Exergy (Availability) of a Heat Stream
Exergy (Availability) of a Heat Stream
Not all heat is equally valuable: a kilowatt of heat at 450 K can do far more useful work than the same kilowatt at 320 K, because the potential to extract work depends on how far the heat's temperature is above the surrounding environment (the "dead state"). Exergy, also called availability, quantifies exactly this — the maximum work a reversible engine could extract from a heat stream before it cools to ambient temperature. Exergy analysis is increasingly used alongside simple energy balances in process and power plant design because a first-law energy balance treats a joule of low-temperature waste heat as equally valuable as a joule of high-temperature process heat, when in fact the low-temperature stream may have almost no capacity left to do useful work — exergy exposes where the real thermodynamic value is being lost.
The exergy of a heat stream is Ex = Q·(1 - T0/Ts), the Carnot factor between the stream and ambient temperature applied to the heat rate. where Q is the heat rate, T0 is the ambient (dead-state) temperature, and Ts is the temperature at which the heat is supplied.
Inputs
Q_str := 500 kW=500000 W
T_0 := 298 K=298 K
T_s := 450 K=450 K
Multiplying the heat rate by the Carnot factor between the stream temperature and ambient gives the maximum work a perfectly reversible engine could extract from that heat — its exergy, or true thermodynamic value.
Ex_str := Q_str·(1 - T_0/T_s)=168888.89 W
Results
The exergy here, roughly 169 kW out of the 500 kW heat stream, shows that only about a third of the heat's energy content is actually convertible to work at this temperature — the rest is energy that can be used for heating but cannot, even in principle, be turned into shaft work or electricity. This gap between energy (500 kW) and exergy (169 kW) is exactly what a waste-heat-recovery project should evaluate before committing capital to install a bottoming cycle, since it caps the theoretical maximum power that stream could ever generate. Streams closer to ambient temperature have proportionally even less exergy, which is why low-grade waste heat below roughly 100°C is rarely worth converting to power and is better used directly for heating.
Assumptions & limitations
- Reversible (ideal Carnot) work extraction assumed — a theoretical maximum, not achievable in practice.
- Ambient (dead-state) temperature T0 must be defined consistently for the whole analysis.
- Heat stream temperature Ts treated as constant, not varying as heat is extracted.
- Chemical and other exergy components (only thermal/thermomechanical) not included.