I. Entropy Increase: Energy Is "Depreciating"
Another formulation of the second law is that the entropy of an isolated system only increases and never decreases. Every heat transfer, every throttling, every mixing increases entropy, meaning the "availability" of energy declines. 1000 kJ of 300°C heat and 1000 kJ of 30°C heat differ in entropy and in their ability to do work.
II. What Is Exergy
Exergy, symbol E, refers to the part of energy that can theoretically be converted into useful work at most under a given environmental reference. Energy = Exergy + Anergy (the unusable part). For heat Q at temperature T, relative to ambient temperature T0:
E = Q · (1 − T0 / T)
As can be seen, the closer the temperature is to the environment, the closer exergy approaches 0. A 35°C cooling wastewater has a large amount of heat, but its exergy is almost zero—recovering it for heating is fine, but trying to generate power from it is a loss.
III. Using Exergy for Recovery Decisions
In engineering, "exergy efficiency" or "recovery cost-performance" is commonly used to judge:
- High-exergy waste heat (high-temperature flue gas): Recover first, high value per unit heat;
- Low-exergy waste heat (low-temperature drainage): Only worthwhile when the heat-use side is also at low temperature and equipment is cheap;
- Diluted large-flow low-temperature heat: Consider concentration or pressurization first, then recovery.
IV. A Practical Judgment Framework
When doing a waste heat project, it is recommended to first draw a "temperature-exergy" table: sort each waste stream by temperature, then match with heat-demand needs. Only pairings where the waste heat temperature is significantly higher than the heat-demand temperature yield positive returns. The root cause of many failed projects is using high-cost equipment to recover a bunch of "anergy"—the book heat is large, but the actual exergy is negative.
Remember: what is recovered is exergy, not total heat. Looking at the total makes you optimistic; looking at exergy keeps you clear-headed.