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:cquote|No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.
The rule was an essential stepping stone towards the formulation of the
second law of thermodynamics. When transforming thermal energyinto mechanical energy, the thermal efficiency of a heat engineis the percentage of energy that is transformed into work. Thermal efficiency is defined as
second law of thermodynamicsrequires The third law of thermodynamicsrequires the use of an absolute temperaturescale. Together they imply a maximum heat-to-work efficiency of: ] Carnot showed that the maximum efficiency possible by any sort of engine has a limit defined by the following efficiency :
: is the work done by the system (energy exiting the system as work),: is the heat put into the system (heat energy entering the system),: is the
absolute temperatureof the cold reservoir, and : is the absolute 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, which operate on the Carnot Cycle. They can extract only a certain proportion of mechanical energy from the heat of the working fluid, and this maximal amount is realized by the ideal Carnot heat engine.
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