Engineering & Technology · Thermodynamics & Energy Systems

Exergy, resource quality and evaluating energy systems

Two sources each supply800 kJ, but one is only a little warmer than its surroundings and the other is much hotter. They have equal energy amounts. Their ability to supply work through a reversible engine is different, because the surrounding state affects what transformations remain possible.

Use Forces & Energy in Simple Systems for force, work, power and boundary accounts; Materials, Properties & Everyday Objects provides property vocabulary. Kelvin, moles, enthalpy and entropy are introduced here. Ratios and graph reading are needed; no calculus is required. Every operating record, diagram and numerical case is constructed. Named physical constants and chemical formulas retain their usual meanings; supplied states are not specifications or operating instructions.

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After reading, you can

Use an environmental reference to distinguish energy quantity from maximum useful-work potential.

Define the reference before naming available work

Exergy describes maximum useful work obtainable as a system comes to equilibrium with a specified reference environment through an ideal reversible process. Temperature T0, pressure p0 and relevant environmental composition belong to that reference. Exergy is therefore not a universal label attached to an energy amount without conditions.

A hot, pressurised or chemically different stream can possess work potential relative to its surroundings. Kinetic and gravitational energy can also matter. A stream already in complete equilibrium with the chosen environment has no remaining useful-work potential relative to it. That does not mean its internal energy is zero. Reference states make energy and exergy accounts answer different questions.

Compare temperature quality with a limited model

For heat Q transferred from a fixed reservoir at T above an environment at T0, the reversible work potential is XQ=Q(1−T0/T). The factor comes from the two-reservoir Carnot limit. Temperatures are absolute. A source cooling across a range cannot generally use its initial temperature for all of Q; its changing temperature must be included.

The figure shows how equal heat amounts can offer different maximum work. This quality comparison does not say low-temperature heat has no use. It can be well suited to a low-temperature heating task. Spending high-quality electrical work on a task that could use available low-temperature heat may sacrifice work opportunity, but feasibility, timing and other impacts still need examination.

At400 K,800(1−300/400)=200 kJ maximum work. At800 K,800(1−300/800)=500 kJ. Both total energy bars are800 kJ, using0.625 units/kJ. Remaining energy is not a destroyed-energy fraction.

Distinguish destruction from an unrecovered crossing

Energy is conserved in a complete account. Exergy can be destroyed by irreversibility. With a fixed reference temperature T0, destroyed exergy is Xdestroyed=T0 Sgen. Exergy may also leave with an exhaust or another unrecovered stream; that crossing is not the same as destruction inside the chosen boundary.

An exergy efficiency needs a defined desired product and supplied resource on a compatible basis. Electrical work delivered divided by supplied heat exergy answers a different question from work divided by heat energy. A useful energy-system assessment also states service, time variation, uncertainty, resource demand, cost and environmental consequences. Exergy identifies thermodynamic opportunities; it does not by itself rank every social or ecological outcome.

Compare energy efficiency with a work-potential account

For two constructed800 kJ heat transfers, take T0=300 K. At400 K, XQ=800(1−300/400)=200 kJ. At800 K, it is 800(1−300/800)=500 kJ. The difference300 kJ concerns maximum possible work, while both supplied energy amounts remain800 kJ.

Suppose the first case delivers100 kJ work. Its heat-to-work energy efficiency is 100/800=12.5%, while its work/exergy ratio is 100/200=50%. The remaining100 kJ exergy might be destroyed or leave unrecovered; that split needs evidence. Separately, Sgen=0.20 kJ/K at T0=300 K would correspond to 60 kJ destroyed exergy, not60 kJ destroyed energy.

Try the reasoning

Does zero exergy mean zero internal energy?
Show the answer and reasoning
No. It means no useful-work potential relative to the specified environmental equilibrium.
Can all unrecovered exhaust exergy be called destruction inside the converter?
Show the answer and reasoning
No. Exergy leaving the boundary and exergy destroyed internally are different terms.
Can the initial source temperature describe the exergy of all heat removed from a cooling finite body?
Show the answer and reasoning
Generally no. The temperature changes during removal and must be accounted for.

What to carry forward

Use energy to track amounts and exergy to track work opportunity relative to a declared environment. Keep destruction and outward transfer distinct.

References

Teaching resources and research supporting this lesson’s explanations and examples.