Generated ERQ

✓ passed B.1 Thermal energy transfers × A.3 Work, energy and power 13 marks SL 3 passes 116.26s $0.7388

``` ## ERQ · 13 marks · Topics: B.1 Thermal energy transfers + A.3 Work, energy and power · Archetype: experimental_analysis **Integration:** primary=B.1 Thermal energy transfers, secondary=A.3 Work, energy and power (strength: supporting) **Stem.** A flat-plate solar thermal collector is mounted on a rooftop to heat domestic water. The absorber plate has area A = 2.0 m² and receives solar irradiance I = 800 W m⁻² normal to its surface. Cold water enters the copper pipes at 18 °C and leaves at 33 °C; a small electric pump circulates the water at a constant mass flow rate of 1.2 × 10⁻² kg s⁻¹. The pump is rated at 25 W of electrical input. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹. A student records the inlet and outlet temperatures with digital probes of uncertainty ±0.5 °C and measures the mass flow rate by collecting outflow in a beaker on a balance over 60 s, giving an uncertainty of ±5 % in the flow rate. The student claims that "the efficiency of the panel is just the thermal power delivered to the water divided by the solar power incident on the absorber". ### Part (a) State [2 marks] · AO1 · Topic: B.1 State the dominant mechanism of thermal energy transfer (i) from the absorber plate to the water flowing in the copper pipes, and (ii) from the absorber plate to the surrounding air on a windy day. ### Part (b) Calculate [3 marks] · AO2 · Topic: B.1 Calculate the rate at which thermal energy is delivered to the water. ### Part (c) Show that [4 marks] · AO2 · Topic: B.1 Using your value from (b), show that the thermal efficiency of the collector, defined as the rate of thermal energy delivered to the water divided by the rate of solar energy incident on the absorber, is approximately 0.47. Then determine the fractional uncertainty in this efficiency, given that the temperature-rise uncertainty contributes ±6.7 % and the flow-rate uncertainty contributes ±5 %. ### Part (d) Evaluate [3 marks] · AO3 · Topic: B.1 + A.3 · ASSUMPTIONS DISCRIMINATOR The student then revises the claim, proposing instead that "because the pump does 25 W of electrical work on the water, the true useful thermal output is (thermal power − 25 W), so the efficiency should be lowered accordingly". Evaluate this revised claim by reference to the first law of thermodynamics and the fate of the pump's work input. ### Part (e) Suggest [1 mark] · AO3 · Topic: B.1 Suggest one modification to the experimental procedure that would reduce the dominant contribution to the uncertainty calculated in part (c). --- ## Mark Scheme ### Part (a) [2 marks] - M1: (i) forced convection (of water through the pipes) / conduction from plate to pipe wall then convection accepted [no ECF] - M2: (ii) (forced) convection — accept "convection by the wind" / do NOT accept "radiation" alone as dominant on a windy day [no ECF] ### Part (b) [3 marks] — Calculate - M1: use of P = ṁ c ΔT with ΔT = 15 K [no ECF] - M2: substitution: P = (1.2 × 10⁻²)(4200)(15) [no ECF] - M3: P = 756 W ≈ 7.6 × 10² W [accept 750–760 W] ### Part (c) [4 marks] — Show that - M1: incident solar power = I A = 800 × 2.0 = 1600 W [no ECF] - M2: η = 756 / 1600 = 0.4725 ≈ 0.47 [ECF from (b)] - M3: fractional uncertainties in η combine as Δη/η = ΔΔT/ΔT + Δṁ/ṁ = 6.7 % + 5 % = 11.7 % (≈ 12 %) [no ECF; accept addition in quadrature giving ≈ 8.4 % as alternative] - M4: hence Δη ≈ 0.12 × 0.47 ≈ 0.06 so η = 0.47 ± 0.06 [ECF from M3] ### Part (d) [3 marks] — Evaluate (position + warrant + quantitative limitation per §4.4.1) - M1 (position + warrant): claim is invalid / oversimplified — subtracting 25 W of electrical work from a thermal power conflates two different categories of energy input and double-counts losses; efficiency must be defined as useful output over input of the same kind [no ECF] - M2 (thermodynamic reasoning): by the first law, essentially all of the 25 W pump work is dissipated by viscous friction into internal energy of the water itself, so it is already included in the measured outlet temperature rise ΔT = 15 K and hence in the 756 W figure [no ECF] - M3 (quantitative correction): a defensible alternative metric is a coefficient including pump cost, η* = thermal gain / (solar + pump) = 756 / (1600 + 25) ≈ 0.465, showing the correct adjustment is to the denominator (≈1 % effect), not by subtracting 25 W from the numerator [ECF from (b), (c)] ### Part (e) [1 mark] — Suggest - M1: any one valid proposal targeting the dominant (temperature) uncertainty, e.g. use temperature probes of finer resolution (±0.1 °C) / increase ΔT by reducing flow rate so the fractional uncertainty in ΔT falls / take repeated readings and average inlet and outlet temperatures [accept any plausible procedural improvement linked to the larger of the two contributions] ### Marker notes - Show-that target in (c): η = 0.4725 given to 4 sig figs; student-derived 0.46–0.48 acceptable. Subsequent uncertainty arithmetic must use the given 0.47, not the student's (b) value, to preserve ECF integrity. - Alternative method accepted for (c) uncertainty: addition in quadrature √(6.7² + 5²) ≈ 8.4 % giving η = 0.47 ± 0.04. - (d) accept any of: pump work is internal to the control volume of the water; pump dissipation appears as part of ΔT; correct treatment places pump energy in denominator not numerator; subtraction would double-count losses already in measured outlet T. - (a)(ii): if candidate writes "radiation and convection", award only if convection is identified as dominant for the windy condition. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: Part (a) is AO1 (State); parts (b) and (c) are AO2 (Calculate/Show that); parts (d) and (e) are AO3 (Evaluate/Suggest). The progression from factual recall through calculation to judgement and critical thinking is properly ordered and meets the SL extended-response contract.
command_structure fail

Part (d) mark scheme violates §4.4.1 for Evaluate command term. While M1 provides a position and M2/M3 provide supporting/limiting considerations, M1 does not explicitly state a claim in the required structure. More critically, M2 and M3 fail to meet §4.4.1's requirement that supporting and limiting considerations must be substantive and clearly differentiated. M2 mentions work-energy equivalence but lacks clear causal reasoning linking the claim to the physics principle. M3 offers two alternatives joined by 'or' rather than a unified limiting consideration with explicit warrant. The mark scheme also lacks clarity on how the three marks map to the three required structural elements (position, supporting, limiting).

FIX: Restructure part (d) mark scheme as follows: M1 (position + warrant): 'The claim is oversimplified because it treats electrical work and thermal energy as equivalent energy forms without accounting for their different thermodynamic quality—work is ordered/high-grade energy while heat at ~33°C is low-grade/disordered [explicit link to A.3 work-energy principle].' M2 (supporting consideration): 'The 25 W pump input is real energy cost to the system and must be accounted for in a rigorous energy balance.' M3 (limiting consideration): 'However, the 25 W of electrical work is largely dissipated as heat within the water itself (friction in pipes, motor inefficiency), so it is not a net energy cost to remove from useful output; additionally, low-grade thermal energy cannot be directly compared to electrical work for subtraction purposes.' Explicitly state that marks are awarded for claim, warrant linking to physical principle, supporting reasoning, and limiting reasoning rather than alternative pathways.
cross_theme pass

The ERQ successfully integrates both B.1 (thermal energy transfers) as primary and A.3 (work, energy and power) as secondary. Part (d) genuinely requires both concepts: students must apply thermal energy knowledge (heat transfer rate, thermal efficiency from B.1) AND work-energy equivalence and energy grade discrimination (A.3 concept of work vs. heat). The pump's electrical work and the collector's thermal output are actively compared using both frameworks, not merely name-checked.
discriminator pass

Part (e) successfully asks students to critique the model assumption that 'all solar energy not delivered to the water is lost from the upper surface.' The question requires identification of an alternative energy loss pathway, which directly evaluates the completeness and realism of the assumed model. This is genuine model critique.
rule_of_one fail

Part (b) is marked [3 marks] but lists 3 distinct award bullets (M1, M2, M3), which appears correct at face value. However, M2 and M3 together represent a single calculation step (computing mass flow rate and expressing the final answer). The three operations should be: (1) incident power formula/substitution, (2) mass flow rate formula/substitution, (3) mass flow rate answer with units. Instead, M2 is the setup and M3 is merely the numerical result—these are not three independent operations. Part (c) is marked [4 marks] with 4 bullets (M1–M4), which correctly aligns formula, substitution, answer-with-units for the power calculation (M1–M3) plus the efficiency calculation (M4). The dimensional inconsistency in part (b) breaks the mark-count/operation-count contract.

FIX: Restructure part (b) as: M1 = incident power formula and substitution (800 × 2.0); M2 = incident power answer (1600 W); M3 = mass flow rate formula and substitution (1.0 × 10³ × 1.2 × 10⁻⁵); M4 = mass flow rate answer with units (0.012 kg s⁻¹). Alternatively, if retaining 3 marks, combine M2 and M3 into a single 'calculation and answer' step, leaving only 2 distinct operations (incident power, mass flow rate), which would require reducing the part to [2 marks].
topic pass

The ERQ authentically integrates both topics. B.1 (Thermal energy transfers) dominates parts (a)–(c) and (e), covering radiation, conduction, and energy balance. A.3 (Work, energy and power) is genuinely invoked in part (d), where students must evaluate the thermodynamic distinction between electrical work (the pump's 25 W) and thermal energy (750 W), requiring understanding of work-energy equivalence and energy quality. The claim being evaluated cannot be properly answered without invoking concepts from both topics.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (State), parts (b)–(c) are AO2 (Calculate/Show that), and parts (d)–(e) are AO3 (Evaluate/Suggest). The progression from recall through calculation to critical analysis and synthesis is properly ordered and unbroken.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 Evaluate structure. M1 states a position and warrant correctly, but M2 and M3 are not properly demarcated as 'supporting consideration' and 'limiting consideration'—they read as two separate arguments rather than a structured evaluation. More critically, M3's physics warrant ("pump dissipation is internal to the water") is asserted but not rigorously connected to the first-law energy balance, making the limiting consideration logically incomplete for an IB strict standard.

FIX: Restructure Part (d) mark scheme to explicitly separate three marking points: (1) Position + Warrant: "The claim is invalid/oversimplified because electrical work and thermal energy are not interchangeable units—subtracting 25 W from thermal power conflates work and heat, violating the definition of efficiency as useful output / input of the same category."; (2) Supporting consideration: "The pump's 25 W is indeed an operational energy cost, so a coefficient of performance (thermal gain ÷ total energy input including pump) would be a fair alternative metric: (756 + 25) / (1600 + 25) ≈ 0.46."; (3) Limiting consideration: "However, most of the 25 W pump work converts to internal heat via friction and is transferred to the water; this internal dissipation is already reflected in the measured ΔT = 15 K, so subtracting the pump work would double-count losses and artificially reduce the reported efficiency below the actual useful thermal delivery." Ensure each mark is awarded only if the corresponding structural element is present.
cross_theme pass

The ERQ properly blends B.1 (thermal energy transfers) and A.3 (work, energy and power). Part (d) genuinely requires both concepts: it asks students to evaluate whether pump work (A.3) should reduce the thermal efficiency calculation (B.1), forcing them to reason about the distinction between ordered mechanical work and disordered thermal energy, and recognize that pump dissipation becomes part of the water's internal energy gain (B.1). The second topic is not merely name-checked but is integral to the evaluation logic.
discriminator pass

Part (d) explicitly asks students to 'Evaluate this claim' — a model-critique task that requires them to assess the validity of a student's assumption/simplification about whether pump work should be subtracted from thermal output. The mark scheme confirms this is a three-tier evaluation (position + supporting + limiting consideration) that directly addresses the thermodynamic reasoning and hidden assumptions in the claim, satisfying the dimension's requirement for critical appraisal of the model/assumptions used.
rule_of_one fail

Part (d) is awarded 3 marks but the mark scheme lists only 2 distinct award criteria (M1 and M2), with M3 presented as a qualifying rider rather than a third independent operation. The scheme conflates position+warrant into M1, then adds support and limitation as secondary considerations rather than three separable calculation or reasoning steps. For a 3-mark Evaluate part, either 3 independent logical operations must be present or the part should be revalued to 2 marks.

FIX: Either: (i) restructure Part (d) to explicitly award 3 marks for three distinct logical steps (e.g., M1: state position; M2: explain why subtraction is invalid with thermodynamic reasoning; M3: calculate corrected efficiency or show that pump work is largely internal), OR (ii) reduce Part (d) to 2 marks and reallocate 1 mark to Part (e) or another part to maintain 13 total marks. The current scheme's three-tier evaluation model (position + supporting + limiting) is descriptive guidance for examiners, not three independent mark-earning operations.
topic pass

The ERQ robustly tests both B.1 (Thermal energy transfers) and A.3 (Work, energy and power). Parts (a)–(c) and (e) centre on B.1 mechanisms (conduction, convection, radiation) and thermal power calculations. Part (d) is the critical integration point: it explicitly requires students to apply A.3 concepts (work input, energy principle, distinguishing ordered vs. disordered energy) to evaluate whether electrical work should be subtracted from thermal output. The physics demand is genuine—students must recognise that work and heat are not directly interchangeable and account for thermodynamic quality and energy dissipation paths. Neither topic is superficial.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: (a) is AO1 (State); (b) is AO2 (Calculate); (c) is AO2 (Show that); (d) is AO3 (Evaluate) with explicit warrant and thermodynamic reasoning; (e) is AO3 (Suggest). Each tier is placed in proper sequence with appropriate command terms and cognitive demand.
command_structure fail

Part (d) mark scheme fails the AO3 'Evaluate' structure requirement. Per §4.4.1, Evaluate must exhibit: position + supporting consideration + limiting consideration. M1 provides position and warrant correctly, M2 provides thermodynamic reasoning, but M3 offers only an alternative metric without a genuine limiting consideration that weighs against the position or acknowledges constraints on the evaluation itself. The scheme lacks an explicit limiting perspective (e.g., practical difficulty of defining system boundaries, or acknowledging the student's intuition about double-counting, before refuting it).

FIX: Revise M3 in part (d) to include a limiting consideration. Example: 'M3 (limiting consideration): one might argue the student's concern about double-counting is superficially reasonable since pump work does add energy; however, the key distinction is that pump work is converted to heat via friction and manifests in the measured ΔT, whereas external solar input is the true energy source to credit. Alternatively, define η* = thermal gain / (solar + pump) ≈ 0.465, which correctly places pump cost in the denominator (~1 % effect), showing the student's numerator subtraction method is both thermodynamically incorrect and quantitatively negligible.' This structure now exhibits position (M1) + supporting thermodynamic warrant (M2) + limiting/alternative perspective (revised M3).
cross_theme fail

Topic A.3 (Work, energy and power) is only invoked in part (d) as a final evaluative discussion about how to treat pump work in an efficiency denominator. The core physics of the solar collector—parts (a), (b), (c), and (e)—are entirely B.1 (thermal energy transfers: conduction, convection, and heat-capacity calculations). A.3 concepts (work, energy conservation, power accounting) do not genuinely blend into the solution methodology; they appear only as a late-stage assumption check, making this a B.1-dominant question with A.3 as decorative appendix rather than integrated content.

FIX: Restructure the question so that work-energy concepts are integral to the primary calculation path, not just a final caveat. For example: (1) require students to apply energy conservation (first law) to derive the thermal power equation itself from first principles in part (b), explicitly accounting for work input; (2) in part (c), have students calculate both a 'solar-only' and a 'solar-plus-pump' efficiency explicitly and compare their magnitudes quantitatively before part (d); or (3) reframe the scenario so that the pump's mechanical work and its dissipation via viscous friction must be modeled as a parasitic loss to be subtracted from the absorber-plate heat balance, making A.3 central to the thermal calculation, not peripheral.
discriminator pass

Part (d) explicitly asks the student to 'Evaluate this revised claim by reference to the first law of thermodynamics and the fate of the pump's work input.' This is a clear model-critique question that requires the student to identify a conceptual error in the student's proposed claim, explain why it violates thermodynamic principles, and discuss the correct treatment of energy accounting. The final part (e) is a minor suggestion task but does not undermine the strong model-critique dimension of (d).
rule_of_one fail

Part (c) is marked as [4 marks] but contains 4 award criteria (M1–M4). However, the dimension requires that a 'Show that' part with 4 marks have exactly 4 distinct operations. While the count matches numerically, the structure violates the principle: M1 and M2 form a single calculation chain (both compute η sequentially), and M3–M4 form another chain (uncertainty combination then final statement). This is 2 calculation sequences compressed into 4 bullets, not 4 independent operations. Part (d) is marked [3 marks] with 3 bullets (M1–M3), which satisfies the count requirement, but M1 is purely qualitative reasoning (position + warrant) while M2 is thermodynamic explanation and M3 is quantitative correction. These are conceptually distinct enough to justify 3 marks, though the heterogeneous nature of (d) is borderline. Part (c)'s structural flaw is the primary issue: the 'show that' followed immediately by uncertainty calculation should either be separated or reframed as 2 distinct sub-parts.

FIX: Restructure Part (c) into two sub-parts: (c)(i) [2 marks] 'Show that η ≈ 0.47' with M1–M2 (incident power; efficiency calculation), and (c)(ii) [2 marks] 'Determine the fractional uncertainty' with M1–M2 (uncertainty combination; statement of result with absolute uncertainty). Alternatively, if keeping a single 4-mark part, rewrite the mark scheme to reflect 4 genuinely independent operations: (M1) incident solar power, (M2) thermal power from (b), (M3) efficiency ratio, (M4) uncertainty propagation and final range—currently M3–M4 are sequential consequences rather than independent steps.
topic pass

The ERQ robustly integrates both topics. Topic B.1 (Thermal energy transfers) is central throughout: part (a) requires identification of convection and conduction mechanisms; parts (b)–(c) apply the heat-transfer rate formula Q̇ = ṁcΔT; part (d) invokes the first law of thermodynamics to trace where thermal energy goes. Topic A.3 (Work, energy and power) appears substantively in part (d), where the 25 W electrical work input must be evaluated within energy conservation, requiring students to distinguish between work and thermal energy, recognize that pump work is dissipated into internal energy, and correctly assign it to the energy balance (denominator, not numerator). Neither topic is superficial; both are necessary to fully answer the question, especially part (d).

Planner output (stage 1)

Archetype: real-world device
Scenario: A solar thermal panel on a rooftop absorbs solar radiation and transfers thermal energy to water circulating through copper pipes. The panel has a surface area of 2 m², receives solar irradiance of 800 W m⁻², and the water flows at a constant rate with a temperature rise of 15 °C. Students must analyze the thermal energy transfer mechanisms, calculate heat transfer rates, and evaluate the efficiency of the system by considering the work input required by a circulation pump.
Cross-pollination part: d
Discriminator part: e

Part	Marks	AO	Command
a	2	AO1	State
b	3	AO2	Calculate
c	4	AO2	Show that
d	3	AO3	Evaluate
e	1	AO3	Suggest

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