Nicolas Léonard Sadi Carnot (French: [nikɔla leɔnaʁ sadi kaʁno]; 1 June 1796 – 24 August 1832) was a French military engineer and physicist. He graduated from the École polytechnique and worked as an officer in the Engineering Arm (le génie) of the French Army. He also studied science and published an essay in June 1824 titled Reflections on the Motive Power of Fire. This book, his only publication, introduced the first successful theory about the maximum efficiency of heat engines.

During his lifetime, Carnot’s scientific work received little attention. However, in 1834, another French engineer, Émile Clapeyron, wrote a detailed explanation of Carnot’s ideas. Clapeyron’s work caught the interest of William Thomson (later Lord Kelvin) and Rudolf Clausius. Thomson used Carnot’s analysis to create an absolute thermodynamic temperature scale, while Clausius used it to define the concept of entropy, which helped to establish the second law of thermodynamics.

Sadi Carnot was the son of Lazare Carnot, a well-known mathematician, engineer, and military leader in the French Revolutionary Army and later the Napoleonic Army. Some challenges Sadi faced in his career may have been linked to the difficult treatment his family received after Napoleon’s defeat in 1815. Sadi Carnot died at the age of 36 without widespread recognition, but today he is often called the "father of thermodynamics."

Life

Sadi Carnot was born on June 1, 1796, in Paris at the Petit Luxembourg palace. His father, Lazare Carnot, lived there as a member of the Directory, which was the highest leadership group of the French First Republic after the Thermidorian Reaction. His mother, Sophie Dupont, came from a wealthy family in Saint-Omer.

Sadi’s father named him after the 13th-century Persian poet Sadi of Shiraz. An older brother, also named Sadi, was born in 1794 but died before his first birthday. The name "Sadi" appears on Sadi’s civil birth certificate, which was dated 14 prairial, year IV, in the French Republican calendar. On July 11, 1796, the child was baptized in the Catholic church of Saint-Louis-d’Antin as "Nicolas-Léonard Dupont." His maternal grandfather, Jacques-Antoine-Léonard Dupont, was the main witness at the baptism. The baptismal record incorrectly listed the father as Jacques-Léonard-Joseph-Auguste Dupont, who was actually the child’s maternal uncle. Later, his brother Hippolyte wrote a biography of Sadi, and most sources now list his full name as "Nicolas Léonard Sadi." There is no evidence that he used any name other than "Sadi."

Sadi had a younger brother, Hippolyte Carnot, born in 1801 in Saint-Omer. Hippolyte later became a prominent politician. Hippolyte’s eldest son, Marie François Sadi Carnot, served as President of France from 1887 to 1894. Another of Hippolyte’s sons was Adolphe Carnot, a chemist, mining engineer, and politician. Sadi remained unmarried and had no children.

As a child, Sadi was educated at home by his father and later at the Lycée Charlemagne in Paris. He studied to prepare for entrance to the École polytechnique, which his father had helped establish. In 1811, at age 16, Sadi entered the École polytechnique, where his classmates included the future mathematician Michel Chasles. His professors were notable scientists such as André-Marie Ampère, Siméon Denis Poisson, François Arago, and Gaspard-Gustave Coriolis. The school was known for its strong teaching in mathematics and physics.

During the Battle of Paris in March 1814, Carnot, Chasles, and other cadets from the École polytechnique helped defend Vincennes. This was Carnot’s only known experience in battle. He graduated in 1814 and attended the École d’application de l’artillerie et du génie in Metz, where he completed a two-year course. Afterward, he became an officer in the French army’s corps of engineers.

Sadi’s father, Lazare, served as Napoleon’s minister of the interior during the "Hundred Days." After Napoleon’s defeat in 1815, Lazare was forced into exile in Magdeburg, Germany. Sadi’s position in the army under the restored Bourbon monarchy of King Louis XVIII became difficult. Lazare never returned to France and died in Magdeburg in 1823.

Sadi became a captain in the Génie and was posted to various locations, where he inspected fortifications, reviewed plans, and wrote reports. However, his recommendations were often ignored, and his career seemed to stall. In September 1818, at age 22, he took a six-month leave to prepare for the entrance exam to the newly formed General Staff in Paris. Carnot passed the exam and joined the General Staff in January 1819 as a lieutenant. From then on, he focused more on private intellectual work and received only two-thirds of his pay.

In Paris, Carnot met Nicolas Clément and Charles-Bernard Desormes. He attended lectures on physics and chemistry at the Sorbonne and the Collège de France. He also studied at the Conservatoire national des arts et métiers, where he listened to lectures on chemistry by Clément and economics by Jean-Baptiste Say. Carnot became interested in improving steam engines, which led him to write Reflections on the Motive Power of Fire, published in 1824.

In September 1827, Carnot was promoted back to captain. However, in April 1828, he left the army after only 15 months of active service and without a pension. A list of École polytechnique alumni from 1828 described Carnot as "maker of steam engines," suggesting he may have worked on practical improvements to steam engines. However, no patents or other proof of this work have been found.

Carnot was interested in political economy. He supported liberal ideas but favored the more interventionist views of Jean de Sismondi over the free-market policies of economists like Say and David Ricardo. Only fragments of his private writings on economics remain.

Carnot welcomed the July Revolution of 1830, which ended the rule of King Charles X and started a new government under King Louis Philippe. His brother Hippolyte said leaders of the new government considered making Sadi a member of the Chamber of Peers, as he might have inherited the title "Count Carnot" from his father. However, this did not happen, possibly because Sadi refused a hereditary title due to his republican beliefs.

According to Hippolyte, Sadi was a devoted reader of Blaise Pascal, Molière, and Jean de La Fontaine. He believed in a powerful, loving God but not in divine punishment. He wrote that "what seems like chance to an ignorant person is not chance to someone more knowledgeable." He criticized organized religion but supported belief in an all-powerful, caring being.

Hippolyte also described Sadi as a skilled violinist who enjoyed the music of Jean-Baptiste Lully and Giovanni Battista Viotti. He also practiced gymnastics, fencing, swimming, dancing, and skating. Historian James F. Challey noted that Carnot was "sensitive and perceptive" but "extremely introverted" and distant from most people. This may explain why his work was not widely recognized during his lifetime

Reflections on the Motive Power of Fire

Sadi Carnot's work on thermodynamics is found in his only published book, Réflexions 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"). The book was published in Paris in June 1824 by Bachelier, and Carnot paid for the printing of 600 copies. During his lifetime, the book received little attention and was nearly forgotten by booksellers and libraries. In 1834, two years after Carnot's death and ten years after the book was published, engineer Émile Clapeyron wrote an article that brought new attention to Carnot's work. Later, Lord Kelvin and Rudolf Clausius used Carnot's ideas to help define important thermodynamic concepts, including absolute temperature, entropy, and the second law of thermodynamics.

Thomas Newcomen created the first practical piston-operated steam engine in 1712. About 50 years later, James Watt made major improvements that greatly increased the usefulness of steam engines. By the 1820s, when Carnot studied steam engines, they were widely used in industry and seen as economically important. Compound engines (engines with multiple stages of expansion) had already been invented, and a basic internal combustion engine, called the pyréolophore, was built by the Niépce brothers. Carnot was familiar with this engine and described it in his book.

At the time, engineers understood some practical aspects of steam engines, but there was little scientific knowledge about the physical processes related to heat. The idea that energy is conserved had not yet been clearly explained, and related ideas were unclear and debated. Carnot believed, as many French scientists did, that heat was a weightless, invisible fluid called "caloric," which could be released by chemical reactions and flowed from hotter to colder objects.

In his book, Carnot asked two key questions: "Is there a limit to the work that can be generated from a given heat source?" and "Can replacing steam with another working fluid improve an engine's performance?" Engineers had tried using high-pressure steam and other fluids to increase efficiency. At that time, typical engines converted only about 5–7% of the heat from fuel into useful work.

Carnot's book was 118 pages long and covered many topics about heat engines in a way he hoped would be accessible to a wide audience. He used little mathematics, relying mostly on basic algebra and arithmetic, except in some notes. He compared the use of air and steam as working fluids, discussed steam-engine design, and suggested possible improvements. However, the most important part of the book described an idealized engine (the Carnot cycle), which helped explain the basic principles of all heat engines, regardless of their design. This idealized system allowed for precise calculations and avoided the complications of real-world engines.

Carnot imagined a process where heat from a hot reservoir slowly flows into a gas in a cylinder with a movable piston, causing the gas to expand and push the piston outward. This is called isothermal expansion and produces useful work. However, the piston must return to its original position for the engine to operate continuously.

Next, Carnot proposed cooling the gas by expanding it without heat exchange (adiabatic expansion), which lowers its temperature to match the colder reservoir. The cylinder then connects to the cold reservoir, and the gas undergoes isothermal compression, releasing heat into the cold reservoir. To complete the cycle, the gas is heated again through adiabatic compression until it reaches the hot reservoir's temperature. This repeating cycle of expansion and compression produces work by transferring heat from the hot reservoir to the cold one.

Carnot argued that this cycle is the most efficient possible heat engine for given reservoir temperatures. This is because it avoids losses from friction, heat leakage, or heat transfer between parts at different temperatures. Carnot recognized that heat transfer between objects at different temperatures is wasteful and irreversible, reducing efficiency.

Because the Carnot cycle is reversible, it can also function as a refrigerator. If work is applied to move the piston, the cycle absorbs heat from the cold reservoir and releases it into the hot reservoir. Carnot believed that no engine operating between two reservoirs could produce more work than his cycle. Otherwise, a more efficient engine could run the cycle in reverse, transferring heat back to the hot reservoir while producing extra work, which would violate the laws of physics by creating perpetual motion.

Carnot understood that his ideal engine had the highest possible efficiency for given temperatures, but he did not calculate its exact value. This was because scientists at the time used unclear temperature scales.

Later in his book, Carnot studied heat engines operating near the boiling point of water or other fluids. He noted that phase changes, like liquid to vapor, involve sudden volume changes and require latent heat. This concept, now called a first-order phase transition, led Carnot to develop an idea that later became the Clausius–Clapeyron relation. In The Feynman Lectures on Physics, physicist Richard Feynman credited Carnot with this discovery.

In 1849, James Thomson applied Carnot's ideas to further develop thermodynamics.

Death and posterity

Sadi's younger brother, Hippolyte, hid details about Sadi's death and destroyed most of his personal papers. Many years later, in 1878, when Carnot's essay was recognized as an important early work in the study of thermodynamics, Hippolyte helped publish a new edition of the essay. This edition included a "Biographical notice on Sadi Carnot" written by Hippolyte and some "Excerpts from unpublished notes by Sadi on mathematics, physics, and other subjects." These materials are the only sources of information about many parts of Sadi's life and ideas. Historian of science Arthur Birembaut said that the confusion created by Hippolyte makes it difficult to understand the details of Sadi's career, his connections with other scientists, and the events surrounding his death.

Among the private notes published by Hippolyte in 1878, there are writings showing that Sadi Carnot had stopped believing in the caloric theory by the spring of 1832 and instead accepted the idea that heat and work are equivalent. In his notes, Carnot wrote:

In those same notes, Carnot estimated that 1 kilocalorie equals 370 kg·m, while the value accepted today is 427 kg·m. Carnot did not publish any of this work. It is possible that his uncertainty about how rejecting the caloric theory might affect the conclusions in his earlier work, Reflections on the Motive Power of Fire, explains why he did not continue his research before his early death.

After the work of scientists Kelvin and Clausius, Carnot became widely known as the "father of thermodynamics." In 1970, the International Astronomical Union named a lunar crater after Carnot. In 1991, the minor planet 12289 was also named in his honor.