristJean-Étienne Esquirol and located inIvry, just south of Paris.[16] According to the hospital record, he was cured from "mania" but then died ofcholera on 24 August.[17] Carnot was buried in the old cemetery of Ivry, close to what is now theMairie d'Ivry station.[18]
Title page of Sadi Carnot'sRéflexions sur la puissance motrice du feu ("Reflections on the motive power of fire"), published in Paris in June 1824
Sadi Carnot's contribution to the development ofthermodynamics is contained in his only published work, a short book titledRéflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance ("Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power") published in Paris in June of 1824 by Bachelier, with Carnot himself paying for the printing of the 600 copies.[19] The work attracted little attention during his lifetime and virtually disappeared from booksellers and libraries.[20] An article published in 1834 (two years after Carnot's death and ten years after the publication of his book) by the engineer and fellowpolytechnicienÉmile Clapeyron finally succeeded in calling attention to Carnot's work, which some years later was used byLord Kelvin andRudolf Clausius to define the concepts ofabsolute temperature,entropy, and thesecond law of thermodynamics.[21]
Thomas Newcomen invented the first practical piston-operatedsteam engine in 1712. Some 50 years after that,James Watt made his celebrated improvements, which were responsible for greatly increasing the usefulness of steam engines. When Carnot became interested in the subject in the 1820s, steam engines were in increasingly wide application in industry and their economic importance was widely recognized. Compound engines (engines with more than one stage of expansion) had already been invented, and there was even a crudeinternal combustion engine, known as thepyréolophore and built by the brothersClaude andNicéphore Niépce, with which Carnot was familiar and which he described in some detail in his book.
That practical work on steam engines and the intuitive understanding among engineers of some of the principles underlying their operation co-existed, however, with an almost complete lack of a scientific understanding of the physical phenomena associated withheat. The principle ofconservation of energy had not yet been clearly articulated and the ideas surrounding it were fragmentary and controversial. Carnot himself accepted the view, prevalent in France and associated with the work ofAntoine Lavoisier, that heat is a weightless and invisiblefluid, called "caloric", which may be liberated by chemical reactions and which flows from bodies at highertemperature to bodies at lower temperature.
In his book, Carnot sought to answer basic questions: "Is there a limit to the work that can be generated from a given heat source?" and "Can the performance of an engine be improved by replacing steam with a differentworking fluid?". Engineers in Carnot's time had tried, using highly pressurized steam and other fluids, to improve theefficiency of engines. In these early stages of engine development, the efficiency of a typical engine – the useful work it was able to do when a given quantity offuel was burned – was only about 5–7%.[22]
Carnot's book was only 118 pages long and covered a wide range of topics about heat engines in what Carnot must have intended to be a form accessible to a wide public. He made minimal use of mathematics, which he confined to elementary algebra and arithmetic, except in some footnotes. Carnot discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam-engine design, and even included some ideas of his own regarding possible practical improvements. However, the central part of the book was an abstract treatment of an idealized engine (theCarnot cycle) with which the author sought to clarify the fundamental principles that govern all heat engines, independently of the details of their design or operation. This resulted in an idealizedthermodynamic system upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engines.
Cross section of Carnot's heat engine. In this diagram,abcd is a cylindrical vessel,cd is a movable piston, andA andB are thermal reservoirs at different temperatures. The vessel may be placed in contact with either reservoir or removed from both. This is Figure 1 in Carnot's book.[23]
Carnot considered an idealized process in which heat from athermal reservoir at a high temperature flows very slowly (and thusreversibly) into the gas contained in a cylinder enclosed by a movable piston. This gives anisothermal expansion of the gas that pushes out the piston and can be used to perform useful work. This does not yet constitute an engine because the piston must be returned to its original position in order for the machine to run cyclically.
Carnot then proposed reducing the temperature of the gas by anadiabatic expansion, during which the cylinder is thermally isolated so as to prevent heat from entering or leaving the gas. Once the temperature of the gas has reached the same value as that of the colder reservoir, the cylinder is put into thermal contact with that reservoir and the gas undergoes an isothermal compression, during which it very slowly (and thus reversibly) rejects heat into the reservoir.
To close the cycle, the temperature of the gas in the cylinder can be raised by adiabatic compression, until it reaches a value equal to the temperature of the hotter reservoir. This succession of isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression can then be repeated as many times as desired, generating a net amount of work each time, at the expense of a transfer of heat from the hotter reservoir to the colder reservoir.
As Carnot explained, such a cycle constitutes the most efficient heat engine possible (given the temperatures of the two reservoirs). This is partly because of the (trivial) absence of friction, heat leakage, or other incidental wasteful processes, but mainly because it involves no conduction of heat between parts of the engine at different temperatures. Carnot understood that the conduction of heat between bodies at different temperatures is a wasteful andirreversible process, which must be minimized if the heat engine is to achieve its maximum efficiency.
Carnot cycle in apressure vs.volume diagram. This graphical representation of Carnot's cycle was introduced byÉmile Clapeyron in 1834.
Because Carnot's cycle is reversible, it can also be used as arefrigerator: if an external agent supplies the needed mechanical work to move the piston, the sequence of transformations of the gas will absorb heat from the colder reservoir and reject it into the hotter reservoir. Carnot argued that no engine operating between reservoirs at two given temperatures could deliver more work than his reversible cycle. Otherwise, the more efficient engine could run Carnot's cycle in reverse as a refrigerator, thus returning all of the "caloric" from the colder back to the hotter reservoir, with some positive amount of work left over to perform a further useful task. Carnot assumed that such a process, in which no net "caloric" was consumed while positive work could be done forever, would be aperpetual motion and therefore forbidden by the laws of physics.
This argument led Carnot to conclude that
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.[24]
Carnot understood that his idealized engine would have the maximum possiblethermal efficiency given the temperatures of the two reservoirs, but he did not calculate the value of that efficiency because of the ambiguities associated with the various temperature scales used by scientists at the time:
In the fall of caloric, motive power undoubtedly increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.[25]
Later in his book, Carnot considered a heat engine operating very close to theboiling point of water, alcohol, or some other working fluid. The transition between the liquid and vapor phases involves a sudden change indensity (and therefore in the volume occupied by the fluid) while alatent heat is needed to transform some amount of the fluid from one phase to the other as the temperature stays constant. This is modernly called a first-orderphase transition. By requiring that the volume change associated with such a transition not be available to construct what he characterized as a perpetual motion device, Carnot arrived at what would later be formalized mathematically as the "Clausius–Clapeyron relation". In theFeynman Lectures on Physics, theoretical physicistRichard Feynman stresses that this result is due to Carnot and gives a modernized version of Carnot's original argument.[26]
In 1849,James Thomson applied Carnot's reasoning to thefreezing of water (i.e., the phase transition between liquid water and ice), and concluded that it predicted that themelting point of ice must decrease if an external pressure is applied to it, an effect that no one had ever proposed or studied before. James Thomson's prediction was later confirmed experimentally by his brother William Thomson (the futureLord Kelvin), who found that the data agreed fully with Carnot's analysis.[27] Kelvin later said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning."[28]
Carnot published his book in June 1824, and it was presented at that time to theFrench Academy of Sciences byPierre-Simon Girard. Girard also published a praiseful but rather broad review of the book in theRevue encyclopédique, but after that the book seems to have fallen into obscurity. It was only after the publication of an extensive commentary and explication of Carnot's work byÉmile Clapeyron in 1834 that engineers and scientists began to take an interest in Carnot's contributions. Clapeyron's article was translated into English in 1837 and into German in 1843.[20]
William Thomson read Clapeyron's paper in 1845, while visiting the Paris laboratory ofHenri Regnault, but it was only at the end of 1848 that Thomson was able to read Carnot's original work, in a copy provided to him byLewis Gordon. Independently of Thomson, the German physicistRudolf Clausius also based his study ofthermodynamics on Carnot's work. Clausius modified Carnot's arguments to make them compatible with themechanical equivalence of heat. This then led Clausius to define the concept ofentropy and to formulate thesecond law of thermodynamics.
Carnot's text was re-printed in 1871 in theAnnales Scientifiques of theÉcole normale supérieure, and again by Gauthier-Villars in 1878 with the collaboration of Hippolyte Carnot. An English translation of the book was published in 1890 byR. H. Thurston.[29] That version has been reprinted in recent decades byDover. In 1892, Lord Kelvin referred to Carnot's essay as "an epoch-making gift to science".
Carnot published his book in the heyday of steam engines. His theory explained the advantage of engines that use superheated steam, since they absorb heat from a reservoir at a higher temperature. Carnot's work did not, however, lead to any immediate practical improvements of steam technologies. It was only towards the end of the nineteenth century that engineers deliberately implemented Carnot's key concepts: that the efficiency of a heat is improved by increasing the temperature at which heat is drawn and by minimizing the flow of heat between bodies at different temperatures. In particular,Rudolf Diesel used Carnot's analysis in his design of thediesel engine, in which heat is injected at a much higher temperature than in the older steam engines, and in which the heat from the combustion of the fuel goes primarily into expanding the air in the cylinder (rather than into increasing its temperature).[30]
Grave of Sadi Carnot in the old cemetery ofIvry-sur-Seine
Sadi's younger brotherHippolyte obscured the details of Sadi's death and destroyed most of his personal papers.[31] Much later, in 1878, when Carnot's essay had come to be widely recognized as a founding document of the new science of thermodynamics, Hippolyte sponsored the publication of a new edition that included a "Biographical notice on Sadi Carnot" written by Hippolyte, along with some "Excerpts from unpublished notes by Sadi on mathematics, physics and other subjects". These are the only sources of information on many aspects of Sadi's life and thought. In the opinion of historian of science Arthur Birembaut, the "smokescreen" that Hippolyte drew over his brother's life makes it impossible now to reconstruct the details of Sadi's career, his relationship with other physicists and engineers, and the circumstances of his death.[32]
Among the private notes published by Hippolyte in 1878, there is material indicating that Sadi Carnot had, by the spring of 1832, rejected the caloric theory and accepted theequivalence of heat and work.[33] In his notes, Carnot wrote that:
Heat is simply motive power, or rather motion that has changed form. It is a movement among the particles of bodies. Wherever there is destruction of motive power there is, at the same time, production of heatin quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, wherever there is destruction of heat there is production of motive power.[33][11]
In those same notes, Carnot estimated that 1 kilocalorie is the equivalent of 370 kg·m, whereas the currently accepted value is 427 kg·m.[34] Carnot did not, however, publish any of that work. It is possible that his uncertainty about the consequences for the validity of his previous analysis in theReflections of rejecting the caloric theory might explain why he did not follow up on his work of 1824 before his untimely death.
Birembaut, Arthur (1974). "À propos des notices biographiques sur Sadi Carnot: quelques documents inédits" [Regarding the biographical notices of Sadi Carnot: some unpublished documents].Revue d'histoire des sciences (in French).27 (4):355–370.doi:10.3406/rhs.1974.1107.JSTOR23631750.
Carnot, Sadi (1988). Mendoza, E. (ed.).Reflections on the Motive Power of Fire And Other Papers on the Second Law of Thermodynamics. Mineola, NY: Dover Publication.ISBN978-0486446417.
Dixit, Uday Shanker; Hazarika, Manjuri; Davim, J. Paulo (2017). "History of Thermodynamics and Heat Transfer".A Brief History of Mechanical Engineering. Springer. pp. 73–98.doi:10.1007/978-3-319-42916-8_4.ISBN978-3-319-42914-4.
Fox, Robert (2012). "Sadi Carnot on Political Economy. Science, Morals, and Public Policy in Restoration France". In Buchwald, Jed Z. (ed.).A Master of Science: History Essays in Honor of Charles Coulston Gillispie. Archimedes. Vol. 30. Springer. pp. 412–427.doi:10.1007/978-94-007-2627-7_23.ISBN978-94-007-2626-0.
Taton, René; et al. (1976).Sadi Carnot et l'essor de la thermodynamique [Sadi Carnot and the rise of thermodynamics] (in French). Paris: Éditions duC.N.R.S.ISBN9782222018186.
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