A power plant's turbine is 90% isentropically efficient, but exergy analysis reveals that the combustion chamber destroys far more exergy than the turbine. What does this reveal about first-law energy analysis alone?
AEnergy analysis is wrong — it must have underestimated turbine losses
BEnergy analysis cannot show where work potential is wasted, since combustion conserves energy while massively generating entropy
CExergy and energy analysis always agree on which component causes the largest losses
DThis result is impossible — a 90% efficient turbine must be the dominant loss component
Energy is conserved in combustion — chemical energy becomes thermal energy of hot gases, with no energy 'lost.' But burning fuel at a flame temperature far above the working fluid temperature is highly irreversible: entropy is generated massively. Exergy analysis converts this entropy generation to destroyed work potential via Ex_destroyed = T₀·Ṡ_gen, revealing that the combustion chamber can dominate losses even when the turbine is highly efficient. Energy analysis treats all joules as equivalent regardless of source temperature; exergy analysis penalizes irreversible temperature differences, making this invisible-to-energy loss visible.
Question 2 Multiple Choice
A heat exchanger operates steadily and generates 5 W/K of entropy at an environment temperature T₀ = 300 K. How much work potential does it destroy per second?
A5 W, because entropy generation rate equals work destruction rate
B300 W, because the dead-state temperature sets the scale
C1500 W, by the Gouy-Stodola theorem: Ex_destroyed = T₀ × Ṡ_gen
DThe work destruction cannot be determined without knowing the heat transfer rate
The Gouy-Stodola theorem states Ex_destroyed = T₀ × Ṡ_gen. With Ṡ_gen = 5 W/K and T₀ = 300 K: Ex_destroyed = 300 × 5 = 1500 W. This converts entropy generation (which has units W/K, not useful for engineering comparisons) into destroyed work potential in watts, the same units as power output. Option A confuses entropy generation rate with power. Option D is wrong because Gouy-Stodola requires only Ṡ_gen and T₀ — no heat transfer details are needed.
Question 3 True / False
Exergy, unlike energy, can be destroyed by irreversible processes — every real process destroys some exergy.
TTrue
FFalse
Answer: True
This is the fundamental distinction between energy and exergy. The first law says energy is always conserved — it transforms from one form to another but never disappears. Exergy measures the ability to do useful work relative to the dead state. Every irreversibility (friction, heat transfer across a temperature difference, mixing, unrestrained expansion) generates entropy, and the Gouy-Stodola theorem directly links entropy generation to exergy destruction: Ex_destroyed = T₀ × Ṡ_gen > 0 for any irreversible process. Only a reversible process achieves zero exergy destruction.
Question 4 True / False
Energy analysis and exergy analysis usually agree on which component of a power cycle causes the greatest thermodynamic losses.
TTrue
FFalse
Answer: False
This is false — and this disagreement is precisely why exergy analysis is valuable. Energy analysis tracks quantities in and out and identifies losses as heat rejected to the environment. It cannot distinguish between heat rejected at high temperature (large work potential squandered) and heat rejected at low temperature (small work potential lost). Exergy analysis penalizes irreversibilities by their Carnot factor (1 − T₀/T), revealing that combustion chambers — which operate at extreme temperatures with massive entropy generation — often destroy far more work potential than the turbine or condenser. Energy analysis would miss this because all joules look the same to it.
Question 5 Short Answer
Why does the Gouy-Stodola theorem (Ex_destroyed = T₀ × Ṡ_gen) make exergy analysis more useful than entropy analysis alone for identifying sources of inefficiency in thermal systems?
Think about your answer, then reveal below.
Model answer: Entropy generation Ṡ_gen has units of W/K, which makes it impossible to compare directly against work outputs or to aggregate losses across components with different temperatures. Multiplying by T₀ converts entropy generation to destroyed work potential in watts — the same units as power output. This allows direct comparison: a heat exchanger generating 2 W/K and a turbine generating 5 W/K can be ranked by their exergy destruction (600 W vs 1500 W at T₀ = 300 K). The result is an engineering diagnostic ranking inefficiencies in units directly relevant to the system's purpose: how much work could have been produced but wasn't.
Exergy analysis is used in industrial process design because it answers the question engineers care about: 'Where is useful work being wasted, and by how much?' Entropy generation is a correct thermodynamic indicator but an inconvenient engineering one. Gouy-Stodola bridges the gap by converting the abstract measure into actionable units.