Generated ERQ

✓ passed B.2 Greenhouse effect × C.2 Wave model 12 marks SL 3 passes 111.75s $0.5996

## ERQ · 12 marks · Topics: B.2 Greenhouse effect + C.2 Wave model **Stem.** A school laboratory uses a tabletop apparatus to model Earth's radiative energy balance. A 150 W tungsten-filament heat lamp acts as the "Sun" and illuminates a horizontal aluminium plate (painted matt black on its upper surface) that represents the Earth's surface. A thin polyethylene sheet, transparent to visible light but opaque to wavelengths longer than 7 μm, is suspended 5.0 cm above the plate to represent a greenhouse-gas layer. The lamp's filament operates at 2900 K and behaves approximately as a black body. With the polyethylene sheet in place, the painted plate reaches a steady-state temperature of 348 K, while without the sheet the plate steadies at 312 K. The Stefan–Boltzmann constant is σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ and Wien's displacement constant is b = 2.90 × 10⁻³ m K. ### Part (a) State [2 marks] · AO1 · Topic: B.2 State two greenhouse gases found in Earth's atmosphere. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: C.2 + B.2 Using Wien's displacement law, calculate the peak wavelength of the radiation emitted by (i) the lamp filament at 2900 K, and (ii) the painted plate at 348 K. Hence state which of these two emissions is blocked by the polyethylene sheet. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: B.2 Treating the painted plate as a black body, determine the power per unit area radiated by the plate when the polyethylene sheet is in place. ### Part (c) Explain [3 marks] · AO3 · Topic: B.2 + C.2 Explain, in terms of the wavelengths calculated in (b)(i) and the selective transmission of the polyethylene sheet, why the plate's steady-state temperature is higher when the sheet is present. ### Part (d) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The plate's measured temperature (348 K) is lower than the value predicted by an idealised single-layer greenhouse model. Suggest, with reasoning: (i) one reason involving heat transfer mechanisms other than radiation, and (ii) one reason involving the emissivity of the real aluminium plate. --- ## Mark Scheme ### Part (a) [2 marks] - Mark 1: One valid greenhouse gas named (e.g. CO₂, H₂O / water vapour, CH₄, N₂O, O₃, CFCs) [ECF: no] - Mark 2: A second, distinct valid greenhouse gas named [ECF: no] ### Part (b)(i) [3 marks] - Mark 1: Correct use of λ_max = b/T with both temperatures substituted [ECF: no] - Mark 2: λ_lamp = 2.90 × 10⁻³ / 2900 = 1.00 × 10⁻⁶ m (1.00 μm) [ECF: yes] - Mark 3: λ_plate = 2.90 × 10⁻³ / 348 = 8.33 × 10⁻⁶ m (8.33 μm); states the plate's emission (8.33 μm > 7 μm) is the one blocked by the polyethylene [ECF: yes] ### Part (b)(ii) [2 marks] - Mark 1: Correct use of P/A = σT⁴ with T = 348 K substituted [ECF: no] - Mark 2: P/A = 5.67 × 10⁻⁸ × (348)⁴ = 832 W m⁻² (accept 830 W m⁻², 2–3 s.f., correct units) [ECF: yes] ### Part (c) [3 marks] - Mark 1: Visible/short-wavelength radiation from the lamp (~1 μm) passes through the polyethylene and is absorbed by the matt black plate [ECF: no] - Mark 2: The plate re-emits in the infrared (~8 μm), which lies in the range (>7 μm) the polyethylene absorbs/blocks [ECF: yes, from (b)(i)] - Mark 3: The trapped IR is re-radiated back to the plate (or the sheet warms and re-emits downward); the plate must reach a higher temperature so that the net outgoing power again balances the incoming power [ECF: no] ### Part (d) [2 marks] - Mark 1 (heat-transfer reason): Identifies convection/conduction of heat from the plate to surrounding air (through gaps or via the underside) as an additional energy-loss channel not included in the pure-radiation model, reducing the steady-state temperature [ECF: no] - Mark 2 (emissivity reason): States that real aluminium (even when painted) has emissivity ε < 1 in the visible, so it reflects/absorbs less of the incoming lamp radiation than a black body; hence absorbed power is lower than the idealised calculation assumes, giving a lower equilibrium temperature [ECF: no] ### Marker notes - (b)(i): Accept λ in m, μm or nm provided units are stated and consistent. - (b)(ii): Accept 830–833 W m⁻². No unit / wrong unit → lose Mark 2 only. - (c): Award Mark 3 for either "back-radiation from sheet to plate" OR "sheet warms and re-emits downward, raising plate's equilibrium T". Do not award if candidate invokes "heat trapped" without mechanism. - (d): Each sub-part assesses one named, pre-specified reason — do NOT credit two heat-transfer points or two emissivity points; the candidate must address both (i) and (ii) separately. For (i) accept conduction through supports, convective air currents, or evaporation. For (ii) accept "paint emissivity < 1 in IR causes reduced re-emission" OR "absorptivity of painted surface in visible < 1" as equivalent.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder strictly. Part (a) is AO1 with State (command term for AO1/AO2). Parts (b)(i) and (b)(ii) are AO2/AO3 with Calculate and Determine (appropriate for middle tiers). Part (c) is AO3 with Explain, and part (d) is AO3 with Suggest. The progression from recall/definition → calculation/determination → explanation/evaluation is clear and correctly sequenced.
cross_theme pass

The ERQ successfully blends B.2 (Greenhouse effect) and C.2 (Wave model). Part (b)(i) genuinely requires Wien's displacement law (C.2 core content—wavelength and temperature relationship) to calculate the peak emission wavelength, and then directly applies that result to explain why polyethylene traps the radiation (B.2). Part (c) then synthesizes both: the wavelength calculation from C.2 becomes essential to explaining the selective absorption mechanism central to B.2 greenhouse physics. The topics are integrated throughout, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to 'Suggest two reasons why this tabletop model gives a poor quantitative prediction of the actual greenhouse warming of Earth's surface.' This is a direct model-critique question that requires students to identify and articulate limitations and assumptions of the analogue apparatus compared to Earth's actual radiative balance system.
rule_of_one fail

Part (b)(ii) has a mark-count mismatch. The scheme lists 2 marks with 2 award bullets (M1: formula setup; M2: numerical answer), but a 2-mark Calculate part requires exactly 2 distinct operations. However, the issue is that M1 describes only formula selection with substitution of values, while M2 is purely the numerical result. The intermediate step of calculating T⁴ terms is embedded within M2's calculation but not explicitly listed as a distinct criterion. More critically, for a 2-mark part, M1 should clearly separate 'correct formula' from 'correct substitution', yet here M1 conflates both. This creates ambiguity: does a student get M1 for writing the formula alone, or must they substitute all four values? The marker notes partially address this (ECF: yes on M2 suggests some leniency), but the scheme itself violates the strict 1-operation-per-mark principle.

FIX: Revise Part (b)(ii) to explicitly separate operations: M1: 'correctly states P_net = σA(T⁴ − T_surr⁴)' [ECF: no]; M2: 'substitutes T = 382 K, T_surr = 295 K, A = 4.0 × 10⁻² m², σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴' [ECF: no]; M3: 'calculates and states P_net ≈ 31 W with units' [ECF: yes]. This requires expanding the mark allocation to 3 marks, or alternatively: consolidate to M1 (formula) and M2 (substitution + answer with units), making the distinction unambiguous.
topic pass

The ERQ robustly tests both B.2 (Greenhouse effect) and C.2 (Wave model). B.2 is tested throughout: part (a) requires greenhouse gas conditions, part (b)(ii) applies Stefan–Boltzmann radiation balance, and part (c) explains the trapping mechanism. C.2 is tested in part (b)(i) via Wien's displacement law (wave properties and blackbody radiation) and implicitly in part (c) through wavelength-selective transparency. The scenario fundamentally requires both topics: understanding how IR wavelengths differ from visible (C.2) and why selective absorption causes warming (B.2) are inseparable.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: Part (a) is AO1 (State); parts (b)(i)–(b)(ii) are AO2/AO3 (Calculate/Determine); part (c) is AO3 (Explain); part (d) is AO3 (Suggest). All command terms, cognitive levels, and mark allocations align properly with IB expectations for a 12-mark SL ERQ.
cross_theme pass

Both theme letters differ (B vs C). The wave model (C.2) is genuinely integrated throughout: part (b)(i) requires Wien's displacement law to find the peak wavelength of the plate's emission; part (c) explicitly contrasts visible light wavelength (500 nm, passes through) with infrared wavelength (7.6 μm, absorbed by polyethylene), making the wavelength distinction essential to explaining the greenhouse effect mechanism. C.2 is not merely named or relegated to assumptions—it is actively used in the calculation and physical reasoning.
discriminator pass

Part (d) explicitly asks students to 'Suggest two reasons for this discrepancy' between calculated and measured net power, requiring critique of the model's assumptions (perfect black body, no convection/conduction, perfect opacity of sheet, uniform surroundings, collimated lamp output). This is a genuine model-critique question that evaluates AO3 reasoning about limitations.
rule_of_one fail

Part (d) violates the mark–criteria contract. It is a 2-mark part but the mark scheme lists 5 distinct reasons as acceptable alternatives (emissivity < 1, conduction/convection, IR transparency, non-uniform surroundings, non-collimated lamp), rather than exactly 2 award criteria. The marking instruction 'Award 1 mark each (max 2) for any two distinct, physically valid reasons' creates ambiguity about what constitutes the assessed operations and makes it impossible for a candidate to know which two reasons will be credited.

FIX: Restructure Part (d) to specify exactly 2 distinct, pre-identified reasons that must be stated for full credit. For example: 'Suggest two reasons: (i) [reason about emissivity/reflectivity of real aluminium], (ii) [reason about heat loss via convection to air].' Alternatively, if the intention is to allow flexible candidate responses, reframe as 'Suggest one reason...' (1 mark) to match the single award criterion, or expand to 4 marks with 4 named bullet criteria.
topic pass

The ERQ successfully integrates both topics. B.2 (Greenhouse effect) is tested throughout: part (a) requires naming greenhouse gases and their IR absorption; parts (b)(ii) and (c) require understanding of radiative balance and the mechanism by which a selective-absorber layer increases equilibrium temperature. C.2 (Wave model) is genuinely tested in part (b)(i) via Wien's displacement law and wavelength identification, and part (c) critically depends on the wavelength asymmetry (visible light in at ~500 nm vs. IR re-emission at ~7.6 μm) to explain why the polyethylene sheet creates the greenhouse effect. Neither topic is superficial; both are necessary to solve and understand the scenario.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly: part (a) is AO1 (State); parts (b)(i) and (b)(ii) are AO2 (Calculate/Determine); parts (c) and (d) are AO3 (Explain/Suggest). The command terms and cognitive demand escalate appropriately through the response.
cross_theme pass

The ERQ genuinely blends B.2 (Greenhouse effect) and C.2 (Wave model). Wien's displacement law (C.2) is essential in part (b)(i) to calculate peak wavelengths, which are then directly used in part (c) to explain the greenhouse mechanism. The wavelength calculations drive the physical explanation of selective transmission—the two topics are functionally integrated, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to suggest reasons why the measured temperature differs from the idealised single-layer greenhouse model, requiring critique of two key modelling assumptions (heat transfer mechanisms and emissivity). This satisfies the dimension's requirement for final-part model critique.
rule_of_one fail

Part (b)(i) is marked as 3 marks but contains 4 distinct award criteria: (1) correct formula use with both temperatures, (2) lamp wavelength calculation, (3) plate wavelength calculation, and (4) identification of which emission is blocked. This exceeds the 3-mark allocation by 1 criterion. Part (d) is marked as 2 marks but the scheme lists only 2 criteria, which is acceptable; however, the mismatch in (b)(i) violates the dimensional contract.

FIX: Restructure Part (b)(i): either reduce to 2 marks by combining lamp and plate wavelength calculations into one criterion with a single answer showing both values, OR expand to 4 marks by separating formula application, lamp result, plate result, and identification into distinct award bullets. The cleaner approach for an SL question is to reduce Part (b)(i) to 2 marks and make the question ask only for the two wavelengths without the reasoning about which is blocked (move that to Part (c)), or keep 3 marks but collapse the two wavelength calculations into one bullet and keep formula, calculation, and identification as the three criteria.
topic pass

The ERQ robustly tests both B.2 (Greenhouse effect) and C.2 (Wave model). Part (b)(i) requires Wien's displacement law to calculate peak wavelengths and identify which emission is blocked—core wave-model physics. Parts (b)(ii), (c), and (d) apply Stefan–Boltzmann radiation, selective transmission, and radiative balance—core greenhouse-effect physics. The physical scenario (polyethylene blocking IR while transmitting visible light) intrinsically demands both the wave concepts (wavelength selectivity) and greenhouse concepts (radiative trapping and energy balance), not merely nominal mention.

Planner output (stage 1)

Archetype: real-world device
Scenario: A simplified Earth–atmosphere model uses an infrared thermometer and heat lamp to simulate radiative energy balance. Visible light from the lamp (wavelength ~500 nm) represents solar radiation; an absorbing surface mimics Earth; and a transparent-to-visible but opaque-to-infrared plastic sheet simulates the greenhouse gas layer. Students measure surface and air temperatures under different conditions and analyse how the 'greenhouse' layer traps outgoing longwave radiation (wavelength ~10 μm).
Cross-pollination part: b(i)
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State
b(i)	3	AO2	Calculate
b(ii)	2	AO2	Determine
c	3	AO3	Explain
d	2	AO3	Suggest

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