Who Wants to Understand the Second Law of Thermodynamics?

The simplest and most precise formulation of the second law of thermodynamics was given by Sadi Carnot himself:

"A cold body is necessary"

That is, heat cannot be cyclically converted into work unless there is some temperature gradient (a hot body, source of heat, and a cold body, receiver of heat, must be available). The problem is that in 1824 Carnot deduced "A cold body is necessary" from a postulate that eventually turned out to be false:

Carnot's (false) postulate: Heat is an indestructible substance (caloric) that cannot be converted into work by the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after realizing that his postulate was false, Carnot found "A cold body is necessary" implausible:

http://www.nd.edu/~powers/ame.20231/carnot1897.pdf
Sadi Carnot, REFLECTIONS ON THE MOTIVE POWER OF HEAT, p. 225: "Heat is simply motive power, or rather motion which has changed form. It is a movement among the particles of bodies. Wherever there is destruction of motive power there is, at the same time, production of heat in quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, wherever there is destruction of heat, there is production of motive power." p. 222: "Could a motion (that of radiating heat) produce matter (caloric)? No, undoubtedly; it can only produce a motion. Heat is then the result of a motion. Then it is plain that it could be produced by the consumption of motive power, and that it could produce this power. All the other phenomena - composition and decomposition of bodies, passage to the gaseous state, specific heat, equilibrium of heat, its more or less easy transmission, its constancy in experiments with the calorimeter - could be explained by this hypothesis. But it would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a warm body, motion cannot be produced."

Generally, a cold body is not necessary, that is, the second law of thermodynamics is false. The cold body is only TECHNOLOGICALLY necessary as it makes heat engines fast-working. Heat engines working under isothermal conditions (in the absence of a cold body) are commonplace but are too slow and impuissant to be of any technological importance. Yet they do violate the second law of thermodynamics.

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