Nicolas Léonard Sadi Carnot (Carnot cycle)

(French: [kaʁno]; 1 June 1796 – 24 August 1832) was a French military engineer and physicist, often described as the "father of thermodynamics". In his only publication, the 1824 monograph Reflections on the Motive Power of Fire, Carnot gave the first successful theory of the maximum efficiency of heat engines. Carnot's work attracted little attention during his lifetime, but it was later used by Rudolf Clausius and Lord Kelvin to formalize the second law of thermodynamics and define the concept of entropy.

Carnot cycle

Carnot sought 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 28 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 improvements of the practical nature. 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 of the hotter reservoir. (Note: This equation probably came from Kelvin.) No thermal engine operating any other cycle can be more efficient, given the same operating temperatures.

The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. Carnot knew that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be eliminated if the heat engine is to achieve maximum efficiency.

Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid. He stated this for emphasis as a general proposition:

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

—Carnot 1890, p. 68

For his "motive power of heat", we would today say "the efficiency of a reversible heat engine", and rather than "transfer of caloric" we would say "the reversible transfer of heat." He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be.

He concluded:

The production of motive power is therefore due in steam engines not to actual consumption of caloric but to its transportation from a warm body to a cold body.^[4]

—Carnot 1960, p. 7

and

In the fall of caloric, motive power evidently increases with the difference of temperature between the warm and cold bodies, but we do not know whether it is proportional to this difference.^[5]

—Carnot 1960, p. 15

The second law of thermodynamics

In Carnot's idealized model, the caloric transported from a hot to a cold body, yielding work, could be transported back by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot further postulated that no caloric is lost. The process being completely reversible, a real heat engine using cycle's reversibility is the most efficient heat machine. The proof for this is as follows: imagine we have two large bodies, a hot and a cold one. If we couple a Carnot machine to this that makes heat flow from hot to cold, an amount Q for each cycle, yielding an amount of work denoted W. If we use this work to power another machine, but one that is more efficient than the Carnot machine, it could, using the amount of work W each cycle, make an amount of heat, Q'>Q flow from the cold to the hot body. The net effect is a flow of Q'-Q of heat from the cold to the hot body, while no net work is done. This would violate the second law of thermodynamics and is thus impossible. This proves that the Carnot engine is the most efficient heat engine.

Though formulated in terms of caloric, rather than entropy, this was an early statement of the second law of thermodynamics.