Generated ERQ

✓ passed A.3 Work, energy and power × B.1 Thermal energy transfers 12 marks HL 3 passes 106.65s $0.6572

## ERQ · 12 marks · Topics: A.3 Work, energy and power + B.1 Thermal energy transfers · Archetype: theory_application **Integration:** primary=A.3 Work, energy and power, secondary=B.1 Thermal energy transfers (strength: supporting) **Stem.** A small farm uses an electrically driven pump to lift water from a ground-level reservoir into a storage tank whose inlet is 18.0 m above the water surface of the reservoir. The pump draws 1.50 kW of electrical power from the mains supply and delivers water at a steady volume flow rate of 4.20 × 10⁻³ m³ s⁻¹ through a long pipe of constant cross-section. Frictional losses occur in the pipework and in the motor. The density of water is 1.00 × 10³ kg m⁻³ and its specific heat capacity is 4.18 × 10³ J kg⁻¹ K⁻¹. Assume the kinetic energy of the water leaving the pipe is negligible and that the system has reached steady state. ### Part (a) Define [2 marks] · AO1 · Topic: A.3 Define the *efficiency* of an energy conversion device and state its SI unit. ### Part (b)(i) Show that [3 marks] · AO2 · Topic: A.3 Show that the useful mechanical power delivered to the water as it is raised to the tank inlet is approximately 741 W. ### Part (b)(ii) Determine [3 marks] · AO2 · Topic: A.3 Determine the overall efficiency of the pump-and-pipe system, expressing your answer as a percentage. ### Part (c) Explain [2 marks] · AO3 · Topic: A.3+B.1 The water in the storage tank is found to be at a slightly higher temperature than the water in the reservoir. Explain, with reference to the energy balance in the pipework, why this temperature rise occurs. ### Part (d) Suggest [2 marks] · AO3 · Topic: A.3+B.1 · ASSUMPTIONS DISCRIMINATOR A student predicts the temperature rise of the water using the assumption that *all* the power lost in the system goes into heating the water. Suggest one reason why the actual temperature rise of the water in the tank would be smaller than this prediction. --- ## Mark Scheme ### Part (a) [2 marks] — Define - M1: efficiency = useful (output) energy / total (input) energy ✓ OR equivalent ratio in terms of power [no ECF] - M2: states that efficiency is dimensionless / has no SI unit (accept "ratio" or "%") ✓ [no ECF] ### Part (b)(i) [3 marks] — Show that - M1: mass flow rate Δm/Δt = ρ × (ΔV/Δt) = 1.00 × 10³ × 4.20 × 10⁻³ = 4.20 kg s⁻¹ ✓ [no ECF] - M2: applies P = (Δm/Δt) g h with substitution: P = 4.20 × 9.81 × 18.0 ✓ [ECF from M1] - M3: P = 741.6 W ≈ 741 W (to 3 s.f.) ✓ — answer must show derivation, not assertion [no ECF — target value given] ### Part (b)(ii) [3 marks] — Determine - M1: identifies η = P_useful / P_input ✓ [no ECF] - M2: correct substitution η = 741 / 1500 ✓ [ECF from (b)(i) if alternative derived value used] - M3: η = 0.494 or 49.4 % (accept 49 %–50 %) ✓ [ECF from M2] ### Part (c) [2 marks] — Explain (causal chain per §4.4.1) - M1: identifies that frictional/viscous forces in the pipe (or turbulence) dissipate mechanical energy as thermal energy / internal energy of the water ✓ - M2: therefore (causal link) this thermal energy raises the internal energy of the water, which means its temperature increases as it travels to the tank ✓ [linking marking point] ### Part (d) [2 marks] — Suggest (proposal + justification per §4.4.1) - M1: **Proposal** — identifies a specific pathway by which dissipated energy does NOT enter the water, e.g. heat conduction through pipe walls to surroundings / energy dissipated in motor windings or casing (not in contact with the water stream) / energy radiated/lost as sound and vibration ✓ - M2: **Justification** — explains that because some of the lost power is therefore transferred to the surroundings rather than to the water mass, less energy is available to raise the internal energy of the water, so ΔT = Q/(mc) is smaller than the prediction ✓ ### Marker notes - (b)(i): accept P = ρ(ΔV/Δt) g h done in a single combined step provided all three numerical factors and the final value 741 W appear; award M1+M2 for combined substitution and M3 for the value. - (b)(ii): alternative method — compute P_lost = 1500 − 741 = 759 W and η = 1 − 759/1500; equivalent marks awarded. - (c): do NOT award M2 for merely re-stating "energy is lost as heat" without linking to the temperature rise of the water specifically. - (d): accept any single valid loss pathway in M1 provided M2 explicitly links it to a *reduction* in energy delivered to the water (and hence smaller ΔT). Do not award M2 for vague statements such as "some energy is lost elsewhere". - Show-that target in (b)(i): 741.6 W given to 3 s.f.; student-derived 740–742 W acceptable.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ demonstrates a properly constructed cognitive ladder: Part (a) uses AO1/AO2 with Define (state equation); parts (b)(i)–(b)(ii) use AO2 with Calculate/Determine (numerical reasoning); part (c) uses AO3 with Explain (causal chain linking energy transfers to temperature rise); part (d) uses AO3 with Suggest (proposal + reasoning for assumptions). Progression from foundational knowledge → procedural application → higher-order synthesis is clear and appropriate for 12-mark HL question.
command_structure pass

All AO3 command-term structures comply with §4.4.1: part (c) 'Explain' exhibits an explicit causal chain (dissipated power → internal energy increase → temperature rise via P = ṁcΔT), and part (d) 'Suggest' provides a clear proposal (heat lost to surroundings) with physics-based justification (temperature gradient drives thermal energy flow). No formula-only marks awarded. ECF annotations correctly placed in method-mark steps of later parts (b)(ii) and (c).
cross_theme pass

The question successfully integrates both A.3 (Work, energy and power) and B.1 (Thermal energy transfers). Part (c) is the genuine integration point: it requires calculation of useful mechanical power (A.3) to find the dissipated power, then applies the thermal energy transfer equation P = ṁcΔT (B.1) to determine the temperature rise. Both concepts are operationally essential—removing either would make the problem unsolvable. Part (d) reinforces the B.1 concept by considering heat loss mechanisms. The second topic is not mere filler.
discriminator pass

Part (d) explicitly asks students to critique the model by suggesting a reason why the calculated temperature rise would be smaller than the actual value. This requires identifying an assumption in part (c) and explaining its limitation—a classic model-critique task. The mark scheme confirms this is asking for proposal + reasoned justification of why the simplifying assumption fails.
rule_of_one fail

Part (c) is marked as 2 marks but contains 3 distinct operations: (1) identify/calculate dissipated power, (2) apply formula P_dissipated = ṁcΔT, and (3) numerical answer with units. The mark scheme lists M1 (concept + calculation of dissipated power) and M2 (formula application + numerical answer), conflating multiple operations into single bullets. This violates the dimension requirement that a 2-mark part should have exactly 2 award criteria.

FIX: Restructure Part (c) as a 3-mark Calculate part with explicit separation: M1 = identify dissipated power (1500 − 741 = 759 W); M2 = apply ΔT = P_dissipated / (ṁcₚ) with correct substitution; M3 = final answer with units (0.043 K). Alternatively, if Part (c) must remain 2 marks, merge the explanation and calculation into a single Explain-and-calculate structure, removing the numerical computation step from the mark scheme.
topic pass

The ERQ genuinely integrates both topics. Part (a)–(b) establish A.3 (work, energy, power, efficiency). Part (c) requires B.1: the non-useful power dissipated (A.3 concept) must be linked to thermal energy transfer and internal energy increase (B.1), then quantified using specific heat capacity (B.1). Part (d) extends the thermal reasoning. Neither topic is superficial or nominally invoked; both are causally necessary to the solution.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define) with command term 'Define'; parts (b)(i)–(c) are AO2 (Show that, Determine, Calculate) with appropriate command terms; part (d) is AO3 (Suggest) requiring reasoning about assumptions. The progression from foundational knowledge through guided calculation to evaluation is properly sequenced.
command_structure fail

Part (d) is a 'Suggest' command term (AO3) but the mark scheme does NOT exhibit the required structure per v5 spec §4.4.1: Suggest = a proposal + a brief physics-based justification. The single marking point M1 lists three alternative proposals but provides only a vague shared justification ('so less thermal energy remains in the water') rather than explicit physics-based warrants linked to physical principles for each proposal or a clear exemplar. Additionally, the marker notes for (d) contain guidance that is not reflected in the mark scheme itself, creating ambiguity about what constitutes a valid response.

FIX: Restructure Part (d) mark scheme to explicitly separate proposal from justification for at least one exemplar option. For example: M1: proposes one valid mechanism (e.g., 'heat conducts through pipe walls to surroundings') ✓ M2: justifies why this reduces temperature rise in water (e.g., 'because dissipated energy is then shared between water and surroundings, so less remains in water mass') ✓. Alternatively, award a single mark but rewrite it as: 'M1: proposes a valid loss mechanism (heat loss to surroundings / energy to motor casing / sound/vibration) AND explains that this removes energy from the water itself, reducing ΔT' ✓. Also integrate the acceptance criteria from marker notes into the main scheme bullets.
cross_theme pass

Both A.3 (Work, energy and power) and B.1 (Thermal energy transfers) are genuinely integrated throughout the question, particularly in part (c) where the dissipated mechanical power is converted into thermal energy and used to calculate temperature rise via specific heat capacity—a core B.1 concept. Neither topic is mere window-dressing.
discriminator pass

Part (d) explicitly asks the student to critique a model assumption: 'Suggest one reason why the actual temperature rise of the water would be smaller than your value in (c).' This requires identifying a limitation of the assumption that 'all the dissipated mechanical energy stays in the water,' prompting evaluation of real-world loss mechanisms (heat loss through pipes, energy to motor casing, sound/vibration). This is authentic model critique, not a calculation.
rule_of_one fail

Part (a) has 2 marks but lists 2 award criteria (definition + unit), which is acceptable. However, Part (b)(i) has 3 marks with 3 criteria (mass flow rate calculation, power formula, numerical answer)—acceptable. Part (b)(ii) has 3 marks with 3 criteria (formula, substitution, final answer)—acceptable. Part (c) has 3 marks with 3 criteria (dissipated power, formula application with substitution, numerical answer)—acceptable. Part (d) has 1 mark with 1 criterion—acceptable. All individual parts pass the dimension check. However, the total mark count is 2+3+3+3+1=12 ✓. Upon strict re-examination: Part (b)(ii) M2 lists 'η = 741 / 1500' as a substitution step, but this is presented as a single bullet where the division operation itself is the award, not a distinct intermediate calculation step separate from M1 (the formula). This creates an ambiguity: is M2 'write down the substitution' or 'perform the division'? The scheme intends M1=formula, M2=substitution, M3=numerical evaluation, which matches the 3-mark structure. This is marginally acceptable but the phrasing 'η = 741 / 1500' blurs the line between substitution and calculation. The scheme is internally consistent and defensible, though part (b)(ii) could be more explicit.
topic pass

The ERQ effectively integrates both topics. A.3 (Work, energy and power) is the primary focus throughout parts (a)–(b)–(c), with power definition, mechanical power calculation, and efficiency analysis. B.1 (Thermal energy transfers) is substantively invoked in part (c), where dissipated mechanical energy is explicitly converted to thermal energy in the water, requiring the specific heat capacity formula ΔT = Q/(mc) applied to the continuous power dissipation. Part (d) deepens the thermal integration by questioning heat loss mechanisms. Neither topic is merely nominal; both are operationally essential to solving the problem.

Iteration 2 — passed

ao_ladder pass

The ERQ strictly obeys the cognitive ladder. Part (a) is AO1 with Define (command word); parts (b)(i)–(b)(ii) are AO2 with Show that/Determine; parts (c)–(d) are AO3 with Explain/Suggest. Difficulty and demand increase monotonically through the tiers, and the mark scheme enforces rigorous causal linkage in final parts (especially part (d) which requires both proposal AND justification).
command_structure pass

All AO3 command terms comply with §4.4.1 structural requirements. Part (c) Explain exhibits explicit causal chain (M1→M2: frictional dissipation therefore temperature rise). Part (d) Suggest includes proposal (M1: energy loss pathway) + physics-based justification (M2: linking to reduced ΔT via Q=mc relationship). All method marks properly annotated with ECF where applicable; no marks awarded for formulas alone.
cross_theme pass

Topics A.3 (Work, energy and power) and B.1 (Thermal energy transfers) are genuinely integrated throughout. Parts (c) and (d) require students to apply both concepts: A.3 energy balance and efficiency analysis frame the problem, while B.1 thermal energy transfer explains the temperature rise mechanism. The second topic is not mere filler—it is essential to explaining *why* temperature rises and *how* energy pathways affect this rise.
discriminator pass

Part (d) is a genuine model-critique question that asks students to identify a limitation of the assumption that all lost power heats the water. It requires proposing an alternative energy pathway and justifying why this makes the predicted temperature rise an overestimate—precisely the critiquing behavior the dimension requires.
rule_of_one pass

Each part's mark count aligns with the number of distinct award criteria. Part (a): 2 marks = 2 bullets (definition + unit). Part (b)(i): 3 marks = 3 bullets (mass flow rate, formula application, numerical answer). Part (b)(ii): 3 marks = 3 bullets (formula identification, substitution, answer). Part (c): 2 marks = 2 bullets (energy dissipation mechanism + causal link to temperature rise). Part (d): 2 marks = 2 bullets (proposal + justification). All divergences are ≤1 and justified by the scheme's detailed annotations.
topic pass

The ERQ genuinely integrates both topics. Parts (a)–(b) anchor firmly in A.3 (work, energy, power, efficiency), while parts (c)–(d) require explicit application of B.1 (thermal energy transfer): students must explain how frictional mechanical dissipation converts to internal energy of the water, then reason about energy pathways and heat losses to surroundings. Neither topic is nominal; both are essential to the causal explanation demanded.

Planner output (stage 1)

Archetype: real-world device
Scenario: A motor-driven pump lifts water from a reservoir to an elevated tank. The pump has an input electrical power and delivers water at a constant volume flow rate against gravitational potential energy and frictional losses in the pipework. Students analyze the mechanical work done, energy conversion efficiency, and the thermal energy dissipated in the system.
Cross-pollination part: c
Discriminator part: d

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

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