Carnot and Entropy

Question

After reading the article History of Entropy on Wikipedia, I noticed that it mentioned Carnot running into problems with entropy. I understand that entropy was fleshed out later by Clausius, but with respect to Carnot, what experiment did he perform that gave him reason to believe there was something else (although he didn't actually figure it out). I'm not looking for any answer that includes Boltzmann and probability, or any answer that includes the word "chaos".

TLDR: What did Carnot do or see that made him think there was something missing? What happened, possibly through an experiment or even thought experiment that made him realize things weren't adding up?

Answer 1

Carnot was not talking about thermodynamics in the same way that Clausius was. Carnot saw the fundamental action as a fluid substance (caloric) being manipulated into motion between a hot place and a cold place. He saw fire as a motive power that could push caloric from one place to another and thus perform work. It was all about "la grande chute du calorique" for Carnot, (the great fall of caloric). Thermodynamics as imagined by Clausius, Maxwell, and others, would abandon the idea of caloric and instead put into place a kinetic theory of heat that called into question the nature of heat itself.

The closest we might come to saying that Carnot "saw" entropy would be if he saw some of his caloric being lost, or if he saw some breakdown in the ability of heat to move it. And it is true that on p. 114 of his "Reflexions" when he calculates the motive power of burning coal, he adjusts (by half) his calculation in order to be conservative. It is not heavily theorized beyond accounting for the difference between theory and practice. But this is really not the same thing as entropy as Clausius framed it.

This is all in his Reflexions, available in Google books.

Answer 2

Carnot did not make any experiments, his work was purely theoretical. He constructed an idealized model of a heat engine, called "Carnot's cycle", and deducted a formula for maximal theoretical efficiency. Second Law of Thermodynamics was not formulated yet at that time. Wikipedia article on Nicolas Leonard Sadi Carnot explains his work pretty well, and the work itself is available in English.