Questions: Exergy and Availability: Useful Work Potential

Question 1

Two tanks each contain exactly 1000 J of thermal energy. Tank A is at 800°C; Tank B is at 50°C. Ambient temperature is 20°C. Which tank has more exergy?

• A. Tank B, because it is closer to ambient temperature and thus easier to extract work from
• B. They have equal exergy because they contain equal amounts of energy
• C. Tank A, because its greater departure from the dead state enables more useful work to be extracted
• D. Tank B, because it requires less cooling to reach the dead state

Answer: (C)

Exergy depends on both the energy content and the quality of that energy — specifically, how far the system is from the dead state. Tank A is far above ambient (800°C vs 20°C ambient), giving it a large temperature differential to exploit in a heat engine. Tank B is only 30°C above ambient, severely limiting the fraction of its energy that can be converted to work. The Carnot efficiency sets the ceiling: for Tank A, η_max ≈ 1 − 293/1073 ≈ 73%; for Tank B, η_max ≈ 1 − 293/323 ≈ 9%. Equal energy content does not mean equal work potential.

Question 2

A power plant analysis shows two heat losses: 10 kJ lost at 800°C and 20 kJ lost at 100°C (ambient = 20°C). Which represents greater exergy destruction?

• A. The 20 kJ at 100°C, because the absolute energy lost is larger
• B. They are equivalent — exergy destruction equals the energy lost in both cases
• C. The 10 kJ at 800°C, because high-temperature energy has far higher quality and more useful work is destroyed per joule
• D. The 20 kJ at 100°C, because the temperature is closer to ambient, making recovery impossible

Answer: (C)

Exergy content per joule = (1 − T₀/T). At 800°C (1073 K): exergy fraction = 1 − 293/1073 ≈ 0.73, so 10 kJ × 0.73 = 7.3 kJ destroyed. At 100°C (373 K): exergy fraction = 1 − 293/373 ≈ 0.21, so 20 kJ × 0.21 = 4.2 kJ destroyed. The smaller high-temperature loss destroys nearly twice as much exergy. This is the central insight of exergy analysis: energy magnitude is a misleading metric for waste; quality matters.

Question 3

A system at the 'dead state' — in full thermal and mechanical equilibrium with its environment — has zero exergy and can produce no further useful work.

• T. True
• F. False

Answer: True

This is the definition of the dead state. Exergy measures the departure from equilibrium with the environment. When a system is at T₀ and P₀ (ambient temperature and pressure), every term in the exergy formula goes to zero: (U − U₀) = 0, (V − V₀) = 0, (S − S₀) = 0. The system has nowhere left to go spontaneously, and no work can be extracted by interacting with an environment at the same state.

Question 4

Exergy, like energy, is conserved in most real thermodynamic processes.

• T. True
• F. False

Answer: False

This is the crucial distinction between exergy and energy. The first law guarantees that energy is conserved — it cannot be created or destroyed. Exergy, by contrast, is destroyed whenever entropy is generated (the Gouy-Stodola theorem: exergy destruction = T₀ × entropy generation rate). Any irreversibility — friction, heat transfer across a finite temperature difference, mixing, combustion — destroys exergy permanently. You end with the same amount of energy but less of it is useful. This is the thermodynamic definition of 'waste.'

Question 5

Why do engineers use exergy analysis instead of (or alongside) first-law energy analysis when designing more efficient thermal systems?

Model answer: First-law analysis tracks energy quantities — inputs, outputs, and losses — but cannot distinguish between high-quality energy that can do work and low-quality waste heat that cannot. Exergy analysis tracks the work potential of energy, accounting for both the quantity and quality of each energy stream. This allows engineers to identify which components in a system are destroying the most valuable energy — not just losing the most energy in absolute terms. A small high-temperature heat loss may represent far greater exergy destruction (lost work potential) than a larger low-temperature loss. Exergy analysis pinpoints the true thermodynamic bottlenecks.

This is why modern energy system design uses both analyses in parallel. The first law tells you where energy goes; the second law (via exergy) tells you where value is being wasted. For example, in a combined-cycle power plant, the combustor destroys enormous exergy (high-temperature combustion is highly irreversible) even though the heat is retained within the cycle. Only exergy analysis reveals this.