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What did Sadi Carnot contribute to the study of heat engines?

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Engraved portrait of Rudolf Julius Emanuel Clausius, a bearded man in formal attire with sideburns, facing forward. — thermodynamics Rudolf Clausius (1822 - 1888) is considered one of the central founders of the science of thermodynamics.

Sadi Carnot made foundational contributions to the study of heat engines in his 1824 work, Reflections on the Motive Power of Fire. He moved beyond mechanical details to analyze the essence of the process, conceptualizing the Carnot cycle—an ideal sequence of pressure and temperature changes used as a standard for engine performance.12

Carnot famously proposed that motive power is produced when heat "drops" from a higher temperature to a lower temperature, analogous to water falling in a waterwheel. Although he worked within the now-outdated caloric theory, he correctly predicted that the efficiency of an idealized engine depends solely on the temperatures of its heat source and heat sink, rather than the specific working substance or mechanical design.13

This principle, known as Carnot's theorem, established that a reversible engine is the most efficient possible engine operating between two given temperatures. His insights were later incorporated into the formal development of thermodynamics by scientists such as Rudolf Clausius and Lord Kelvin.321