I Carnot's Argument (Cryptic passage in Feynman Lectures v. 1)

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In chapter 44 of Feynman Lectures on Physics, Volume I, which covers thermodynamics, we find this passage:

p 44-2 said:
At the time when Carnot lived, the first law of thermodynamics, the conservation of energy, was not known. Carnot's arguments were so carefully drawn, however, that they are valid even though the first law was not known in his time! Some time afterwards, Clausius made a simper derivation that could be understood more easily than Carnot's very subtle reasoning. But it turned out that Clausius assumed, not the conservation of energy in general, but that heat was conserved according to the caloric theory, which was later shown to be false. So it has often been said that Carnot's logic was wrong. But his logic was quite correct. Only Clausius' simplified version, that everybody read, was incorrect.

The so-called second law of thermodynamics was thus discovered by Carnot before the first law! It would be interesting to give Carnot's argument that did not use the first law, but we shall not do so because we want to learn physics, not history. We shall use the first law from the start, in spite of the fact that a great deal can be done without it.
Does anyone know what this argument of Carnot's is? I'm not sure exactly what it is that he is supposed to have derived without using the first law. The efficiency of a reversible engine? Feynman doesn't say explicitly. Anyway, I'm very interested to know how Carnot did this without having to use the fact that

Qhot-Qcold = Work done
 
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This reference may explain it:



Introduction

Sadi Carnot (1796–1832) may rightfully be considered the ‘Founder of the Second Law of Thermodynamics’—despite having used the subsequently discredited caloric theory of heat in the only work he published during his lifetime, his Reflexions sur la puissance motrice du ´ feu et sur les machines propres a developper cette puissance ´ [1]. After the publication of his Reflexions ´ he continued his research, and his Notes[2, 3] indicate that he abandoned the caloric theory for the mechanical theory of heat. These Notes were only published posthumously. In this paper we will try to show how Carnot’s theoretical ideas on heat engines in his slim (118 pages), partly incorrect, book secured for him a major position in the history of physics.
 
Thank you. I'll read that paper. Feynman made it sound like Carnot never really made an invalid argument based on caloric theory--that people had simply misread him. Maybe this paper will clear up the situation.

Also, sorry for the duplicate thread. I was having connection issues and it didn't look like it posted the first time.
 
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This rather reminds me of how Archimedes was able to derive the volume of a sphere without Calculus. It turns out that his argument is very similar to a Calculus one using limits and cleverly slicing up the sphere:



and we think we are so smart standing on the shoulders of giants.
 
That Archimedes proof was really something. Thanks for that. Amazing what the human mind can do. I also like these "low-tech" proofs that show off the power of careful reasoning and imagination.

The Erlichson paper was very helpful, but it does not contain the "secret" argument of Carnot. He rejects the view of Feynman and others that Carnot knew exactly what he was doing all along, and never based his argument on an incorrect theory of heat. Apparently there are papers from the 50's by V. K. La Mer and M. A. Hirshfeld in Am. J. Phys. that present an alternative interpretation of Carnot's arguments in modern terms. Their idea seems to be that when he said "calorique", he had in mind what would later be called entropy. And when he said "chaleur", he meant heat. It could be that Feynman read these papers and formed his opinion. Unfortunately I can't find a free copy of either online. There is only a very short "preview" of La Mer's paper that was published in Science in 1947.
 

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