Exergy, also called availability, measures the maximum useful work a system can deliver as it comes to equilibrium with its surroundings. It matters because energy is conserved, but useful energy can be degraded by real processes. A hot gas, a spinning shaft, or a pressurized tank may contain energy, but only part of that energy can usually be converted into useful work.
Engineers use exergy to compare the quality of energy sources and to find where performance is lost.
Key Facts
- Exergy is the maximum useful work obtainable as a system reaches equilibrium with the environment.
- At the dead state, a system has no exergy because it is in thermal, mechanical, and chemical equilibrium with the environment.
- For a heat transfer Q at boundary temperature T, the exergy transfer is Ex_Q = Q(1 - T0/T), where T0 is the environment temperature.
- For steady-flow devices, an exergy balance can be written as Ex_in - Ex_out - W_useful = Ex_destroyed.
- Exergy destruction is caused by irreversibility and is related to entropy generation by Ex_destroyed = T0 S_gen.
- Energy is conserved in every process, but exergy is not conserved in real processes because some availability is destroyed.
Vocabulary
- Exergy
- Exergy is the maximum useful work that can be obtained from a system as it comes to equilibrium with its environment.
- Availability
- Availability is another name for exergy, emphasizing the portion of energy available to do useful work.
- Dead state
- The dead state is the condition where a system is in complete equilibrium with the environment and has zero exergy.
- Irreversibility
- Irreversibility is the effect of real processes such as friction, heat transfer through a finite temperature difference, and mixing that prevents maximum work output.
- Exergy destruction
- Exergy destruction is the loss of useful work potential caused by entropy generation in an irreversible process.
Common Mistakes to Avoid
- Treating energy and exergy as the same thing is wrong because energy is conserved while exergy can be destroyed by irreversibilities.
- Ignoring the environment temperature T0 is wrong because exergy depends on the system's ability to interact with its surroundings.
- Assuming all heat can become useful work is wrong because heat at a temperature near the environment has little work potential.
- Calling lost exergy lost energy is wrong because the energy still exists, but its ability to produce useful work has been degraded.
Practice Questions
- 1 A heat engine receives 500 kJ of heat from a reservoir at 600 K while the environment is at 300 K. What is the maximum useful work associated with this heat transfer using Ex_Q = Q(1 - T0/T)?
- 2 A process generates 0.80 kJ/K of entropy while the environment is at 298 K. Calculate the exergy destroyed using Ex_destroyed = T0 S_gen.
- 3 Two systems contain the same amount of energy: one is a tank of compressed air and the other is warm water only slightly above room temperature. Explain which has higher exergy and why.