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Commerce · II.06 · MMXXVI · daylight

La Bourse  /  Volume II  /  Nº II.06  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter II.06 · Thermodynamics and Economic Flow

A term of practice. One project, carried the whole way. Applied to a life you actually live.

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WHY THIS WORKBOOK IS DIFFERENT

Most courses that touch thermodynamics ask you to solve a cycle on paper and then hand the paper in. This one asks you to keep an account.

The reason is that the chapter's whole claim is that exergy is the economically meaningful quantity and almost nobody counts it. You cannot learn that by agreeing with it. You learn it by counting something for eleven weeks and watching what the count tells you that the energy bill did not.

You need three things and no laboratory: a thermometer that reads to a degree, a spreadsheet, and the willingness to write down a temperature every time you write down an energy figure. That is the entire apparatus. The chapter's central tool — the Carnot factor 1 − T₀/T — is one cell.

One rule before you start, and it will save the whole term. Declare your dead state in writing on day one, on the first line of the spreadsheet, and do not change it. Ten degrees Celsius — 283.15 K — is a defensible annual mean for most temperate places. If you change it mid-term, every figure you have recorded becomes incomparable and you will not notice. Write it down. Sign it, even if the only signature is yours.

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PART ONE — DISCOVERY

Weeks 1–3: find the grade mismatches

Exercise 1.1 — The household audit.

List every place in your home where energy is converted. Kettle, shower, radiator, laptop, oven, car if you have one. For each, write three columns: what grade goes in, what grade comes out, what the task actually required.

You are looking for one thing only: where something of high grade is being spent on a task that needed something ordinary. An electric resistance heater is the purest case — it takes electricity, which is pure exergy, and produces room warmth, which against a freezing outside carries a Carnot factor of 0.0714. Nearly everything the electricity could have done is destroyed on the way.

Do not fix anything yet. Count first.

Exercise 1.2 — The boiler, computed.

Work the chapter's example yourself, without looking at the answer. A gas boiler at ninety percent first-law efficiency, a room at twenty-one degrees, an outside at zero.

  methane LHV                    802.3   kJ/mol
  methane chemical exergy        831.65  kJ/mol
  heat delivered at 90 %         722.07  kJ/mol
  Carnot factor                    0.0714
  exergy delivered                51.55  kJ/mol
  second-law efficiency             6.20 %

Then do the heat pump at COP 3.5 and get 24.99 percent, a ratio of 4.03.

The point of doing it by hand is that the arithmetic is trivial and the conclusion is not. You will not forget a number you computed. You will forget every number you read.

Exercise 1.3 — Find the cascade near you.

Every city has one and almost nobody points at it. A bakery above a flat that never needs heating. A data centre warming a swimming pool. A brewery selling its spent grain. A laundry, a greenhouse, a district heating pipe under a road with a manhole that steams in January.

Find one. Go and look at it. Write half a page on what grade enters, what grade leaves, and who the next user is. If you cannot find one, that is also a finding, and the question becomes: what would the first one here be?

Exercise 1.4 — The dispersal walk.

Choose five objects you own. For each, name one material in it and write where the atoms are at end of life: in a lump, in an alloy, in a coating, in a solution, in a plume. Aluminium in a drinks can is a lump, and remelting costs 0.70 kWh/kg against 14.00 for smelting — a 95.0 percent saving earned entirely by not dispersing. Zinc in a tyre is a dispersion, and it is gone.

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PART TWO — THE ARITHMETIC

Weeks 4–6: compute before you argue

Exercise 2.1 — Build the Carnot sheet.

One spreadsheet, four columns: temperature in Celsius, temperature in Kelvin, dead state, Carnot factor. Fill it for every temperature that appears in your life: 0.0714 for a winter room, 0.1501 for sixty-degree water, 0.2203 for ninety-degree district heat, 0.5060 for a three-hundred-degree stack, 0.8634 for a flame.

Then make the graph. You are looking at the reason grade matters, and the shape of the curve — steep at the bottom, flattening at the top — is the reason low temperatures are so expensive to work with and so cheap to supply.

Exercise 2.2 — The dilution problem.

Compute R·T₀·ln(1/x) for copper at two concentrations: 5.00e-03 in ore and 7.1e-11 in seawater. You should get 13.13 kJ/mol and 57.93 kJ/mol, or 0.0574 and 0.2532 kWh/kg.

Now answer, in writing, before reading on: the dilution between these is 7.042e+07 times and the energy rises by 4.41 times. Why did you expect otherwise?

Then compute the mass. 200 kg of ore per kilogram of copper against 4,000,000,000 kg of seawater: a ratio of 20,000,000. Pumping alone, at 0.10 kWh per tonne, is 400,000 kWh per kilogram.

This is the exercise the whole chapter is built to make you do. Nothing you read replaces having watched the logarithm refuse to grow while the throughput term ran away.

Exercise 2.3 — The growth decomposition.

Reproduce the century. Aggregate efficiency 2.5 percent to 13.0 percent over ninety-eight years is 1.682 percent a year. Primary energy 9.6 to 94.8 quads is 2.337 percent a year. Useful work therefore grows at 4.019 percent a year — a multiple of 51.4 — against real output at 3.2 percent, or 23.0 times.

Then build the attribution table for elasticities of 0.30, 0.50 and 0.70, and find the value that absorbs Solow's 87.5 percent residual exactly. It is 0.697.

Exercise 2.4 — Now argue against yourself.

Write one page attacking the result you just produced. The strongest attack is the wedge: an elasticity of 0.50 against a cost share of 6.0 percent is 8.3 times, and competitive factor pricing says elasticity equals cost share. Make that argument as well as you can. A result you cannot attack is a result you do not yet understand, and this one has a real weakness that you should be able to state before anybody asks you to.

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PART THREE — DREAM AND DESIGN

Weeks 7–9: build the instrument

Exercise 3.1 — The exergy column.

Take one real energy bill — yours, your department's, a building you have access to — and add the delivered temperature. Compute exergy delivered and exergy destroyed for a month. Two numbers.

Then write one paragraph: what does the second number say that the bill did not?

Exercise 3.2 — Design a cascade on paper.

Choose a real site you know: a campus, a hotel, a farm, a small factory. List every thermal demand and order it by required grade, descending. Match against whatever streams exist. Draw it as a staircase, not a flow chart.

Then mark the step where the match fails, and price a heat pump to lift the stream one grade. That step is where the capital goes.

Exercise 3.3 — Write the indexed tariff.

One clause, in plain language: price(T) = base × f(T)/f(90 °C). Work a case. At a base of 38.04 EUR/MWh-thermal, ninety-degree heat costs 172.69 EUR per megawatt-hour of exergy and sixty-degree heat costs 253.48 — an overcharge of 46.8 percent that the indexed price reduces to 25.92 EUR/MWh-thermal.

Then write the paragraph you would say out loud to the counterparty. That paragraph is the deliverable, not the formula.

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PART FOUR — DESTINY AND DELIGHT

Weeks 10–11: make it hold, and notice that you enjoy it

Exercise 4.1 — Write the failure modes before they happen.

Four are named in the chapter: exergy fetishism, dead-state drift, rebound, and cascade lock-in. For each, write one sentence describing how it would show up in your project specifically, and one control that would catch it.

Exercise 4.2 — The threshold test.

Compute where your account stops discriminating. At energy 30.0 percent of cost, a twenty-percent exergy saving moves total cost by 6.00 percent; at 10.0 percent it moves 2.00 percent; at 2.0 percent it moves 0.40 percent. Decide honestly which side of that line your chosen site is on.

If it is on the wrong side, say so and keep the account anyway — as a national-scale question rather than a management one. Knowing your instrument's range is part of owning it.

Exercise 4.3 — The walk.

Go back to the cascade you found in week three and take somebody with you. Do not explain it first. Let them look, then ask what they notice. The chapter's Delight movement claims that once you can see the Carnot factor you cannot stop seeing it. Test that claim on a person.

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Exercise 4.4 — Read the objection literature, not the summary.

Two papers, in this order. Bianciardi, Tiezzi and Ulgiati (1993), which shows that complete material recycling is thermodynamically possible given a sufficient energy flux through an open system — the refutation of the fourth law. Then Ayres (1999), which accepts the refutation and rebuilds the economic claim on a firmer footing.

Write one page answering a single question: what exactly did Georgescu-Roegen get right, and what exactly did he get wrong? You must be able to state both in separate sentences without hedging either. A student who can do that can be trusted with the rest of the programme; a student who can only defend or only dismiss cannot.

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THE TERM CALENDAR — eleven weeks at a glance

Weeks five and six are the load-bearing ones. If a week has to be lost, lose week three and keep those two.

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THE TERM PROJECT

One site, one account, one page

Choose one site in week two and stay with it.

The deliverable is three pages and a spreadsheet.

1. The account. Energy and exergy, side by side, for at least eight weeks, with the dead state declared on the first line and never changed.
2. The cascade ladder. Every thermal demand ordered by grade, with the available streams matched against it and the failure point marked.
3. The one page. Baseline, the mismatch you found, what it would cost to fix, and the return against a stated hurdle rate. The chapter's worked cascade returns 22.70 percent against a WACC of 8.00 — yours will differ and the number is not the point. The structure of the argument is.

Marked on three things. Is the arithmetic reproducible by someone who has only your spreadsheet? Is the dead state declared and constant? And does the final page state the honest negative — the place your own result is weakest — without being asked?

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SELF-ASSESSMENT

Score yourself honestly. Nobody sees this.

Six or more in the right-hand column and you can hold this material in a room with an engineer. Fewer, and the fastest route is Exercise 2.2 — do the copper by hand and the rest follows.

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CARRYING IT FORWARD

Three things to take out of the term.

The column travels. Whatever you do next — a firm, a lab, a council, a farm — the move is the same: take the energy data that exists, add the temperature, and publish two numbers. It costs a week and it changes what gets approved.

The honest negative travels further. You now have a technical result with a named weakness you can state yourself. That combination is rare and it is worth more in a room than either half alone.

And the sense stays. You will not stop seeing the Carnot factor. The kettle, the hotel bathroom, the plume over the ring road — the world is legible in one more dimension than it was in September, and almost everything in it is being done at a fraction of what it could be. That is not a complaint. It is an inventory of headroom, and you now know how to count it.

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APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. When has someone in this room computed something and had the answer change their mind? What was it, and what made the computation persuasive?
2. Where on this campus is grade already being matched to task well, and who set that up?
3. If every building here published exergy destroyed alongside energy bought, what would the first term's argument be about?
4. What would it take for the economics faculty and the engineering faculty to use the same worked example — and who would have to agree to it?
5. Which of us has found a cascade nobody else here has seen? Describe it.
6. What is the best question this chapter made you ask that it did not answer?