So, the second-law efficiencies are needed to gain a more realistic picture of a system's effectiveness.
The destruction of exergy is closely related to the creation of entropy and as such any system containing highly irreversible processes will have a low energy efficiency.
As an example the combustion process inside a power stations gas turbine is highly irreversible and approximately 25% of the exergy input will be destroyed here.
For fossil fuels the free enthalpy of reaction is usually only slightly less than the enthalpy of reaction so from equations (3) and (4) we can see that the energy efficiency will be correspondingly larger than the energy law efficiency.
Fuel cells, for instance, can theoretically reach much higher efficiencies than a Carnot engine; their energy source is not thermal energy and so their exergy efficiency does not compare them to a Carnot engine.
[1][2] Neither the first nor the second law of thermodynamics includes a measure of the rate of energy transformation.
When a measure of the maximal rate of energy transformation is included in the measure of second law efficiency it is known as second law efficiency under maximum power, and directly related to the maximum power principle (Gilliland 1978, p. 101).
Applications that seek changes in flow streams, like species concentration, require more careful definitions of control volumes and desired end states.
For example, for HVAC systems seeking to cool and dehumidify, it is reasonable to define their second law efficiencies for cooling and dehumidification by calculating exergy changes of all incoming and outgoing air and water streams, while assuming a target supply air temperature and humidity.
[3] In contrast, in thermal desalination for instance, the temperature of streams in real systems isn't important, so calculations should include control volumes that allow for outgoing brine and pure water streams to reach thermal equilibrium with their environment.