and invisible fluid that flowed when out of equilibrium. Engineers in Carnot's time had tried, by means such as highly pressurized steam and the use of fluids, to improve the efficiency 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 of fuel was burned—was only 3%. Carnot cycle Carnot wanted to answer two questions about the operation of heat engines: "Is the work available from a heat source potentially unbounded?" and "Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?" He attempted to answer these in a memoir, published as a popular work in 1824 when he was only 27 years old. It was entitled Réflexions sur la Puissance Motrice du Feu ("Reflections on the Motive Power of Fire"). The book was plainly intended to cover a rather wide range of topics about heat engines in a rather popular fashion; equations were kept to a minimum and called for little more than simple algebra and arithmetic, except occasionally in the footnotes, where he indulged in a few arguments involving some calculus. He 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. The most important part of the book was devoted to an abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are generally applied to all heat engines, independent of their design. Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine, as they were known in his day, into a more general and idealized heat engine. This resulted in a model thermodynamic system upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engine. By idealizing the engine, he could arrive at clear and indisputable answers to his original two questions. He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T1−T2)/T1, where T1 is the absolute temperature