Carnot's theorem is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.
This maximum efficiency is defined to be:
where
- 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 temperature of the cold reservoir, and
- is the absolute temperature of the hot reservoir.
A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient.
In other words, maximum efficiency is achieved if and only if no new entropy is created in the cycle. Otherwise, since entropy is a state function, the required dumping of heat into the environment to dispose of excess entropy leads to a reduction in efficiency. So Equation (1) gives the efficiency of any reversible heat engine.
The Coefficient of Performance (COP) of the heat engine is the reciprocal of its efficiency.
Read more about this topic: Carnot Heat Engine
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