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Happy 200th birthday, Carnot’s theorem!

  • Nicolas Léonard Sadi Carnot proved a fundamental limitation on engines’ efficiencies, which governs engines that draw energy from heat, rather than from, say, the motional energy of water cascading down a waterfall.
  • Carnot cap the engines’ efficiencies that prevents engineers from wasting their time on daydreaming about more-efficient engines.
  • Carnot’s theorem encapsulates the second law of thermodynamics, which helps us understand why time flows in only one direction.
  • The engine mustn’t waste heat and one can keep the gas quiescent only by running the cycle infinitely slowly, so perfect efficiency is achievable only in principle, not in practice.
  • Carnot’s theorem provides what physicists call a sanity check whenever researchers devise a new heat engine.
  • Carnot’s theorem also serves as a school exercise and a historical tipping point.
  • Carnot’s theorem is practical and fundamental, pedagogical and cutting-edge.
  • Carnot upper-bounded the efficiency achievable by every heat engine of the sort described above.
  • Capping engine efficiencies caps the output one can expect of a machine, factory, or economy.
  • The Carnot cycle provides intuition, serving as a simple example on which thermodynamicists try out new ideas, such as quantum engines.

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