La Bourse / Volume II / Nº II.06 / Quiz, reflection, essays

A woman walking away along a path through a glasshouse of palms, sunlight breaking through the canopy ahead of her. — Plate II.06 · Quiz, reflection, essaysThe Glasshouse Behind the Turbine Hall.The turbine took the work out of the steam. The glasshouse is what was left, and what was left is warm, and warmth is not nothing.

ASSESSMENT · Chapter II.06 — Thermodynamics and Economic Flow

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. Define exergy, and state what it is measured against.

Exergy is the maximum work obtainable from a system as it comes into equilibrium with a defined reference environment — the dead state. One mark for the definition, one for naming the dead state as a required and declared choice. An answer that omits the reference environment has defined nothing: exergy is a relation, not a property.

2. Write the Gouy–Stodola relation and say what each term is.

W_lost = T₀ · S_gen — the work destroyed in a real process equals the dead-state temperature times the entropy generated. Credit any answer that notes the practical consequence: an energy audit always balances and an exergy audit never does, and the gap is the finding.

3. State Georgescu-Roegen's central claim about the economic process, and then state his proposed fourth law.

Central claim: the economic process is entropic and irreversible — it converts low-entropy inputs into high-entropy waste, so the economy has a physical direction that a circular-flow model omits. Fourth law: in a closed system available matter degrades irrevocably into unavailable matter, so complete recycling is impossible even with unlimited energy. Full marks require both, stated separately. The distinction is the whole chapter.

4. Why did physicists reject the fourth law, and what survives it?

Bianciardi, Tiezzi and Ulgiati (1993) showed complete material recycling is thermodynamically possible given a sufficient energy flux through an open system; Earth is open, receiving 173,000 TW against 19.0 TW of human primary power. What survives is the practical claim — recovering dispersed matter is brutally expensive — which is a cost curve rather than a law, and therefore moves when technology moves.

Four on application.

5. A facilities manager reports that the site's new boilers are 90 percent efficient, up from eighty-two, and proposes no further action on heating. Diagnose the reasoning.

The figure is first-law and the decision needs a second-law answer. A 90 percent boiler delivering room heat has a second-law efficiency of 6.20 percent; a heat pump at COP 3.5 delivers 24.99 percent, 4.03 times better, for the identical service. The boiler upgrade improved a number that was never the constraint. The stronger answer notes that both figures are correct and that the error is in which question was asked.

6. A colleague argues that because energy is only about six percent of the economy's cost, energy efficiency cannot be a major driver of growth. What is the strongest reply, and what is the strongest reply to the reply?

Reply: the relevant factor is useful work, not energy, and it grew at 4.019 percent a year over the American century against output growth of 3.2 percent; at an elasticity near 0.70 it accounts for 87.9 percent of growth. Reply to the reply: an elasticity of 0.50 against a cost share of 6.0 percent is a wedge of 8.3 times, and under competitive factor pricing elasticity equals cost share — so the claim requires markets to misprice energy by nearly an order of magnitude. Full marks require both halves. A candidate who gives only the first has learned an advocacy position.

7. Two proposals arrive: recover a metal from a tailings dam at 0.2 percent concentration, or redesign a product so the same metal ends its life in a separable component. On the chapter's arithmetic, which is more promising, and why?

The redesign, decisively. The thermodynamic minimum for separation rises only logarithmically with dilution — a seventy-million-fold dilution raises it by 4.41 times — but the mass handled rises as 1/x, and that is what the recovery bill is made of. Avoiding dispersal at design time removes the throughput term entirely, which is why remelting aluminium scrap costs 0.70 kWh/kg against 14.00 in a smelting cell. Credit any answer that names the throughput term rather than entropy as the binding cost.

8. Your site has no neighbouring heat customer. Does the cascade principle still apply?

Yes. The principle is matching grade to task, not selling to a third party. A site can lift its own low-grade streams with a heat pump for a priced amount of exergy, or store the tail in a water tank and use it to flatten its own morning demand. The stronger answer observes that the absence of a counterparty changes the instrument — no offtake agreement — but not the physics, and that the first three design mechanisms in the chapter cost no capital at all.

Two that require the arithmetic to be done.

9. A process stream carries 6.0 MW of heat at two hundred and fifty degrees Celsius, against a dead state of fifteen degrees. Compute its exergy. A CHP alternative would instead deliver 2.1 MW of electricity. Compare, and say what the first law would have told you.

f = 1 − 288.15/523.15 = 0.4492, so the exergy of the stream is 6.0 × 0.4492 = 2.695 MW. Electricity is pure exergy, so 2.1 MW is 77.9 percent of the stream's entire work capacity. The same 6.0 MW delivered as sixty-degree hot water carries only 0.810 MW of exergy — 30.1 percent. The first law, comparing 2.1 MW against 6.0 MW, says the electricity route throws away two thirds of the resource; the second law says it captures more than three quarters of what was there. Full marks require the comparison to be stated in both laws, and the conclusion that they disagree.

10. A plant delivers 40,000 MWh of heat a year at fifty-five degrees, against a dead state of five degrees. Today it burns gas in a 92 percent boiler. A heat pump at COP 3.2 is proposed. Compute both second-law efficiencies and the change in exergy input.

f(55 °C) = 0.1524, so exergy delivered is 40,000 × 0.1524 = 6,095 MWh. Gas route: 40,000 / 0.92 = 43,478 MWh of fuel, second-law efficiency 14.02 percent. Heat pump: 40,000 / 3.2 = 12,500 MWh of electricity, second-law efficiency 48.76 percent. Exergy input falls by 71.2 percent for the identical service. Credit any method reaching a fall near seventy percent. The point of the question is that the service is unchanged and the resource consumed is cut by two thirds — which is a capital decision, not a virtue.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

Where in your own week do you spend something of high grade on a task that needed something ordinary? Answer about attention and skill before answering about fuel.

Think of a time you improved a number that turned out not to be the constraint. What told you afterwards, and what could have told you before?

What in your work is genuinely irreversible — what, once spent, does not come back in any form? Name it precisely. Most people name the wrong thing first.

Where have you accepted a claim because the person making it was right about the important part? What did the overstatement cost when somebody found it?

What is the tail of your own work — the by-product you discard that somebody downstream of you could use? Who is downstream of you, and have you asked?

Recall an argument you lost because a figure of yours was loose. What would you give now to have had that one number tight?

What are you measuring because it is easy rather than because it decides anything? What would the deciding measurement cost to start this month?

Where in your life have you designed something so that it could be taken apart again — and where have you mixed things together in a way you cannot undo? Write both, without judging either.

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. The wedge. The useful-work account credits a factor paid around six percent of national income with a large majority of measured growth. Argue either that this proves factor markets systematically misprice energy — and say through what mechanism — or that the elasticity is an artefact of the chosen functional form and the cost share is the better estimate. Use Ayres and Warr (2005) directly, and at least one source on production-function identification or the estimation of factor elasticities that the chapter does not cite.

2. Was the fourth law a useful error? Georgescu-Roegen's fourth law is false as physics and his practical claim about dispersal survives. Argue whether the overstatement advanced the field — by forcing a serious refutation that clarified what was true — or set it back by giving critics a costless dismissal. Engage Bianciardi, Tiezzi and Ulgiati (1993) and Ayres (1999), and find at least one later assessment of Georgescu-Roegen's legacy that the chapter does not cite.

3. Thermodynamics as a theory of value. Exergy is a scalar with no preference content: two goods of equal exergy can differ in worth by orders of magnitude. Argue either that exergy should be treated as a constraint on production and never as a basis of value, or that an exergy-denominated accounting captures something real that price does not. Use Kåberger and Månsson (2001), and one source in the economics of value — classical, neoclassical or ecological — that the chapter does not cite.

4. Rebound and the honest saving. The chapter's cascade returns 22.70 percent on the facility against a WACC of 8.00 percent. Argue whether such savings should be reported net of an expected rebound effect, and if so how it should be estimated and who should verify it. Use Sorrell, Dimitropoulos and Sommerville (2009), and one empirical study of rebound in an industrial rather than household setting that the chapter does not cite.

5. The threshold. The chapter states its own boundary: below roughly two percent of cost, an exergy account is bookkeeping rather than management. Take a position on what a service-dominated economy should therefore do with thermoeconomics — confine it to the industrial core where it discriminates, extend the accounting to embodied exergy in purchased inputs, or abandon it as a management tool and keep it only as a national statistic. Use Cullen and Allwood (2010), and one source on embodied energy, consumption-based accounting or supply-chain footprinting that the chapter does not cite.