Exergy is a measure of the energy available to be used. Two energy sources can have the same stored energy but different exergy. Exergy captures the quality of a source of energy rather than just its total storage.
Energy is never destroyed, it merely changes from one form to another. Exergy is always destroyed in any real process and accounts for the irreversibility of the real world.
100% energy efficient sounds good …
If we burn fuel to produce 1kJ of heat energy and use all of that heat energy to produce hot water then our heating system is 100% energy efficient. Many domestic heating systems are >90% efficient and that certainly sounds good.
Unfortunately, the fact that domestic heating systems are approaching 100% efficient is a misleading comfort blanket. We have ignored the quality of the two energy stores.
… but not all energy is created equal
If the energy is stored in a gas, such as heated air, then the Carnot Efficiency tells us how much of that energy we can recover as useful work.
If the temperature of the environment is 20°C, the hot water is 60°C and the flame temperature is 1000°C then using Carnot heat engine equivalents, the 1kJ at the flame temperature can perform 770J of useful work but the 1kJ at the water temperature can only perform 120J of useful work. Same energy but very different exergy.
Exergy efficiency is more informative
This very simple example shows how the energy efficiency measure is unhelpful as it ignores the quality of the energy and treats all energy as equal.
In this example, 1kJ of energy in a flame is transferred to 1kJ of energy in hot water. 100% energy efficient.
But hot water at 60°C is far less useful (lower quality energy and so lower Exergy) compared to 1kJ at the flame temperature. Exergy analysis is more informative. 1kJ at flame temperature can perform 770J or useful work whereas 1kJ at the hot water temperature can perform 120J of useful work using Carnot cycle equivalents. The system is only 16% exergy efficient using this analysis, a figure that reflects the conversion of energy from a useful form into a less useful form.