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Thermal Physics

The Efficiency of a Heat Engine

Heat engines are often represented by diagrams like the one below.

During each cycle:

w is the net work done by the engine

DELT01QH is the energy taken from the (hot) source

DELT01QC is the energy given to the (cold) sink


The thermodynamic efficiency (or just efficiency), NSMALL, 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 NSMALL= 50%.

It should be clear that w = DELTA02QH - DELTA02QC so,


Experiments show that NSMALL 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 DELTA02Q/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, DELTA02S, of the body. So, in general, we have the following definition of entropy

where DELTA01Q 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.

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