Questions: Exergy Destruction and Sources of Irreversibility

Question 1

Steam passes through a throttling valve, reducing its pressure. Downstream, the steam's enthalpy is unchanged — the process conserves energy. What can be said about the steam's exergy?

• A. Exergy is also conserved, since energy is conserved and exergy is a form of energy
• B. Exergy is destroyed, because throttling is irreversible and generates entropy, and Ex_d = T₀ · Ṡ_gen > 0
• C. Exergy increases, because lower-pressure steam is more useful for downstream expansion
• D. Nothing can be said about exergy from an adiabatic, steady-flow process

Answer: (B)

Throttling is the canonical example that reveals the gap between first-law and exergy analysis. The first law says energy is conserved (enthalpy is constant). But throttling is highly irreversible — the pressure drop is unrestrained, generating entropy. Since Ex_d = T₀ · Ṡ_gen and Ṡ_gen > 0, exergy is destroyed. The lower-pressure steam has less capacity to do useful work than the high-pressure steam, even though its energy content is identical. Exergy analysis reveals what the energy balance hides.

Question 2

Two heat exchangers each transfer 1 MW of heat from a hot stream to a cold stream. Exchanger A maintains a small temperature difference (ΔT = 5°C); Exchanger B operates with a large temperature difference (ΔT = 80°C). Which correctly describes their exergy destruction?

• A. Both destroy the same exergy, since they transfer the same energy and satisfy the same first law
• B. Exchanger B destroys more exergy, because larger ΔT drives greater entropy generation
• C. Exchanger A destroys more exergy, because the small ΔT indicates inefficient thermal contact
• D. Exergy destruction depends only on the working fluids, not on the temperature difference between streams

Answer: (B)

Entropy generation due to heat transfer across a finite temperature difference is proportional to ΔT/T₁T₂. Larger ΔT means more entropy generated per unit of heat transferred, hence more exergy destroyed (Ex_d = T₀ · Ṡ_gen). Exchanger B, with its 80°C temperature difference, is far more irreversible than Exchanger A at 5°C — both move the same energy, but B squanders far more work potential doing so. This is why high-temperature process integration (keeping ΔT small) is a primary tool for thermodynamic efficiency improvement.

Question 3

If a process satisfies the first law of thermodynamics (energy is conserved), it also conserves exergy.

• T. True
• F. False

Answer: False

Energy conservation and exergy conservation are completely independent. The first law is satisfied by all real processes — energy cannot be created or destroyed. But exergy, unlike energy, is destroyed by every irreversible process. Throttling conserves energy but destroys exergy. Heat transfer across a finite ΔT conserves energy but destroys exergy. Friction conserves energy (converting kinetic energy to thermal energy) but destroys exergy. Exergy destruction is the thermodynamic measure of lost work potential — it is precisely what the first law is blind to.

Question 4

The exergy destroyed in a process is directly proportional to the entropy generated within that process, with the dead-state temperature T₀ as the proportionality constant.

• T. True
• F. False

Answer: True

This is the Gouy-Stodola theorem: Ex_d = T₀ · Ṡ_gen (or for steady processes, Ex_d = T₀ · σ̇). The dead-state temperature T₀ converts entropy generation (which has units of W/K) into an equivalent power loss (W). This makes exergy destruction actionable: instead of saying 'this process generates 2 kW/K of entropy,' the engineer says 'this process wastes 600 kW of work potential at T₀ = 300 K.' The proportionality to T₀ also means that higher ambient temperatures amplify the exergy cost of a given irreversibility.

Question 5

A throttling valve and a frictionless adiabatic expansion turbine both reduce gas pressure from P₁ to P₂. Both processes conserve energy. Explain why their exergy destructions differ, and what this implies for engineering design.

Model answer: Throttling is an unrestrained, irreversible pressure drop: no work is extracted, entropy is generated (Ṡ_gen > 0), and exergy is destroyed by Ex_d = T₀ · Ṡ_gen. The high-pressure gas could have pushed a turbine rotor, converting its pressure potential into shaft work — throttling discards all of that opportunity as waste heat. A frictionless adiabatic turbine extracts shaft work from the pressure drop with zero entropy generation (isentropic, reversible), so Ṡ_gen = 0 and no exergy is destroyed — all the pressure exergy is converted to useful work. For engineering design: wherever pressure must be reduced, replacing a throttle valve with an expansion turbine recovers that work potential rather than destroying it. This is the principle behind turboexpanders used in LNG plants and industrial gas separation to recover otherwise-wasted exergy.

The first law cannot distinguish between the throttle and the turbine — both conserve enthalpy (or nearly so). Only exergy analysis reveals that the throttle is an unambiguous thermodynamic disaster compared to the turbine, because it converts pressure exergy entirely into entropy rather than work.