La Bourse / Volume IV / Nº IV.02 / Quiz, reflection, essays

A watercolour of a man at a desk beneath a great tree inside a glass room, plants all around him. — Plate IV.02 · Quiz, reflection, essaysThe Assay Bench.A material is not what it was called when it arrived. It is what it assays at, and the assay is the only sentence in this chapter a buyer will pay for.

ASSESSMENT · Chapter IV.02 — Materials and the Return Loop

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. State the Circularity Gap Report's metric as a formula, and name three things in its denominator that cannot physically return within the period.

cycled / (virgin + cycled) — a share of total material input. The denominator contains fossil energy carriers that are burned, net additions to in-use stock that will not come back for decades, and biomass that is eaten. One mark for the expression, one for naming at least two of the three. The stronger answer adds that the same 2005 account gives 6.5 percent against input and 34.0 percent against what could physically return.

2. Distinguish the end-of-life recovery rate ρc from the process yield Y, and say why most published recycling rates overstate both.

ρc is what comes back; Y is what survives sorting, washing and refining into saleable material. Published rates usually include new scrap — factory off-cuts that never left the plant and were never at risk of loss. Copper's quoted 32 percent recycling input rate becomes about 17 percent when only post-consumer metal is counted.

3. Write the secondary supply ceiling and define each term.

c = ρc·Y / (1+g)^L. Material reaching end of life this year entered service L years ago, when demand was smaller by (1+g)^L. c is the maximum share of this year's demand that returns can supply.

4. Give the steady-state stock formula and state what K/D converges to as growth goes to zero.

K = D(1 − e^(−gL))/g, and K/D → L. At zero growth the in-use stock equals mean product life times annual demand.

Four on application.

5. A supplier tells you their aluminium is "ninety-five percent recyclable." What have they told you, and what four things would you need instead?

They have told you a property of the material, not a rate of anything. Recyclability is a chemistry claim; what prices a decision is ρc (what comes back), Y (what survives processing), L (how long before it comes back) and g (how fast demand is growing while it waits). Credit any answer that notices "recyclable" has no denominator.

6. A vendor offers a chemical recycling plant for mixed coloured PET, quoting 55 MJ/kg of feed and "up to 80 percent yield." Virgin PET is 83 MJ/kg. What is the first question, and what is the threshold?

Y = 55/83 = 66.3 percent. The first question is what yield the plant achieves on this stream, not in the brochure, because below 66 percent the route costs more energy than making PET from oil. Full marks note that "up to" is not a yield, and that the assay should be written into the contract.*

7. Your shredder residue assays 1.5 percent copper. A smelter will take it if it clears the primary route on energy. Does it, and what would change the answer?

At 3 MJ/kg of feed the threshold grade is 3.0/45.0 = 6.67 percent. At 1.5 percent it is more than four times below the line. What changes the answer is physical pre-concentration: at 1.0 MJ/kg of feed the threshold falls to 2.22 percent, and at 0.5 MJ/kg to 1.11 percent. The stronger answer names dismantling at the point of arising rather than a better smelter.

8. Explain why recycled paper can use less total energy than virgin kraft and still buy more fossil energy.

A kraft mill separates cellulose from lignin and burns the lignin in a recovery boiler, so much of its energy is self-generated biomass and a modern mill exports power. A deinking mill buys essentially all of its energy from the grid. Total energy 30 against 18 MJ/kg favours recycling; purchased fossil energy 10 against 12 MJ/kg does not. Credit answers that keep both facts and note recycled fibre still wins on land, water and fibre.

Two that require the arithmetic to be done.

9. Aluminium has an end-of-life recovery rate of 0.70, a process yield of 0.93, a mean product life of twenty years, and demand growing at three percent. Compute the maximum secondary share of demand, and compare with the observed 34 percent. Show your working.

ρ = 0.70 × 0.93 = 0.651. 1.03^20 = 1.806. c = 0.651 / 1.806 = 0.360 — 36.0 percent. Observed global recycled content is about 34 percent, so the formula is two points high. The point of the question is that a two-term expression with published inputs predicts an industry's measured performance. The residual is metal still in service and scrap exported out of the account. Credit any method reaching 35–37 percent.

10. Now set the recovery rate to a perfect 1.00 with no yield loss at all, and use steel's forty-year life at two percent growth. What share of demand can returns supply, and what does the answer imply about where the constraint sits?

c = 1.00 / 1.02^40 = 1.00 / 2.208 = 0.453 — 45.3 percent, so 54.7 percent must still be mined by a recycler that loses nothing. The implication is the chapter's central claim: the binding constraint on circularity is the growth rate, not the recovery rate. The stronger answer notes that L is in the exponent, so extending product life moves the ceiling further than any feasible recovery programme — and computes one case to show it, e.g. at L = 20 the same perfect recycler reaches 67.3 percent.

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.

Think of something you threw away this month that you knew, while you were doing it, still had value. What stopped you — was it the value or the handling?

What in your life is currently at its cleanest and will never be this clean again? Household, work, relationships, your own knowledge of something. What would it cost to keep it separated now rather than sort it later?

Where are you drawing on a stock whose regeneration you have never estimated? Write down its L — how long a unit of it lasts — and your honest g.

What have you called "recyclable" about your own habits — a practice you believe you could resume at any time — without ever checking the recovery rate?

Recall a time you were told something was impossible and later found it was simply not yet built. What did the difference cost you before you saw it?

Which of your commitments is being diluted rather than improved? Name the clean input you would have to add, and the honest ratio.

What do you own that is a mine above ground — already made, already paid for, embodied with somebody's work, and currently idle?

Where have you accepted a headline ratio about your own life without asking what was in the denominator? Rewrite that ratio with a denominator you would defend.

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 metric that governs the conversation. The Circularity Gap Report's figure is arithmetically correct and, this chapter argues, routinely misread as a score for the recycling industry. Argue either that the metric should be replaced by a returnable-fraction measure, or that its present breadth is precisely its value — that a measure of total throughput is what the debate most needs and a narrower measure would flatter. Use Haas et al. (2015) and one national or sectoral material-flow account the chapter does not cite.

2. Growth, or recovery. The chapter's central claim is that growth rather than recovery binds circularity, and that L matters more than ρ because it sits in the exponent. Argue either that industrial policy should therefore target product life and durability regulation, or that this understates what step changes in sorting and dismantling can do. Engage Allwood and Cullen (2012) directly, and at least one source on durability regulation or right-to-repair that the chapter does not cite.

3. Cradle to Cradle, twenty years on. Write an assessment of McDonough and Braungart's two-cycle framework on the evidence. Argue either that its technical cycle has been vindicated and its biological cycle was always a logistics claim in chemistry's clothing, or that the framework's value was never predictive and judging it by adoption rates is a category error. Use Bjørn and Hauschild (2013) and one post-2015 empirical evaluation the chapter does not cite.

4. The thermodynamic argument. The chapter computes the entropy of mixing for copper in steel at 0.93 kJ per kilogram — under five thousandths of one percent of primary production energy — and concludes that downcycling is a missing process rather than an entropy tax. Argue the counter-case: that the ideal-mixing floor is the wrong quantity, and that the relevant limit is set by kinetics, by the free energy of solid solution, or by the exergy of real separation processes. Use Gutowski et al. (2013), and at least one source on separation thermodynamics or exergy analysis that the chapter does not cite.

5. The rebound. Assume every recommendation in this chapter is implemented and secondary material becomes reliably cheaper than primary. Argue either that this is an unambiguous gain, or that it reduces the price of materials, raises total consumption, and partly or wholly offsets the saving. Use Zink and Geyer (2017) on circular economy rebound and Geyer et al. (2016) on displacement rates, and one empirical rebound study from another sector — energy efficiency, transport, lighting — that the chapter does not cite.