Sadi Carnot, a son of the eminent geometer Lazare Nicholas Marguerite Carnot, was the most eminent of Fourier's contemporaries who were interested in the theory of heat. Sadi Carnot was born at Paris, France, in 1796, and died there of cholera in 1832; he was an officer in the French army.
In 1824 he issued a short work entitled Réflexions sur la puissance motrice du feu, in which he attempted to clarify how to get the most work out of an engine, such as a steam engine, from a given quantity of heat, such as from burning a lump of coal. Engineers of Carnot's time had tried various mechanical means, such as high pressure of steam or using some fluid other than steam, to maximize the amount of work from engines.
But Carnot argued correctly that all that mattered, after removing inefficiencies such as friction and heat loss, was to maximize the ratio of the temperature of heat input to the temperature of heat exhaust, see Carnot heat engine. To do his calculations, he made the simplifying assumption that heat was a weightless fluid, which it is not. However, his essay may be taken as initiating the modern theory of thermodynamics.
The text of part of an earlier version of this article was taken from the public domain resource A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908)