Carnot's Perfect Engine

France watched British engines

By the early nineteenth century, steam engines powered British mines and factories. Engineers could compare machines, but they lacked a theory that separated real improvement from extra complexity.

Sadi Carnot asked an unusually clean question: without friction, leaking heat, or weak materials, how efficient could the best possible engine be?

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Diagram description

Static physics diagram: carnot_heat_engine.

Learn from an engine that cannot be built

Carnot imagined a working substance moving through a completely reversible cycle between hot and cold reservoirs. The ideal efficiency depends only on their temperatures:

$$\eta_{\max}=1-\frac{T_c}{T_h}.$$

As long as the cold side is above absolute zero, no heat engine can turn all incoming heat into work.

Carnot still believed in the discarded “caloric” picture of heat, yet found the right structural limit from the wrong microscopic story. He died of cholera at thirty-six, and many papers were burned with his belongings. His small book survived to teach a durable method: before improving a real machine, discover the boundary that no real machine can cross.