Summary

Nicolas Léonard Sadi Carnot was a French physicist and engineer born on June 1, 1796 in Paris and died on August 24, 1832 in Ivry-sur-Seine.

During his short career (he died of cholera at the age of 36), Sadi Carnot published only one book (like Copernicus): Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance, in 1824, in which he expressed, at the age of 27, what turned out to be his life's work and an important book in the history of physics.

In this work he laid the foundations of an entirely new discipline, thermodynamics. At the time, the term did not even exist; it was William Thomson who invented it in the mid-19th century. However, it was Sadi Carnot, despite the imprecision of some of his concepts (his acceptance of the theory of heat and the axiom of the conservation of heat), who discovered this science that was as fundamental from a theoretical point of view as it was fruitful in practical applications.

Sadi Carnot formulated the reasoned account of the heat engine and the basic principles according to which any power plant, any combustion or jet engine is designed today. More remarkably, this genesis took place when no predecessor had yet defined the nature and scope of the subject. By relying on purely technical concerns, such as improving the performance of the steam engine, Sadi Carnot's intellectual path is original and heralds important developments that took place at this pivotal time for modern science.

The eldest son of Lazare Carnot (1753-1823), known as "the Great Carnot" or "the organizer of Victory," Sadi Carnot was born in Paris, at the Petit-Luxembourg Palace, where his father, one of the five executive directors of the Republic, had his apartments. His first name comes from the name of the Persian poet Saadi of Shiraz, much admired by his father.

At the time of Sadi's birth, Lazare Carnot was at the height of his career. A mathematician and engineer, student of Gaspard Monge, author of an Essay on machines in general (1783), Lazare Carnot was also a soldier, a leader of men and a revolutionary. He was elected to the Constituent Assembly of 1789 and then to the Convention, and voted the death of King Louis XVI. During the wars of the French Revolution, as a member of the Committee of Public Safety, he acquired the nickname of "organizer of the Victory". After being a member of the Directory, he was Napoleon Bonaparte's Minister of War for six months in 1800 and then Minister of the Interior during the Hundred Days in 1815. In October of the same year, after Napoleon's defeat, he was exiled as a regicide. He lived in Belgium, then in Poland and Germany, where he died, without ever returning to France.

His mother, Sophie Dupont (1764-1813), came from a wealthy family in Saint-Omer.

Sadi Carnot had a younger brother, Hippolyte Carnot (1801-1888), who had a political career: he was a deputy from 1839 to 1848, minister of education in 1848, refused to support the Second Empire and became a deputy again under the Third Republic, then was elected to the Senate in 1875 and a member of the Académie des sciences morales et politiques in 1887. Sadi Carnot was the uncle of Marie François Sadi Carnot (also commonly known as Sadi Carnot), who was elected President of the French Republic in 1887 and assassinated in 1894 by the anarchist Sante Geronimo Caserio.

He never married and had no descendants.

Young years

Following the coup d'état of September 4, 1797, Lazare Carnot had to leave France, a situation that lasted until January 1800, when he was pardoned by Bonaparte; during this period, Sadi Carnot lived with his mother in the family home in Saint-Omer. In August 1807, Lazare Carnot, returned to private life by the suppression of the Tribunate, decides to take care of the education of his two sons, teaching them mathematics, sciences, languages and music.

In 1811, Sadi Carnot entered the Lycée Charlemagne, in Pierre-Louis Marie Bourdon's preparatory class, to prepare for the competitive examination for the École Polytechnique. Having reached the minimum age of 16 on June 1, 1812, Sadi Carnot was able to take the competitive examination the following August, where he was accepted 24th out of 179 and incorporated in the second division on November 2.

Polytechnician

In 1812-1813, the courses functioned normally despite the setbacks suffered by the imperial armies. His teachers were Reynaud for analysis, Poisson for mechanics, Hachette for descriptive geometry, Louis Jacques Thénard for general and applied chemistry, Jean-Henri Hassenfratz for physics, and François Arago for infinitesimal calculus and machine theory. During this first year, he was also taught by men such as Alexis Petit for physics and Pierre Louis Dulong for chemistry, whose work he later used. It seems that they even thought of transferring him immediately to the artillery section of the École de Metz in October 1813, but that they finally considered him too young.

The second year was to prove less fruitful in terms of teaching. At the end of January 1814, the integration of the students into three companies of the artillery corps of the National Guard was to gradually interrupt the progress of the teaching. On March 29 and 30, 1814, Sadi Carnot, who was one of the six corporals in the company, fought with the battalion of polytechnicians and came under fire in a harmless skirmish in the defense of the fort of Vincennes against the allies; this was probably his only battle experience. Classes resumed on April 18, but Sadi did not return until May 12. On October 12, 1814, he was declared eligible for public service, 10th on the general list of the 65 students who remained in his class. He was ranked 5th on the special list of ten students admitted to the military engineering as second lieutenants at the École d'application de l'artillerie et du génie in Metz. Thus ends a key period in his training, to which he referred when he published his Réflexions by signing his work "Sadi Carnot, former student of the École Polytechnique.

Metz School

Sadi Carnot received his brevet as an engineer cadet on October 1, 1814, and entered the École de Metz in the last days of 1814 after a leave of absence. In this prestigious school of application, heir of the Royal School of Engineering of Mézières, he followed the courses of applied mathematics and physics of François-Marie Dubuat and Jacques Frédéric Français, those of chemistry applied to military arts and pyrotechnics of Chevreuse. His certificate of second lieutenant in the 2nd regiment of sappers, marking his graduation from the school and his real entry into the military career, is dated April 2, 1817. According to tradition, he was immediately granted a three-month leave of absence, which he extended until October 15, 1817. He probably spent most of this time at the family home in Nolay with his uncle, Lieutenant General Carnot de Feulins.

First assignments

With the advent of peace in 1815, he found himself forced into the routine existence of the garrison, with few prospects. As the son of an exiled republican leader, he was considered unsafe, so his duty station was arranged to be far from Paris.

Sadi Carnot was regularly transferred, he inspected fortifications, drew up plans and wrote numerous reports. But his recommendations were apparently ignored; his career stagnated.

The ordinance of May 6, 1818 established a royal staff corps and a training school for the service of the general staff of the army. On September 15, 1818, Sadi Carnot was granted a six-month leave of absence to prepare for the entrance exam in Paris.

Installation in Paris

By order of January 20, 1819, he was admitted to the staff of Paris, with the rank of lieutenant, and placed on leave of absence, receiving two-thirds of his gross pay as a scientific worker. Living near his uncle Joseph in a small apartment in the working-class district of the Marais, which he occupied until the middle of 1831, Sadi Carnot attended classes at the Sorbonne and the Collège de France, but not at the École des Mines, for which he needed authorization from the higher administration, which he never requested, and where he could have met the young Emile Clapeyron. He was a student at the Conservatoire National des Arts et Métiers where Clément-Desormes taught a course in chemistry applied to the arts and Jean-Baptiste Say a course in industrial economics. He also frequented the Jardin des plantes and the King's Library, but also the Louvre Museum and the Italian Theatre of Paris. Sadi Carnot was interested in industrial problems, visited workshops and factories, studied the theory of gases and the latest theories of political economy. He left detailed proposals on current problems such as taxes, but mathematics and the arts fascinated him.

The members of the circle he frequented were of radical and republican tendencies, and his closest friends were Nicholas Clément and Charles Desormes, men of science and industrial chemists, editors of a "Mémoire sur la théorie des machines à feu" and the only physicists with whom he actually made contact before writing the Réflexions.

During the summer of 1820, Sadi saw his brother Hippolyte again, who had come to spend a few days in France, and who was living with his father. On June 23, 1821, the Ministry of War granted him unpaid leave to visit his father in exile in Magdeburg. There, together with his father, he began to take an interest in steam engines, since it was in Magdeburg three years earlier that the first machine had been built. As soon as he returned to Paris, he began to think about what became known as thermodynamics. His first important works date from the years 1822-1823. When his father died in August 1823, his brother Hippolyte returned to Paris and helped him to write his works "in order to make sure that they would be understood by people devoted to other studies". Since his release, Sadi stayed away from the political currents that attracted the liberal youth. He did not seem to be attracted by the organized scientific groups such as the Philomathic Society of Paris whose members had the ambition to reach the Academy of Sciences. However, he participated in a Polytechnic - industrialists meeting where it seems that he gave a presentation on a formula to represent the driving power of water vapor.

End of availability

In October 1824, the staff lieutenant woke up as Sadi, who carried out topographical work on the road from Coulommiers to Couilly-Pont-aux-Dames. In 1825 he did a similar work on the road from Villeparisis to the ferry at Gournay-sur-Marne. On December 10, 1826, the ordinance organizing the royal staff corps was signed, and on December 31, Sadi was detached to the 7th infantry regiment garrisoned in Thionville. "Engaged in matters of interest that I could not suddenly abandon without very significant losses for me," Sadi obtained a three-month leave of absence with half pay. On March 6, 1827, he reiterated his request, pointing out his lack of aptitude for service in the infantry, and obtained his reinstatement in the engineers as of March 25, 1827 and his continuation on leave, this time without pay, until September 15, 1827. After a reorganization of the staff, he was sent to Auxonne, a former stronghold of the Côte-d'Or. On September 27, 1827 he was promoted to the rank of second captain of the engineers.

Resignation

On April 21, 1828, Sadi offered his resignation from the army "for the management of my personal affairs and particularly for the care to be given to a lawsuit in which I am interested, I am far from seeing the end, seeing myself by my position out of state to exercise my functions today without compromising what I possess. On May 19, 1828, the Ministry of War accepted his resignation: since his graduation from the School of Metz, Sadi Carnot had barely completed fifteen months of active military service, including topographical surveys. As for the lawsuit in which he seems to have been involved, it is difficult to know more, even though his address book mentions the name of Giraudeau, who had a law firm on rue Sainte-Anne. Although not having attained the status of demi-solde, Sadi could now return to Paris and devote himself to a life of study and personal research.

Sadi's godfather, his maternal grandfather Dupont, had left at his death in 1807 nearly a million gold francs, of which Lazare Carnot had received a third. Sadi's share of the inheritance allowed him to lead the quiet life of a modest annuitant, but this life free of ardor and dynamism was undoubtedly made necessary by his poor health. When asked about his profession by the librarian Ambroise Fourcy for his Histoire de l'École polytechnique, Sadi Carnot declared himself to be a "builder of steam engines. However, his name does not appear in any list of manufacturers such as the one published each year in the Almanach Bottin. Did he intend to enter this profession, did he play the role of consulting engineer, did he lend money to a manufacturer, or was it just a joke? It should also be noted that Sadi Carnot never filed a patent and that he did not hold a chair or an examining position at the École centrale des arts et manufactures created in 1829 and charged with training engineers for private industry. On August 17, 1830, the Polytechnic Association was created, which brought together former students of the school and to which Sadi Carnot immediately joined.

The ordinance of February 10, 1831 provides for the creation of a company of cannoneers in each district and "at the end of petty harassments, sometimes very insignificant" Sadi is admitted into the 8th artillery company with the rank of non-commissioned officer or corporal at the most.

In August 1831, the publication of two memoirs by Pierre Louis Dulong encouraged him to resume his work on the physical properties of gases. That same year, he had an attack of scarlet fever and became seriously ill, with attacks of delirium for some time. In April 1832, the Revue Encyclopédique reported on Baron Blein's work in an article signed S.C., probably Sadi Carnot. The portrait that the artist Despoix drew of Sadi at this time shows the face of a tired man, with a worried look, whose mental equilibrium no longer seems assured.

His state of health prevented him from attending the meeting of the Polytechnic Association on June 20, 1832, and Hippolyte noted in his bibliographical note that "the excessive application to which he gave himself up made him ill towards the end of June 1832. On August 3, he was admitted to the nursing home of the alienist physician Jean-Etienne Esquirol, located at 7, rue de Seine (today rue Lénine), where the latter diagnosed mania, i.e. generalized delirium with excitement. Shortly after, the register of the Ivry nursing home indicates "cured of his mania, died on August 24, 1832 cholera". The death is declared the same day at the town hall of Ivry by the bursar of the nursing home and, it seems in a way to avoid any allusion to it, as if he had received instructions from Hippolyte. The latter also had to declare the death to the city hall of the 12th district. The civil funeral was celebrated in conditions close to anonymity. He is buried in the old cemetery of Ivry-sur-Seine. After his death, his personal effects (including his archives) were burned to prevent the spread of the disease.

Technical-scientific context

To understand Sadi Carnot's book and to appreciate the originality of the work, it is necessary to specify the situation of science and technology in the field considered during the second decade of the 19th century.

When the young Sadi Carnot entered the École Polytechnique, the only well-established science, based on mathematics, was mechanics. Chemistry, electricity, magnetism, and heat were making rapid progress but had not reached the stage of mathematical abstraction.

The science of heat had been made possible by the invention of the thermometer in the 17th century (notably that of Santorio) but remained a preoccupation of chemists and physicians. They had issued the axiom of conservation of heat that they conceived then as a substance: the "caloric".

The work of Benjamin Thompson (Lord Rumford), Pierre-Simon de Laplace, Jean-Baptiste Biot, Siméon Denis Poisson and Joseph Fourier allowed mathematicians and physicists to take an interest in heat and in particular to study heat transfer.

At the same time, meteorologists were gaining a better understanding of the role of heat in the wind or ocean current system, heat that was seen as the great driving force of the world. In particular, adiabatic heating and cooling of the air was invoked to explain field observations such as the stability of snowfields at the equator.

The first steam engines of practical application appeared at the beginning of the 18th century and functioned in the following way: steam was used to expel air from a cylinder, then the cylinder was cooled so that the steam condensed and the external atmospheric pressure caused the piston to fall back down. The steam was then allowed to refill the cylinder and the cycle was repeated (See Thomas Newcomen's machine). These machines had a slow and irregular operation but were well suited to pumping water from mines. In this context, water was the most suitable working substance, especially since it expands to about 1,800 times its original volume when transformed into steam.

In the 1760s, in order to eliminate the wasteful heating and alternating cooling of the cylinder, James Watt condensed the steam in a separate cold cylinder, or condenser, while the main cylinder was kept hot at all times. In addition, he used hot steam to move the piston down the cylinder, thus further reducing heat loss. Watt noticed that a considerable saving could be made if the steam supply was cut off before the piston moved into the cylinder: the trapped steam would continue to move the piston down with a slightly decreasing pressure. When the steam passed into the condenser, it would have some "elasticity" (pressure) left: this was called expansion action. On the other hand, James Watt never believed in high-pressure machines, which he considered too dangerous for everyday use; his influence was such that this type of machine only really developed after his death.

In 1805, a Cornish engineer, Arthur Woolf, patented the high-pressure compound engine using two successive cylinders (double compound) to achieve complete expansion of the steam: this principle has the advantage of reducing the amplitude of heating and cooling of each of the cylinders and thus saving fuel to gain in performance. Jacob Perkins, an American engineer, showed that it was possible to build a steam engine working at pressures close to 35 atmospheres. Sadi Carnot appreciated this work but pointed out that this engine had the defect of not using James Watt's principle of expansion correctly.

Carnot, like his contemporaries, was greatly impressed by England's industrial superiority over France, a power he attributed to the extensive use of the steam engine. From 1811 to 1840, the art of pumping water from the mines of Cornwall was reported regularly in the Monthly Engine reporter published by Thomas and John Lean and repeated by publications such as the Annals of Chemistry and Physics. These reports established the superiority of high-pressure machines. Moreover, by 1820, most engineers seemed convinced that there was a definite limit to the amount of work that could be done with a given amount of heat.

These data, true ephemeris, had the advantage of translating the action of the various pumping machines in a simple way and directly into units of work (weight of water and height to which it was raised). Sadi Carnot was inspired by this in his reflection on the basic principles of thermal machines.

At the beginning of the 19th century, the steam engine had undergone such improvements that some people already perceived the limits of its improvement. An engineer by the name of A. R. Bouvier had stated in 1816 that to obtain further improvements, it would be necessary to resort to mathematics and physics and not only to mechanical improvements.

At that time the Scottish engineer Ewart argued that a given amount of heat could ideally produce only a given amount of work.

Boerhaave had noticed that the system formed by bodies at different temperatures tended to reach a thermal equilibrium and that an isolated body would never spontaneously heat up.

Finally, Joseph Fourier had pointed out in 1817 that radiant heat must obey a sinusoidal law of emission. His demonstration that the rejection of this law would lead to the admission of the possibility of perpetual motion was probably the first use of this type of reasoning outside of Galilean mechanics. It should be noted that Sadi Carnot used this same reasoning in the second part of the Réflexions with the maximum efficiency theorem.

Publication

The work, which contains 118 pages and five figures, was published by A-J-E Guiraudet Saint-Amé (X 1811) with mention of the house Bachelier and printed in 600 copies. In spite of the unquestionable clarity of the style, the series of delicate reasonings exposed by the author is difficult to follow because he deliberately renounced in the text the algebraic language, which he relegated in some footnotes. If the author intends to introduce new conceptions, he uses the vocabulary of contemporary physicists of his time: law, moving force and does not use the terms of cycles, adiabatic or reversible transformation even if he appeals to the notions they designate. On the substance, it is convenient to distinguish four parts in Sadi Carnot's book and if the text does not contain any division, the author follows a very assertive plan, while concealing his transitions by short linking sentences, according to the rhetorical usage of the time.

Heat and motive power

The first part contains a philosophical exposition of the field covered by the science of heat, considered from an entirely new point of view: heat as a driving agent. In his book, Carnot is not concerned with the nature of heat; nor is he interested in the heating and cooling of different bodies, nor in the conditions under which heat is transmitted, as were Joseph Fourier and his followers. Nor is he concerned with the chemical and physiological effects of heat.

Heat interests him as the cause of the great natural movements that occur on earth, the wind system, the ocean currents...; in this respect, he exaggerates its importance. Nevertheless, Sadi Carnot was aware, and seems to have been the first to make this remark, that the efficiency of the best and most powerful steam engines is derisory compared to the enormous mechanical effects produced by heat in the natural world.

Sadi Carnot was able to adopt a philosophical point of view, drawing on both his knowledge of the operation of steam engines and his expertise in meteorology or geophysics. In view of the textbooks of the time, it seems unlikely that any other engineer would have been able to do this, nor would a physicist: the former would not have been interested in such an abstract generalization, while the latter would not have been particularly interested in motive power. Only Lord Rumford, a few years earlier, noting a significant release of heat during the reaming of guns, concluded that work could be converted into heat and that these two notions came from the same essence.

This preliminary part of the Reflections contains the fundamental idea that wherever there is a difference in temperature, there is the possibility of generating motive power, an idea which plays a central role in thermodynamics. And its corollary is no less important: it is impossible to produce motive power unless there is both a cold and a hot body. This can be considered as the first statement of the second law of thermodynamics, also called Carnot's principle, even if it is still in an imprecise form.

It is likely that at the time, Sadi Carnot was guided by the idea that the most efficient hydraulic machines were those that made use of the greatest head of water: he saw in this an analogy, with all the nuances that make the difference with a strict similarity, between this height and the difference in temperatures for thermal engines. However, if a study of the data published in the Monthly Engine Reporter on the performance of high-pressure engines did not confirm this reasoning, his intuition was correct.

Ideal cycle of a perfect engine

The second part defines a perfect engine and its ideal operating cycle. To do this, he imagines an ideal machine, commonly called a Carnot machine, which can easily exchange heat alternately with a hot and a cold body (Figure 6). In his study, the heat engine is strictly reduced to its essential elements:

Carnot confirms that it is the difference in temperature between the hot and cold bodies, and not the difference in pressure undergone by the acting substance, that determines the work done by the engine. It seems that he owes this important idea to his friends Clément and Desormes.

The ideal cycle is subject to this condition: the substance that acts in the cylinder must never be in contact with a body that is colder or hotter than it is, so that there is no unnecessary heat flow. It is interesting to note that this condition corresponds to those that his father had stated to determine the maximum efficiency of hydraulic machines.

All temperature changes must be caused by the expansion or compression of the working substance. Initially compressed to high pressure, the working substance expands freely, pushing the piston and extracting heat from the hot body with which the cylinder is in contact (Figure 1). The cylinder is then moved away from the hot body, and the substance continues to expand adiabatically, so that its temperature decreases until it is equal to that of the cold body (Figure 2). This part of the cycle corresponds to the "expansion" operation of James Watt's machine; but it is now the temperature of the cold body and not the pressure of the condenser that marks the end of the expansion. The cylinder is then brought into contact with the cold body, and the working substance is compressed, the heat being "expelled" from it (and the compression continues so that the working substance is heated adiabatically (Figure 4). The cycle ends when the acting substance is returned to its original pressure, volume, and temperature (Figure 5).The net result has been only a transfer of heat from the hot body to the cold body and the production of external work; the acting substance has returned to its original state and no heat has been wasted.

Reversibility of the Carnot cycle

Sadi Carnot points out that the cycle is exactly reversible: the engine can be operated in the opposite direction and the net result would then be the consumption of work equal to that produced by operation in the direct direction and the transfer of the same quantity of heat, but in this case from the cold body to the hot body. The reversibility of the cycle is possible because there is no unnecessary heat flow at any point in the cycle. If there were such a flow, the engine would not be reversible. Now the reversible engine is the one that gives the best possible efficiency and Carnot concluded, as a consequence of the impossibility of perpetual motion, that steam is at least as satisfactory as any other acting substance. When he asserted that this was well founded in theory, the engineers of the time saw it as nothing more than an abstract confirmation of what they had learned in practice.

Applications to gas physics

In the third part, Sadi Carnot shows that the fact that all ideal heat engines have the same efficiency, no matter what gas or steam is used, has fundamental implications for the physics of gases. Carnot demonstrates that all gases that expand or are compressed from one pressure and volume to another pressure and volume at constant temperature either absorb or release the same amount of heat. He can also deduce relationships between the specific heats of gases, that is, the specific heat at constant pressure and the specific heat at constant volume. In a footnote, which was overlooked by early commentators, he suggests that the efficiency of an ideal heat engine could be used as a basis for an absolute temperature scale.

Air engine intuition

In the last part of the book, Sadi Carnot notes that the superiority of high-pressure steam engines is unquestionable because they make use of a greater temperature drop than low-pressure engines. Carnot recognizes that the great advantage of water as a source of steam, the fact that it expands enormously over a very small temperature range, made the realization of the early steam engine possible. However, he came to the remarkable conclusion that this advantage would make water less suitable for the heat engine of the future. Indeed, the enormous increase in pressure for very small temperature rises above 100 °C makes it almost impossible to operate over the entire temperature range, from that of coal combustion to that of cold water condensation.

Consequently, Sadi Carnot predicted that, when various technical problems concerning lubrication and combustion had been solved, the most efficient engine would probably be the air engine.

Acceptance of the work

The work was well received, including by the Academy of Sciences, to which Pierre-Simon Girard, director of a scientific journal, presented Carnot's work at the session of June 14, 1824, completed by an analytical account, in oral form, to his colleagues on July 26. It is obvious that a presentation to the Academy in the form of a memoir would have undoubtedly drawn more attention from the scientific community to the work of Sadi Carnot, with a publication in the Recueil des Savants étrangers as a normal follow-up. Thus, neither the "great French science" represented by the Institut de France, nor the famous École Polytechnique really reacted to the publication of Carnot's work, because they did not fully realize its significance. For his part, Carnot, who apparently had no sense of publicity, failed to send a copy to the libraries of the École des mines and the École des ponts et chaussées, thus depriving himself of a choice audience, just as he did not send a review to the Annales de chimie et de physique or the Annales des mines. Moreover, it should be noted that, in spite of a limited edition, some unsold copies were found uncut.

On the engineering side, only the academician Pierre-Simon Girard gave a glowing review. By the time the Réflexions appeared, engineers had already learned from experience that steam was at least as satisfactory as any other acting substance. When Carnot asserted that this was theoretically true, it was seen as nothing more than an abstract confirmation.

Moreover, the explanations he gave for the superior efficiency of high-pressure steam engines were based on data published in the Monthly Engine Reporter and on the performance of the Woolf engines, operating by expansion at high pressure, which were built in France by Humphrey Edwards. However, these performances were probably more related to a sum of detail improvements than to a real thermodynamic advantage. It was therefore not right for Sadi Carnot to invoke the superiority of high-pressure steam engines in support of his fundamental theories.

With the exception of Nicolas Clément-Desormes who, as shown in a lecture given on January 25, 1825, recommended that his listeners read the book, physicists and other scientists were undoubtedly confused by fundamental reasoning based on the principles of the steam engine.

It was not until 1834 that Émile Clapeyron published an article in the journal of the École polytechnique showing how Sadi Carnot's ideas could be expressed mathematically while emphasizing their explanatory value, and it was only with the republication of the Réflexions by this same author, supplemented with his comments, that Sadi Carnot gradually began to influence the scientific community.

It was through this means that William Thomson became aware of Carnot's work in 1851. In a long series of articles, Thomson and Rudolf Clausius, from 1850 onwards, laid down the principle of conservation of energy (and no longer of heat) as the basic foundation of thermodynamics. To recognize the contribution of Rudolf Clausius, the Carnot principle was named the Carnot-Clausius principle. This principle makes it possible to determine the maximum efficiency of a thermal machine as a function of the temperatures of its hot and cold sources, an efficiency that varies between 8% and 30% depending on the design of the machines.

The question remains: why did Sadi Carnot not publish anything between the eight years that separated the publication of the Réflexions and the date of his death? Although several explanations can be advanced, the most likely reason is that he had lost confidence in his theories and found himself unable to found a new theory of heat. With caloric, Sadi Carnot was faced with one of the most difficult epistemological obstacles to overcome, one that was dear to Gaston Bachelard: substantialism, that is, the monotonous explanation of physical properties by substance.

Among his posthumous writings, a manuscript entitled Recherche d'une formule propre à représenter la puissance motrice de la vapeur d'eau (Research for a formula to represent the motive power of water vapor), written between November 1819 and March 1827 but probably after the Reflections, was preserved. In it, he sketched the first law of thermodynamics, trying to clarify the link between work and heat. This note was finally published in 1878, i.e., too late to influence the development of science, by Hippolyte Carnot, in a volume published in homage to his brother, in which he inserted a "Biographical note on Sadi Carnot". It was undoubtedly in the spring of 1832 that Sadi discovered the principle of equivalence and that he took up, in brief notes, the conclusions of a long memoir, which was finally destroyed by Hippolyte. These notes, also published in 1878, indicate that he had by then abandoned the theory of caloric which still permeated his 1824 essay, and about which he had already expressed doubts in the Réflexions. It seems that he had admitted that heat is nothing more than motive power (we would say energy today), proposing a numerical value of the mechanical equivalent of heat to within 2%, ten years ahead of Julius Robert von Mayer, and apparently obtained with more scientific rigour.

To validate his advances, he had sketched out detailed experiments, which we would say today are constant enthalpy experiments, similar to those of Benjamin Thompson. But unlike Thompson, he intended to measure the work done and the heat produced, while varying the materials used. In this sense, he firmly hoped to find a constant mechanical equivalent of heat that would have the same value for all experiments. He also considered measurements using gases and liquids to calculate the mechanical equivalent of heat.

It is difficult to know whether he would have been able to perform these experiments satisfactorily. The history of thermodynamics still had to run before he could arrive at the theory, so the difficulties he would have had to overcome can hardly be underestimated.

It would also have been necessary to convince in particular the great body of chemists and all those who were doing research on electricity: all were deeply attached to the theory of caloric. Finally, it was not until James Prescott Joule that the dynamic theory of heat was finally formulated. Seven years separated his first publication (1843) and the publication of Rudolf Clausius, who brought the dynamic theory of heat (Joule) into agreement with the theories of Sadi Carnot.

Finally, it is regrettable but unfortunately probable that Sadi Carnot died believing that he had failed, whereas he simply founded a vast and fundamental branch of science, with complex structures, thermodynamics, which links physics, chemistry, biology and even cosmology.

Influence of the work of Lazare Carnot on that of his son

For the historian of science, several questions arise regarding the relationship between the works of the two engineers:

Work of synthesis

For D.S.L. Cardwell, Sadi Carnot's book, although much less well known than Copernicus' De revolutionibus orbium coelestium, has a comparable importance in the history of modern science because it allowed, in a particularly rare event, to lay the foundations of an entirely new discipline: thermodynamics.

Yet Carnot's work has an original dimension. Copernicus worked in a clearly defined and recognized discipline; he could rely on a heritage of reflections and observations accumulated over two millennia (the ephemerides). Sadi Carnot, on the other hand, had to synthesize different scientific and technical disciplines. To do this, he had to select the data to be studied, to construct theories from concepts, laws and principles drawn from the sciences of heat and mechanics, which were still separate, from technologies in full development such as steam or already more established such as hydraulics, but which were also still unrelated. On the other hand, he alone saw in 1824 the need for this new science, both for its practical applications and for more fundamental reasons.

Carnival Revolution

From the historical point of view, the work of Sadi Carnot was concomitant with what Jacques Grinevald calls the Carnot Revolution, which led to a shift to a thermo-industrial society with the massive use of fossil energy (coal and then oil). From then on, the power of fire allowed the advent of a new machine, built around an engine, and which constituted a bifurcation in the history of the tool. It allows the eviction of the driving force of the man, of the animal, of the usual natural elements like the wind and the water to give sense to the old collective representation of the animated creatures which goes from Hephaïstos to the electric ghost of Hadaly. At the same time, this driving power of fire is going to distend the millenary link between technique and immediate geographical environment, with the unprecedented development of networks and flows and the geographical concentration of equipments which becomes possible by the delocalization of this power.

Balance sheet and posterity

Sadi Carnot discovered the two laws on which the whole science of energy is based, despite obstacles that seemed insurmountable. He gave a measure of the exceptional power of his intuition by stating his laws when the facts were insufficient in number, their precision crude and especially when the progress of the nascent science was held back by the erroneous theory of indestructible caloric.

He intuitively saw that the steam engine resembled the old water mill, which produces energy by dropping water from a high level to a lower level, that it produces energy by dropping heat from the high temperature of the boiler to the lower temperature of the condenser. He felt that this difference in temperature was a clear phenomenon, but that the fall of heat itself was much less so, and he was careful in his law to give the essential role to the fall of temperature. We would say today that he guessed that there was a difference between heat-energy and heat-falling like water from the mill. We know that it took 40 years after his book to define entropy from the quantity of heat as the equivalent of mill water and we admire that he avoided this delicate problem and finally rejected the theory of caloric first.

With its universal scope, his work probably constitutes a unique case in the history of modern science and, in this sense, Nicolas Léonard Sadi Carnot was certainly one of the most penetrating and original thinkers that our civilization has produced.

For some, he will remain "a meteor in the history of science", a singular figure for whom "with a sheet of paper, a pencil pen and a mind, to have created the basis of a new science, is a matter of a quite admirable spirit". "The death of great men leaves as many regrets as new hopes.

In 1970, the International Astronomical Union named the lunar crater Carnot after the French physicist and later the asteroid (12289) Carnot.

The Carnot method, an exergy allocation procedure for evaluating cogeneration products and calculating the physical value of the heat output, is named after him.

In 2006, the Carnot label was created in France to develop the interface between public research and socio-economic actors in response to their needs: this dedication salutes what Sadi Carnot brought to fundamental physics by exploring a very applied question.

Sources

1. Nicolas Léonard Sadi Carnot
2. Sadi Carnot (physicien)
3. Sadi est le seul prénom mentionné pour l’état civil, Nicolas et Léonard étant des prénoms de baptême.
4. Il fut successivement affecté à Besançon, détaché à Salins, Montpellier et Langres pour lever la place.
5. Probablement liées à sa petite taille ou à la remise en cause de sa participation à la défense du fort de Vincennes.
6. 1 kg d’eau occupe un volume d’1 dm3 ; 1 kg de vapeur d’eau à 100 °C occupe 1 673 dm3. Voir l’article vapeur d’eau.
7. ^ (US) M. Hippolyte Carnot, Life of Sadi Carnot , Second revised edition, John Wiley & Sons, 1897
8. ^ (FR) Autori vari, Sadi Carnot et l'essor de la thermodynamique, CNRS Éditions 1 Septembre 1998 ISBN 2-222-01818-8
9. ^ "Sadi Carnot - Biography". Maths History. Retrieved 2022-06-02.
10. ^ a b Sadi Carnot et l’essor de la thermodynamique, CNRS Éditions
11. ^ Thomass, T (2003). "Nicolas Léonard Sadi Carnot (1796-1832)" (PDF). Université de Technologie de Compiègne. Archived from the original (PDF) on 2017-02-15. Retrieved 2014-07-19.
12. ^ Chisholm 1911.
13. 2,0 2,1 MacTutor History of Mathematics archive. Ανακτήθηκε στις 22  Αυγούστου 2017.
14. «Большая российская энциклопедия». (Ρωσικά) Μεγάλη Ρωσική Εγκυκλοπαίδεια. Η Μεγάλη Ρωσική Εγκυκλοπαίδεια. Μόσχα.
15. Sadi Carnot et l'esor de la thermodynamique, CNRS Éditions
16. Thomass, T (2003). «Nicolas Léonard Sadi Carnot (1796-1832)» (PDF). Université de Technologie de Compiègne. Αρχειοθετήθηκε από το πρωτότυπο (PDF) στις 15 Φεβρουαρίου 2017. Ανακτήθηκε στις 26 Ιανουαρίου 2019.