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

The thermodynamic efficiency (or just efficiency), h, of the engine is defined to be
......

h =

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 h = 50%.

It should be clear that w = DQ_H - DQ_C so,

h = =

Experiments show that h increases as the difference between T_H and T_C increases. It has been shown that the theoretical maximum efficiency of a heat engine is given by

hmax =

therefore, for an engine operating at maximum efficiency

or

In other words, for an engine operating at the theoretical maximum efficiency, the quantity DQ/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, DS, of the body. So, in general, we have the following definition of entropy

where DQ 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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