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The Efficiency of a Heat Engine
Heat engines are often represented by diagrams like the one below.
The thermodynamic efficiency (or just efficiency),
, of the engine is defined to be
This fraction is usually multiplied by 100 to give a % so, if the net work done is only equal to half of the energy taken from the source, the engine has an efficiency of = 50%.
It should be clear that w = QH - QC so,
Experiments show that increases as the difference between TH and TC increases. It has been shown that the theoretical maximum efficiency of a heat engine is given by
therefore, for an engine operating at maximum efficiency
In other words, for an engine operating at the theoretical maximum efficiency, the quantity Q/T for the source will be equal in magnitude to the same quantity for the sink.
Realising the importance of this quantity, Clausius named it the change in entropy, S, of the body. So, in general, we have the following definition of entropy
where Q represents the quantity of energy entering or leaving the body and T represents the absolute (or Kelvin or thermodynamic) temperature at which the energy transfer takes place.