The Carnot (Ratio) Equality, Qrev/T = constant (as named here in Carnot’s honor, to resound the integral Clausius equality, being its precursor), is much more important than what it appears at first. Actually, the “Carnot Equality” is probably the most important equation in Thermodynamics and among the most important equations in natural sciences. Carnot’s ingenious reasoning opened the way to the generalization of Thermodynamic reversibility and energy process-equivalency, definition of absolute thermodynamic temperature, and a new thermodynamic material property “Entropy”, as well as the Gibbs Free Energy, one of the most important Thermodynamic functions for the characterization of electro-chemical systems and their equilibriums, thus resulting in the formulation of the universal and far-reaching Second Law of thermodynamics [Kostic: 2008 & 2011 & 2014 & 2020 & 2023].
Note that Carnot erroneously assumed that the same caloric (heat) passes through the engine and extracts (produces) work by lowering its temperature, similar to how the same water flow passes through the water-wheel and produces work by lowering its elevation potential. This error (violating energy conservation), considering the knowledge at the time, in no way diminishes Carnot’s ingenious reasoning and conclusions about limiting, reversible processes and its accurate limitations of heat to work conversion .
https://en.wikipedia.org/wiki/Reflections_on_the_Motive_Power_of_Fire * and Historic ASME Landmark
"Carnot stated that motive power is due to the fall of caloric (heat) from a hot to a cold body."
"Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power" is a book/monograph published in 1824 by French physicist Sadi Carnot,his only publication. The 65-page book's French title was Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. It is a significant publication in the history of thermodynamics about a generalized theory of heat engines. ... Carnot stated that motive power is due to the fall of caloric (heat) from a hot to a cold body."
No wonder that Sadi Carnot’s “Réflexions sur la puissance motrice du feu (Reflections on the Motive Power of Fire),” original treatise published in 1824, was not noticed at his time, when his ingenious reasoning of ideal heat engine reversible cycles, is not fully recognized, and may be truly comprehended by a few, even nowadays (M. Kostic).
Carnot, S. Reflections on the Motive Power of Heat (English translation by R.H. Thurston), Accompanied by "An Account of Carnot's Theory" by Sir William Thompson (Lord Kelvin),
Chapman & Hall, Ltd., London 1897. (10158 KB, 196 pages large PDF file)
Hosted by Prof. M. Kostic at kostic.niu.edu/
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Sadi Carnot (1824) laid ingenious foundations for the Second Law of Thermodynamics and discovery of Entropy before the First Law of energy conservation was even known (Joule, 1843), and long before thermodynamic concepts were established in the second half of the nineteenth century. In historical context, it is hard to comprehend now, how Carnot then, at age 28, ingeniously and fully explained the critical concepts of reversible thermo-mechanical processes and the limits of converting heat to work at inception of the heat engines’ era, when nature of heat was not fully understood. No wonder that Sadi Carnot’s “Réflexions sur la puissance motrice du feu (Reflections on the Motive Power of Fire ),” original treatise published in 1824, was not noticed at his time, when his ingenious reasoning of ideal heat engine reversible cycles, is not fully recognized, and may be truly comprehended by a few, even nowadays.
"Nothing occurs locally, nor globally in the universe, without mass-energy exchange/conversion and entropy production.
It is crystal-clear (to me) that all confusions related to the far-reaching fundamental Laws of Thermodynamics, and especially the Second Law (Abstract & FULL paper), are due to the lack of their genuine and subtle comprehension." > Sadi Carnot's Reflections <*> Clausius Theory of Heat <*> Kelvin Theory of Heat <