The Carnot cycle consists of the following steps:
The amount of work produced by the Carnot cycle, wcy, is the difference between the heat absorbed in step 1, qH and the heat rejected in step 3, qC. Or in equation form:
wcy = qH - qC (1)
The efficiency of a heat engine is defined as the ratio of the work done on the surroundings to the heat input at the higher temperature. Thus for the Carnot cycle:
efficiency = wcy/qH = (qH - qC)/qH = 1 - qC/qH (2)
It can also be shown that for the Carnot cycle qC/qH = TC/TH, so in terms of temperature, the efficiency is:
efficiency = 1 - TC/TH (3)
From Equation 3 it is clear that in order to maximize efficiency one should maximize TH and minimize TC.
Carnot's theorem states that No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs. Thus, Equation 3 gives the maximum efficiency possible for any engine using the corresponding temperatures. A corollary to Carnot's theory states that: All reversible engines operating between the same heat reservoirs are equally efficient. So Equation 3 gives the efficiency of any reversible engine.
In reality it is not practical to build a thermodynamically reversible engine, so real heat engines are less efficient than indicated by Equation 3. Nevertheless, Equation 3 is extremely useful for determining the maximum efficiency that could ever be expected for a given set of thermal reservoirs.
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