Questions: Exergy (Availability) Balance for Control Volumes

Question 1

A first-law energy analysis of a power plant shows 65% of fuel energy is 'lost,' with most of that attributed to heat rejected in the condenser. An exergy analysis then reveals that the combustor — not the condenser — is responsible for the largest avoidable losses. Why does the first-law analysis fail to identify the combustor as the priority for efficiency improvement?

• A. First-law analysis ignores the combustor because it is not a heat exchanger
• B. First-law analysis tracks energy quantity but not quality — it cannot distinguish unavoidable heat rejection from irreversible destruction of useful work potential
• C. The combustor operates at such high temperatures that calorimetric measurements are unreliable
• D. Entropy generation in the combustor is zero because the reaction is exothermic

Answer: (B)

The first law says energy is conserved — it accounts for where energy goes but not how much useful work potential is destroyed along the way. Condenser heat rejection is 'large' by energy accounting but mostly unavoidable. The combustor destroys enormous exergy because high-temperature combustion is inherently irreversible (large entropy generation at high T). Only exergy analysis — which penalizes entropy generation via T₀Ṡ_gen — reveals this distinction.

Question 2

What is the physical meaning of the term T₀Ṡ_gen in the exergy balance for a control volume?

• A. The heat transferred to the environment at the dead-state temperature T₀
• B. The maximum shaft work the device could produce under reversible conditions
• C. The rate at which useful work potential is irretrievably destroyed by irreversible processes inside the control volume
• D. The entropy of the fluid stream entering the system boundary

Answer: (C)

T₀Ṡ_gen is the exergy destruction rate: the product of the dead-state temperature and the entropy generation rate. Since entropy generation is always ≥ 0 (second law), T₀Ṡ_gen ≥ 0 — exergy can only be destroyed, never created by irreversibility. It quantifies the gap between what a reversible device would deliver and what the real device actually delivers: the irretrievable penalty for friction, mixing, heat transfer across gradients, and other irreversibilities.

Question 3

Exergy is destroyed whenever heat is transferred across a finite temperature difference, even though the total energy involved is conserved.

• T. True
• F. False

Answer: True

True. The first law is satisfied — energy is conserved in the heat transfer. But heat flowing from a hot reservoir to a cold one generates entropy (Ṡ_gen = Q/T_cold − Q/T_hot > 0 for finite ΔT), and that entropy generation destroys exergy at rate T₀Ṡ_gen. This is why heat exchangers with large temperature differences are significant sources of exergy destruction even when no energy is 'lost.'

Question 4

A device that converts 95% of its input energy into useful output (near-perfect first-law efficiency) should also have near-perfect second-law (exergy) efficiency.

• T. True
• F. False

Answer: False

False. A throttle valve, for example, converts essentially 100% of its inlet enthalpy into outlet enthalpy (ΔH ≈ 0, first-law efficiency ≈ 100%) yet destroys significant exergy through irreversible pressure drop. The second-law efficiency measures how close actual performance is to the reversible limit in terms of useful work potential, not energy quantity. A device can be first-law efficient while performing far below its thermodynamic optimum.

Question 5

Explain why exergy destruction — rather than energy 'loss' — is the appropriate diagnostic for identifying where to invest in efficiency improvements in a complex thermodynamic system.

Model answer: Energy is conserved by the first law, so it is never truly 'lost' — it merely changes form or location. In a power plant, most of the energy that leaves as condenser heat is unavoidable and not improvable. Exergy destruction, T₀Ṡ_gen, measures only the irreversible penalty: the work potential permanently destroyed by irreversibilities such as friction, heat transfer across temperature gradients, and mixing. By computing exergy destruction for each component, engineers can rank them by how much avoidable loss each causes, and direct investment toward those with the greatest improvement potential. Without this, optimization efforts may target large energy flows that are actually unavoidable rather than the smaller but improvable irreversibilities.

The key insight is that second-law analysis converts the second law from a qualitative principle ('irreversibility costs you something') into a quantitative accounting tool. Component-by-component exergy destruction accounting gives engineers a ranked list of thermodynamic liabilities, which is impossible to construct from energy balances alone.