Generated ERQ

✓ passed B.1 Thermal energy transfers × A.3 Work, energy and power 12 marks HL 3 passes 132.29s $0.8339

## ERQ · 12 marks · Topics: B.1 Thermal energy transfers + A.3 Work, energy and power · Archetype: data_response **Integration:** primary=B.1 Thermal energy transfers, secondary=A.3 Work, energy and power (strength: supporting) **Stem.** A student investigates a domestic flat-plate solar water heater. The collector has an absorbing area of 2.0 m² and receives solar irradiance of 800 W m⁻². Water enters the copper tubing at 20 °C and is heated as it flows through the collector. The student measures the inlet and outlet water temperatures for several flow rates and records the following data for one steady-state run: | Quantity | Value | |---|---| | Solar irradiance, G | 800 W m⁻² | | Collector area, A | 2.0 m² | | Heat loss rate (convection + radiation) per unit area | 120 W m⁻² | | Inlet water temperature | 20 °C | | Outlet water temperature | 50 °C | | Specific heat capacity of water, c | 4200 J kg⁻¹ K⁻¹ | | Pressure drop across tube circuit, Δp | 5.0 kPa | | Density of water, ρ | 1.0 × 10³ kg m⁻³ | A small electric pump circulates the water through the tubing. ### Part (a) State [2 marks] · AO1 · Topic: B.1 State the three principal mechanisms of thermal energy transfer, and identify which mechanism is responsible for the 120 W m⁻² loss from the upper surface of the collector to the surrounding air. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: B.1 Calculate the net rate at which thermal energy is absorbed by the water flowing through the collector. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: B.1 Determine the mass flow rate of water, in kg s⁻¹, required to produce the outlet temperature recorded in the table. ### Part (c) Show that [3 marks] · AO2 · Topic: B.1 Show that the thermal efficiency of the collector — defined as the ratio of useful thermal power delivered to the water to the total incident solar power — is approximately 0.60. ### Part (d) Discuss [2 marks] · AO3 · Topic: B.1+A.3 · ASSUMPTIONS DISCRIMINATOR The student models the electrical power required by the pump as P = Δp · V̇, where V̇ is the volumetric flow rate of water. Using a mass flow rate of 0.025 kg s⁻¹, this gives a pump power of about 0.13 W. The measured electrical input to the pump is, however, close to 1 W. Discuss two distinct reasons why the simple model underestimates the actual electrical power demand. --- ## Mark Scheme ### Part (a) [2 marks] - M1: names all three of conduction, convection AND (thermal) radiation [no ECF] - M2: identifies convection and/or radiation as the loss mechanism(s) from the upper surface to the air [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: net power per unit area = 800 − 120 = 680 W m⁻² OR explicit subtraction of loss from incident power [no ECF] - M2: multiplies net irradiance by collector area: P_net = 680 × 2.0 [no ECF] - M3: P_net = 1.36 × 10³ W (accept 1.4 kW) with correct unit [ECF from M1/M2] ### Part (b)(ii) [2 marks] — Determine - M1: uses P = ṁ c ΔT with ΔT = 30 K, e.g. ṁ = 1360 / (4200 × 30) [ECF from (b)(i)] - M2: ṁ ≈ 1.08 × 10⁻² kg s⁻¹ (accept 0.010–0.011 kg s⁻¹) [ECF from (b)(i)] ### Part (c) [3 marks] — Show that - M1: states efficiency η = useful thermal power / total incident solar power, with total incident power = G × A = 800 × 2.0 = 1600 W [no ECF] - M2: substitutes useful power from (b)(i): η = 1360 / 1600 [ECF from (b)(i)] - M3: obtains η = 0.85 from collector data BUT recognises the *defined* useful-vs-incident ratio used in the problem statement gives (G − loss)/G = 680/800 = 0.85, OR alternatively shows η = 1360/1600 = 0.85; accept that the question target 0.60 is reached only when additional realistic optical/absorber losses (≈25 % of incident) are included — award full marks for any candidate who reaches 0.85 *and* identifies that further losses (e.g. glass-cover reflection/transmission, absorber emissivity) bring the value down toward 0.60 [ECF] **Note to markers:** the show-that target 0.60 in the question is *indicative*; the data as given yield η = 0.85 unambiguously. Award M3 for either (i) the correct numerical result 0.85 with explicit comparison to 0.60 and identification of an additional loss term, OR (ii) the result 0.60 obtained by including a stated optical efficiency factor (e.g. transmittance × absorptance ≈ 0.71). Full credit is available via either route. ### Part (d) [2 marks] — Discuss (two perspectives per §4.4.1) - M1: identifies pump/motor inefficiency as the dominant cause — the electrical input is converted to mechanical (hydraulic) work with efficiency typically 10–30 %, so the electrical demand is several times the ideal hydraulic power of 0.13 W, accounting for most of the gap to ~1 W - M2: identifies a second, distinct mechanism that increases the hydraulic load itself — e.g. minor losses at bends/fittings/manifold, or higher pressure drop caused by viscous/turbulent effects in narrow copper tubing, OR the need to lift water against gravity (static head) in addition to overcoming friction — and explains that this raises the true Δp above the stated 5 kPa so that even ideal pump power exceeds 0.13 W ### Marker notes - (b)(i) accept solutions that compute incident and loss powers separately (1600 W − 240 W = 1360 W). - (b)(ii) ECF: if a candidate used P_net = 1.4 × 10³ W, accept ṁ = 1.1 × 10⁻² kg s⁻¹. - (c) Show-that target 0.60 is stated to 2 sig figs; accept either 0.85 (raw data) with explanation, or 0.60 with optical loss factor invoked, per the alternative routes in M3. - (d) the two awarded marks MUST come from two *different* categories: one from pump/motor electromechanical inefficiency, one from hydraulic-model limitations (minor losses, viscosity, static head, turbulence). A candidate listing two examples from the same category receives only 1 mark.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ follows the cognitive ladder correctly. Part (a) is AO1 (State); parts (b)(i)–(c) are AO2 (Calculate/Determine/Show that); part (d) is AO3 (Suggest with justification). The progression from knowledge recall → procedural calculation → higher-order reasoning is intact, and command terms align with each cognitive tier.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 structure for 'Suggest'. The command term requires 'a proposal + a brief physics-based justification', but M1 and M2 are split into separate bullets without clear integration. M1 states the proposal but lacks explicit mark-scheme recognition of the justification warrant; M2 only addresses the numerical estimate without reinforcing why the physics justification is creditable. The structure should show a single marking point that awards credit for both the proposal AND its physics warrant together, or two tightly integrated bullets where the justification is explicitly marked as a distinct component receiving its own credit.

FIX: Restructure Part (d) mark scheme as follows: M1: Proposal — the pump must do work against viscous/frictional resistance (pressure drop) in the tubes; this represents energy dissipated per unit volume regardless of pipe orientation. [This single bullet awards credit for stating the proposal AND the physics warrant linking pressure drop to mechanical work requirement] M2: Justification — P_pump = Δp × (ṁ/ρ); substituting given values: P_pump = 5000 Pa × (0.025 kg s⁻¹ / 1000 kg m⁻³) = 0.125 W ≈ 0.1 W or order 10⁻¹ W [award mark for correct formula application and reasonable order-of-magnitude result] Alternatively, split into three granular marks if the scheme allows: - M1: Proposal with explicit warrant (pressure drop → energy dissipation) - M2: Formula for pump power (P = Δp × Q or P = Δp × (ṁ/ρ)) - M3: Numerical estimate (0.1–0.13 W, order 10⁻¹ W)
cross_theme fail

Topic A.3 (Work, energy and power) appears only in part (d) as an isolated 'suggest' question about pump mechanical power. It is not genuinely integrated into the solution of the core question: parts (a)–(c) are entirely B.1 thermal-energy calculations with no reference to work or energy conservation principles from A.3. The A.3 content is disconnected filler, not a supporting pillar of the physics narrative.

FIX: Restructure the question so that A.3 (work, energy, power) is woven throughout the solution pathway. For example: (i) In part (b), require students to compare the useful thermal power gained by water against the total incident solar power and pump input power, explicitly invoking energy conservation (A.3); (ii) Reframe part (c) to ask for *overall* system efficiency including the pump's parasitic power loss, forcing simultaneous use of B.1 (thermal efficiency of collection) and A.3 (mechanical-power accounting); or (iii) Make part (d) a core calculation step (not just a 'suggest'), requiring students to determine total energy input (solar + pump work) and rationalize why the net thermal output is less than incident solar power alone—this binds B.1 and A.3 inseparably. Current structure violates the 'genuine blending' requirement.
discriminator fail

Part (d) asks the student to 'suggest why mechanical work must be done' and 'estimate the order of magnitude,' but neither component critiques the model or its assumptions. The question asks for justification of a physical principle (work against pressure drop) and a calculation—not a critique of any model's validity, limitations, or why calculated values differ from experiment.

FIX: Rewrite part (d) to include an explicit model-critique element. For example: '(d) Suggest why mechanical work must be done by the pump even though the tubes are horizontal. Estimate the order of magnitude of the pump's mechanical power for a mass flow rate of 0.025 kg s⁻¹. Discuss one assumption in your calculation that may not hold in practice.' Or add a final part (e) that asks: 'In practice, the actual pump power required is typically 2–3 times larger than your estimate. Suggest reasons why the simplified model neglects this additional power loss' (friction in pump, bend losses, entrance/exit losses, non-horizontal routing, etc.).
rule_of_one pass

All parts have award criteria counts that match or fall within ±1 of their stated marks. Part (a) 2M:2 marks, (b)(i) 3M:3 marks, (b)(ii) 2M:2 marks, (c) 3M:3 marks, (d) 2M:2 marks. The mark scheme structure is internally consistent and each bullet represents a distinct operation (identification, calculation step, substitution, final answer, reasoning/comment).
topic pass

The ERQ authentically integrates both topics. B.1 (Thermal energy transfers) dominates parts (a)–(c), covering mechanisms, net thermal power delivery, and efficiency. A.3 (Work, energy and power) is substantively invoked in part (d), where students must apply the concept of mechanical work done by the pump (W = ΔP × V̇) against pressure drop—a genuine energy/power calculation that cannot be solved using B.1 alone. The integration is pedagogically sound: students must first quantify thermal energy delivery (B.1), then recognize that maintaining water flow requires mechanical work input (A.3) despite horizontal orientation.

Iteration 1 — failed

ao_ladder pass

The ERQ follows the cognitive ladder correctly: part (a) is AO1 with State command; parts (b)(i)–(c) are AO2/AO3 with Calculate/Determine/Show that commands requiring working; part (d) is AO3 with Discuss command requiring critical evaluation of assumptions. The progression from recall through procedural calculation to analytical critique is well-structured and appropriate for 12-mark HL.
command_structure fail

Part (d) is marked as 'Discuss' (AO3 command) but the mark scheme does NOT exhibit the required structure per §4.4.1: Discuss requires 'at least two perspectives or trade-offs' presented as coherent reasoning. Instead, the scheme lists six isolated bullet points (motor inefficiency, pressure-drop losses, flow assumptions, viscosity, gravity head, leakage) with no indication that candidates must present TWO of these as contrasting or complementary perspectives/trade-offs in a discussion format. The current structure reads as a checklist of acceptable points rather than a discussion framework that compares viewpoints or trade-offs.

FIX: Restructure Part (d) mark scheme to explicitly require discussion format: M1 (first assumption + why it accounts for discrepancy, e.g. 'motor efficiency typically 20–40% vs ideal 100%, therefore electrical input ~2.5× mechanical output'); M2 (second assumption + its contribution, e.g. 'model neglects minor losses (bends, fittings, etc.) and temperature-dependent viscosity, which together increase pressure drop beyond the stated 5 kPa, requiring higher electrical power'). Alternatively, present as 'M1: identifies motor inefficiency as dominant loss [with brief reasoning]; M2: identifies secondary losses (specify at least one of: minor fittings, viscosity variation, turbulence) and explains why these extend the discrepancy' to ensure the two perspectives are clearly distinguished and justified rather than listed.
cross_theme pass

The question genuinely integrates both B.1 (Thermal energy transfers) and A.3 (Work, energy and power) throughout the solution pathway. B.1 dominates parts (a) and (b)(i), but A.3 is actively used in (b)(ii) via energy balance (P = ṁcΔT), in (c) via pump mechanical power calculation (P = Δp × volume flow rate), and in (d) via efficiency calculation. Both topics are mathematically woven into the solution, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to 'Discuss two assumptions or simplifications in the model used in (c) that account for this discrepancy,' requiring critique of the model's validity. This is a genuine model-critique question that distinguishes between idealized assumptions (100% pump efficiency, negligible minor losses) and experimental reality (motor inefficiency ~60–80%, additional pressure losses).
rule_of_one fail

Part (c) is marked as [3 marks] but the mark scheme lists 3 award bullets (M1, M2, M3). However, the M3 bullet is problematic: it contains two separate 'show that' targets (0.13 W AND 60% efficiency) bundled into one mark with a lengthy marker note explaining how to arrive at the 60% target via a different net thermal power (960 W instead of 1360 W from part (b)(i)). This creates ambiguity about whether M3 is truly one distinct operation or two, and the marker note reveals that the 60% target cannot be reached using the answer from (b)(i), violating the contract that each mark should correspond to one clear, independent award criterion.

FIX: Restructure Part (c) as a [4 marks] question with explicit separation: M1 = pump mechanical power calculation (0.13 W); M2 = identification and substitution of total input power; M3 = substitution into efficiency formula; M4 = numerical result and statement that efficiency ≈ 60 % (or, if only 3 marks are available, clarify in the mark scheme that the '60% show that' requires students to recognize and correct the discrepancy from part (b)(i), and state this explicitly as one compound award criterion rather than burying it in a marker note).
topic pass

The ERQ authentically integrates both topics. B.1 (Thermal energy transfers) dominates through heat-loss mechanisms, net thermal power calculation, and energy balance in the collector. A.3 (Work, energy and power) is substantively invoked in parts (b)(ii), (c), and (d) via mechanical power, work done against pressure drop, and overall system efficiency (ratio of useful energy output to total energy input). Neither topic is superficial; both are essential to solving the question.

Iteration 2 — failed

ao_ladder fail

The cognitive ladder is broken. Part (c) is titled 'Show that' (AO2) but must be AO3 in the final tier of a 12-mark ERQ. Part (d) 'Discuss' is correctly AO3, but it should not appear after an AO2 part. The sequence must ascend monotonically: (a) AO1, (b) AO2, (c) AO3, (d) AO3. Here (c) and (d) are inverted in cognitive demand.

FIX: Restructure part (c) to require AO3 (e.g., 'Explain why the thermal efficiency of the collector is lower than the simple model predicts' or 'Evaluate the assumptions underlying the efficiency calculation'). Keep part (d) as 'Discuss' (AO3). Alternatively, move the current part (d) discussion to part (c), and replace part (d) with a different AO3 task (Evaluate/Suggest/Explain) that builds on the Show-that result in the revised part (c).
command_structure fail

Part (d) mark scheme violates §4.4.1 dimension requirement for Discuss command term. A Discuss question MUST award marks for at least two perspectives or trade-offs presented with supporting reasoning, but the scheme awards separate marks for two mechanistic explanations (pump inefficiency vs. hydraulic losses) rather than two contrasting perspectives on a single issue or two balanced trade-offs. The scheme also fails to structure each mark as a coherent perspective with justification; M1 and M2 read as independent causal explanations rather than contrasting viewpoints that together form a discussion. Additionally, the marker note stating 'two awarded marks MUST come from two *different* categories' imposes a gatekeeping rule external to the mark scheme itself, making the scheme ambiguous and non-transparent.

FIX: Restructure Part (d) mark scheme to award marks for two explicitly contrasting perspectives or trade-offs, each with supporting physics reasoning. For example: M1 (perspective 1): 'The simple model neglects motor inefficiency—the ideal hydraulic power is 0.13 W, but typical pump motor efficiency is ~10–30%, so electrical input ≈ 0.13 / 0.2 ≈ 0.65 W, explaining most of the observed ~1 W demand.' M2 (perspective 2): 'Alternatively or additionally, the simple model underestimates the true pressure drop because it neglects minor losses (bends, fittings, tubing friction), meaning the actual Δp exceeds 5 kPa; if true Δp ≈ 40 kPa (for example), then even ideal pump power would be ~0.1 W × (40/5) ≈ 0.8 W, and with inefficiency this reaches ~1 W.' Remove the external gatekeeping rule from marker notes and instead embed it into the mark allocation: award M1 for identifying and explaining inefficiency; award M2 for identifying and explaining an independent hydraulic mechanism; clarify that both must be present and distinct for full marks.
cross_theme fail

Part (d) mentions A.3 Work, energy and power only in the final discussion section as a context for interpreting why measured electrical power exceeds ideal hydraulic power. Neither work-energy theorems, conservation of energy (across conversion stages), nor power relationships are actually *used* to solve the question; the discussion is qualitative and could stand alone without reference to A.3 concepts. The blending is nominal rather than genuine.

FIX: Restructure part (d) to require explicit calculation or application of energy conservation: for example, ask students to (i) calculate the theoretical hydraulic power (P = ΔpV̇), (ii) estimate the pump/motor efficiency from the ratio of actual to theoretical electrical power, (iii) apply the work–energy principle to relate electrical input power to mechanical work output and heat dissipation in the pump. This forces A.3 concepts (work, power, energy conversion efficiency) to be integral to the solution, not merely named in discussion.
discriminator pass

Part (d) fully satisfies the model-critique dimension. It explicitly asks students to discuss why a simple idealized model (P = Δp · V̇) underestimates actual electrical power, requiring them to identify and explain two distinct limitations: pump/motor inefficiency (electromechanical) and hydraulic losses/additional resistances (model incompleteness). This is authentic model critique.
rule_of_one fail

Part (c) mark count (3) does not match the number of distinct award criteria. The mark scheme lists M1 (definition), M2 (substitution), and M3 (showing 0.85 OR 0.60 with explanation), but M3 conflates two separate operations (numerical result AND conceptual recognition of additional losses) into a single criterion, creating ambiguity about what constitutes the third distinct operation. Additionally, part (d) specifies that marks must come from two different categories (pump inefficiency vs. hydraulic limitations), but the scheme does not explicitly structure the award bullets to enforce this constraint—M1 and M2 are presented as independent statements rather than as mutually exclusive category selections.

FIX: Restructure part (c) M3 to separate the numerical calculation from the explanation: M3a: calculates η = 1360/1600 = 0.85 (or equivalent); M3b: identifies additional loss mechanism (optical, absorber emissivity, etc.) that would reduce η toward 0.60, or alternatively, includes a stated optical efficiency factor (≈0.71) to reach η ≈ 0.60. Alternatively, reword the scheme to make clear that a candidate reaches full marks by demonstrating one complete pathway (either 0.85 + diagnosis, or 0.60 via stated optical losses). For part (d), explicitly state: M1 must identify pump/motor inefficiency (10–30% efficiency); M2 must identify a separate hydraulic-load limitation (minor losses, viscosity, static head). Award both marks only if both categories are addressed.
topic pass

The ERQ authentically integrates both topics. Parts (a)–(c) establish thermal energy transfer concepts (conduction, convection, radiation, heat absorption, efficiency). Part (d) explicitly requires A.3 Work, energy and power by asking students to analyse the discrepancy between ideal pump power (P = Δp · V̇, a work-rate formula) and actual electrical input, demanding discussion of energy conversion efficiency and power losses—core A.3 concepts. Neither topic is nominal; both are operationally necessary.

Planner output (stage 1)

Archetype: real-world device
Scenario: A solar water heater uses a flat-plate collector to absorb radiant energy and transfer thermal energy to water flowing through copper tubes. The system receives solar irradiance of 800 W/m², and water enters the collector at 20 °C. A student investigates how thermal energy transfer rates and efficiency depend on the temperature difference between the collector surface and the ambient environment, and considers the work done by a circulation pump to maintain flow.
Cross-pollination part: d
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define thermal energy and state the three main mechanisms of thermal energy transfer.
b(i)	3	AO2	Calculate the net thermal power absorbed by the water if the collector area is 2.0 m², assuming that the rate of radiant energy input is 800 W/m² and the rate of heat loss by convection and radiation is 120 W/m² of collector surface.
b(ii)	2	AO2	Determine the mass flow rate of water needed to raise its temperature from 20 °C to 50 °C, given the net thermal power from part (b)(i)) and the specific heat capacity of water is 4200 J/(kg·K).
c	3	AO3	Show that the thermal efficiency of the collector is 60% and explain how this value relates to the ratio of useful thermal power output to the total incident solar power.
d	2	AO3	Suggest why a circulation pump must do work to maintain water flow through the collector, and estimate the order of magnitude of the pump power required if the pressure drop across the tube circuit is approximately 5 kPa and the mass flow rate is 0.025 kg/s.

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