Carnot was the eldest son of the French Revolutionary figure Lazare Carnot and was named for a medieval Persian poet and philosopher, Saʿdī of Shīrāz. His early years were a period of unrest, and the family suffered many changes of fortune. His father fled into exile soon after Sadi’s birth; in 1799 he returned to be appointed Napoleon’s minister of war but was soon forced to resign. A writer on mathematics and mechanics as well as military and political matters, the elder Carnot now had the leisure to direct his son’s early education.
Sadi entered the École Polytechnique in 1812, an institution providing an exceptionally fine education, with a faculty of famous scientists aware of the latest developments in physics and chemistry, which they based on a rigorous mathematics. By the time Sadi graduated in 1814, Napoleon’s empire was being rolled back, and European armies were invading France. Soon Paris itself was besieged, and the students, Sadi among them, fought a skirmish on the outskirts of the city.
During Napoleon’s brief return to power in 1815, Lazare Carnot was minister of the interior, but, following the emperor’s final abdication, he fled to Germany, never to return to France.
Sadi remained an army officer for most of his life, despite disputes about his seniority, denial of promotion, and the refusal to employ him in the job for which he had been trained. In 1819 he transferred to the recently formed General Staff but quickly retired on half pay, living in Paris on call for army duty. Friends described him as reserved, almost taciturn, but insatiably curious about science and technical processes.
The mature, creative period of his life now began. Sadi attended public lectures on physics and chemistry provided for workingmen. He was also inspired by long discussions with the prominent physicist and successful industrialist Nicolas Clément-Desormes, whose theories he further clarified by his insight and ability to generalize.
The problem occupying Carnot was how to design good steam engines. Steam power already had many uses—draining water from mines, excavating ports and rivers, forging iron, grinding grain, and spinning and weaving cloth—but it was inefficient. The import into France of advanced engines after the war with Britain showed Carnot how far French design had fallen behind. It irked him particularly that the British had progressed so far through the genius of a few engineers who lacked formal scientific education. British engineers had also accumulated and published reliable data about the efficiency of many types of engines under actual running conditions; and they vigorously argued the merits of low- and high-pressure engines and of single-cylinder and multicylinder engines.
Convinced that France’s inadequate utilization of steam was a factor in its downfall, Carnot began to write a nontechnical work on the efficiency of steam engines. Other workers before him had examined the question of improving the efficiency of steam engines by comparing the expansion and compression of steam with the production of work and consumption of fuel. In his essay, Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance (Reflections on the Motive Power of Fire), published in 1824, Carnot tackled the essence of the process, not concerning himself as others had done with its mechanical details.
He saw that, in a steam engine, motive power is produced when heat “drops” from the higher temperature of the boiler to the lower temperature of the condenser, just as water, when falling, provides power in a waterwheel. He worked within the framework of the caloric theory of heat, assuming that heat was a gas that could be neither created nor destroyed. Though the assumption was incorrect and Carnot himself had doubts about it even while he was writing, many of his results were nevertheless true, notably the prediction that the efficiency of an idealized engine depends only on the temperature of its hottest and coldest parts and not on the substance (steam or any other fluid) that drives the mechanism.
Although formally presented to the Academy of Sciences and given an excellent review in the press, the work was completely ignored until 1834, when Émile Clapeyron, a railroad engineer, quoted and extended Carnot’s results. Several factors might account for this delay in recognition; the number of copies printed was limited and the dissemination of scientific literature was slow, and such a work was hardly expected to come from France when the leadership in steam technology had been centred in England for a century. Eventually Carnot’s views were incorporated by the thermodynamic theory as it was developed by Rudolf Clausius in Germany (1850) and William Thomson (later Lord Kelvin) in Britain (1851).
Little is known of Carnot’s subsequent activities. In 1828 he described himself as a “constructor of steam engines, in Paris.” When the Revolution of 1830 in France seemed to promise a more liberal regime, there was a suggestion that Carnot be given a government position, but nothing came of it. He was also interested in improving public education. When absolutist monarchy was restored, he returned to scientific work, which he continued until his death in the cholera epidemic of 1832 in Paris.