Carnot's theorem (thermodynamics)

Carnot's theorem, also called Carnot's rule is a principle which sets a limit on the maximum amount of efficiency any possible engine can obtain, which thus solely depends on the difference between the hot and cold temperature reservoirs. Carnot's theorem states:

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The rule was an essential stepping stone towards the formulation of the second law of thermodynamics. When transforming thermal energy into mechanical energy, the thermal efficiency of a heat engine is the percentage of energy that is transformed into work. Thermal efficiency is defined as

,

  Carnot showed that the maximum efficiency possible by any sort of engine has a limit defined by the following efficiency η:

where:

W is the work done by the system (energy exiting the system as work),

Q_H is the heat put into the system (heat energy entering the system),

T_C is the absolute temperature of the cold reservoir, and

T_H is the temperature of the hot reservoir.

Carnot's theorem sets essential limitations on the yield of a cyclic heat engine such as steam engines or internal combustion engines: they can extract only a certain proportion of mechanical energy from the heat of the working fluid; this maximal amount is realized by the ideal Carnot heat engine.