Generated ERQ

✓ passed B.3 Gas laws × A.3 Work, energy and power 12 marks SL 3 passes 107.08s $0.7248

``` ## ERQ · 12 marks · Topics: B.3 Gas laws + A.3 Work, energy and power · Archetype: theory_application **Integration:** primary=B.3 Gas laws, secondary=A.3 Work, energy and power (strength: supporting) **Stem.** A horizontal piston-cylinder assembly is used in a laboratory demonstration of slow gas compression. The cylinder contains dry air, treated as an ideal gas, initially at a pressure of 101 kPa, a temperature of 295 K, and a volume of 500 cm³. A motor drives the piston inward at a very low constant speed so that the air is compressed to a final volume of 50.0 cm³. The cylinder is surrounded by a water jacket that maintains the gas at 295 K throughout the compression. There is measurable friction between the piston ring and the cylinder wall, and the mechanical work supplied by the motor is monitored using a torque sensor. ### Part (a) State [2 marks] · AO1 · Topic: B.3 Gas laws State the equation of state of an ideal gas and identify the meaning of each symbol. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: B.3 Gas laws Calculate the pressure of the air in the cylinder once the volume has been reduced to 50.0 cm³. ### Part (b)(ii) Show that [4 marks] · AO2 · Topic: B.3 Gas laws The work done on an ideal gas during a slow isothermal compression from volume V₁ to V₂ is given by W = nRT ln(V₁/V₂). Using this expression, show that the work done on the air in this compression is approximately 116 J. (You may take the amount of gas as n = 2.06 × 10⁻² mol.) ### Part (c) Suggest [2 marks] · AO3 · Topic: B.3 Gas laws + A.3 Work, energy and power The motor's torque sensor records that the mechanical work actually supplied to the piston exceeds 116 J. Suggest, with reference to the first law of thermodynamics, why this is the case. ### Part (d) Evaluate [1 mark] · AO3 · ASSUMPTIONS DISCRIMINATOR Evaluate the assumption that the gas remains at 295 K throughout the compression if the piston were instead driven inward rapidly. --- ## Mark Scheme ### Part (a) [2 marks] — State - M1: equation written as pV = nRT [no ECF] - M2: all four symbols correctly identified — p = pressure (Pa), V = volume (m³), n = amount of substance (mol), T = absolute temperature (K); R need not be defined as it is a constant from the data booklet, but accept "molar/ideal gas constant" [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: recognition that at constant T, p₁V₁ = p₂V₂ (Boyle's law) with correct substitution: (101 × 10³)(500) = p₂(50.0) [no ECF] - M2: rearrangement giving p₂ = 101 × 10³ × (500/50.0) [no ECF] - M3: final answer p₂ = 1.01 × 10⁶ Pa (= 1010 kPa ≈ 10 atm) [ECF from M1/M2] ### Part (b)(ii) [4 marks] — Show that - M1: substitution into W = nRT ln(V₁/V₂): W = (2.06 × 10⁻²)(8.31)(295) ln(500/50.0) [no ECF] - M2: evaluation of nRT = 50.5 J (accept 50.4–50.6) [no ECF] - M3: evaluation of ln(500/50.0) = ln(10) = 2.30 (accept 2.30–2.303) [no ECF] - M4: product gives W ≈ 116 J (student-derived value in range 115–117 J acceptable) [ECF from M2/M3] ### Part (c) [2 marks] — Suggest (proposal + warrant per §4.4.1) - M1: PROPOSAL — friction between the piston ring and the cylinder wall dissipates energy as thermal energy, which is carried away by the water jacket [no ECF] - M2: WARRANT — by the first law, for the gas ΔU = Q + W_on_gas; since the process is isothermal ΔU = 0, so the 116 J represents only the reversible work done on the gas, therefore the motor must additionally supply the work lost to friction, giving W_motor > 116 J [ECF from M1] ### Part (d) [1 mark] — Evaluate - M1: the assumption breaks down — rapid compression does not allow sufficient time for heat to be transferred to the water jacket, so the gas temperature rises (process becomes approximately adiabatic) and the isothermal form pV = constant no longer applies, although pV = nRT itself remains valid at each instant [no ECF] ### Marker notes - (b)(i): accept answers expressed as 1.01 MPa, 1010 kPa, or 1.01 × 10⁶ Pa; do not penalise omission of unit if pressure ratio is clearly stated. - (b)(ii): "Show that" target 116 J given to 3 sig figs; any student-derived value in 115–117 J earns M4. ECF applies from M2/M3 — a candidate using n = 2.0 × 10⁻² mol giving W ≈ 113 J still earns M4 provided working is shown. - (c): accept equivalent first-law phrasings using Q + W or U = Q − W conventions provided sign treatment is internally consistent. M2 requires explicit linking word ("therefore", "so", "hence") connecting friction loss to the inequality W_motor > 116 J. - (d) accept any of: rapid compression → near-adiabatic behaviour; insufficient time for thermal equilibration with surroundings; T rises so isothermal assumption invalid; pV = nRT still holds but pV ≠ constant. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ follows the cognitive ladder correctly: Part (a) is AO1 (State); Parts (b)(i) and (b)(ii) are AO2 (Calculate, Show that); Parts (c) and (d) are AO3 (Suggest, Discuss). Command terms and cognitive demands are appropriately sequenced and matched to learning objectives.
command_structure fail

Part (c) 'Suggest' fails the required §4.4.1 structure. The mark scheme provides M1 (identifies friction dissipation) and M2 (links to first law), but M1 does not constitute a 'proposal + brief physics-based justification' as a single marking point. Instead, it is a bare observation. M2 attempts the justification but is structurally separated, violating the requirement that 'Suggest = a proposal + a brief physics-based justification' as ONE coherent marking unit. The structure must be reorganized so that a single mark explicitly awards both the proposal (why mechanical work > 116 J) AND its physics warrant in a unified causal statement.

FIX: Restructure Part (c) marks as: M1: proposes that friction at the piston–cylinder interface dissipates additional mechanical energy as heat, and the first law requires that external work input = work done on gas + energy dissipated as friction (+ heat removed by jacket); therefore W_input > 116 J. M2: identifies that this energy dissipation (friction, viscous resistance) means the mechanical input at the piston rod must exceed the thermodynamic work done on the gas alone. This creates a single 'proposal + warrant' unit for M1, with M2 as reinforcement or alternative perspective. Alternatively, collapse to a single 2-mark point: 'Friction between piston and cylinder dissipates mechanical energy; by the first law, the external work input must equal the work done on the gas plus the energy lost to friction and heat removal, so W_input > 116 J [2 marks for complete proposal + justification].' Also verify Part (d) explicitly labels the two perspectives (for/against) to confirm 'balanced discussion' is unambiguous.
cross_theme pass

The question successfully blends both B.3 (Gas laws) and A.3 (Work, energy and power). Part (b)(ii) is the integrative core: it uses the ideal gas law (isothermal condition p₁V₁ = p₂V₂) to derive the pressure, then applies the work integral W = −∫p dV (a central A.3 concept) to calculate work done on the gas. Parts (c) and (d) build on this integration by discussing energy dissipation via the first law and the validity of isothermal assumptions. Both physics concepts are genuinely used in the solution, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to 'Discuss whether the assumption that the compression is truly isothermal is justified, and how a departure from this assumption would affect the validity of the calculation in part (b)(ii).' This is a clear model-critique question requiring evaluation of assumptions and their consequences—fully aligned with the dimension's intent.
rule_of_one pass

Each part's mark count matches its award criteria count precisely: (a) 2 marks / 2 bullets, (b)(i) 3 marks / 3 bullets, (b)(ii) 3 marks / 3 bullets, (c) 2 marks / 2 bullets, (d) 2 marks / 2 bullets. All Calculate and Show-that parts have the required formula/substitution/answer structure; all Suggest and Discuss parts meet AO3 rubric with justification. The scheme is internally coherent.
topic pass

The ERQ authentically tests both B.3 Gas laws and A.3 Work, energy and power. Part (b)(i) and early (b)(ii) apply the ideal gas law and isothermal condition (B.3). Part (b)(ii) then requires integration of W = −∫p dV for an isothermal process, which is a core A.3 concept (work calculation via integration). Parts (c) and (d) reinforce this integration by invoking the first law of thermodynamics and energy dissipation—connecting gas behavior to thermodynamic work. Neither topic is superficial; both are essential to solving the problem.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (State), parts (b)(i)–(b)(ii) are AO2 (Calculate/Show that), and parts (c)–(d) are AO3 (Suggest/Discuss). The progression from recall through application to synthesis and evaluation is properly sequenced with appropriate command terms at each tier.
command_structure fail

Part (c) mark scheme violates §4.4.1 Suggest structure. The command requires 'a proposal + a brief physics-based justification,' but the scheme conflates two distinct concepts (friction as dissipative mechanism AND first law energy balance) into a single M1 award, with no clear separation between the proposal itself and its warrant. Additionally, the alternative phrasing 'external mechanical work supplied by the motor must equal...' states a principle rather than explicitly proposing a reason why W_motor > 116 J; the causal linkage is implicit rather than explicit. Part (b)(ii) also lacks proper §4.6 ECF annotation on M3 (the final numerical step should carry forward uncertainty from M1's value of n, yet is marked 'no ECF').

FIX: Restructure Part (c) M1 as follows: 'M1: PROPOSAL — friction between piston ring and cylinder wall causes energy dissipation.' M2: 'WARRANT — by the first law of thermodynamics, ΔU = Q + W_motor + W_friction; since the gas is isothermal (ΔU = 0) and Q is removed by the jacket, W_motor must supply both the reversible work (116 J) and compensate for friction losses, therefore W_motor > 116 J.' This separates proposal from warrant explicitly. For (b)(ii), either change M3 from '[no ECF]' to '[ECF from M1 if n rounded]' or explicitly note that the target value 116.3 J tolerates ±1–2 J due to rounding in M1. Alternatively, award M3 full marks provided the student's result lies within 115–117 J (as stated in marker notes), with ECF noted if their n value differs slightly.
cross_theme pass

The ERQ successfully blends B.3 Gas laws (primary) and A.3 Work, energy and power (secondary). Part (b)(i–ii) applies gas laws exclusively; part (c) genuinely integrates both: it requires the 116 J work calculated from gas law theory, then demands application of the first law of thermodynamics (A.3) to explain why motor work exceeds this value, invoking friction-driven energy dissipation. The second topic is not filler—it is essential to answer (c) fully.
discriminator pass

Part (d) explicitly asks students to 'Discuss whether the assumption that the air remains at 295 K throughout the compression is justified', requiring balanced critique of the isothermal model against real-world constraints (finite compression time, heat-conduction limits). This is a genuine model-critique task, not a calculation.
rule_of_one fail

Part (c) declares 2 marks but the mark scheme shows only 1 distinct award criterion (a unified proposal–warrant unit), with a fallback to 1 mark for partial responses. This violates the dimension requirement that a 2-mark part must have exactly 2 award bullets. The scheme conflates M1 into a single holistic criterion rather than splitting it into two discrete operations.

FIX: Restructure Part (c) mark scheme to split the proposal–warrant structure into two explicit criteria: M1 (1 mark) for identifying friction and the first law separately, and M2 (1 mark) for linking them to explain why W_motor > 116 J. Alternatively, reduce Part (c) to 1 mark and redistribute those marks to (a), (b), or (d) to maintain the 12-mark total. The current scheme's award of '2 marks awarded together for a unified proposal–justification unit' does not align with the 2-mark labeling and breaks the mark-count/bullet-count contract.
topic pass

The ERQ genuinely integrates both topics. Parts (a)–(b) establish the gas law framework (B.3 primary). Part (c) requires the first law of thermodynamics to explain why motor work exceeds the isothermal work calculated in (b)(ii)—this directly invokes energy conservation and dissipative work (A.3 supporting role). Part (d) deepens the isothermal assumption critique by invoking thermal timescales and adiabatic deviation, which bridges both topics. Neither topic is superficial; B.3 provides the physical model and A.3 provides the energy-balance warrant for the discrepancy.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly follows the cognitive ladder: (a) is AO1 with State command; (b)(i)–(b)(ii) are AO2 with Calculate and Show that commands; (c) is AO3 with Suggest; (d) is AO3 with Evaluate. All parts progress appropriately in cognitive demand without inversion or missing tiers.
command_structure fail

Part (c) mark scheme violates §4.4.1 AO3 Suggest structure. M2 does provide a warrant ('by the first law...therefore...'), but M1 states only the proposal without the required 'brief physics-based justification' component integrated into a single mark point. The structure should present proposal + justification as one unified marking point, not separated into two independent bullets. Additionally, Part (d) Evaluate lacks the required 'position + supporting consideration + limiting consideration' three-part structure; it provides only position + mechanism, missing explicit supporting and limiting considerations.

FIX: Part (c): Merge M1 and M2 into a single unified mark point that reads: 'friction between piston and cylinder wall dissipates mechanical work as heat; by the first law ΔU = Q + W_on_gas, and since ΔU = 0 (isothermal), the 116 J represents only reversible work on gas, so the motor must supply additional work to overcome friction, giving W_motor > 116 J.' This delivers proposal + physics-based warrant in one bullet. Part (d): Revise to: 'Position: the isothermal assumption is invalid. Supporting: rapid compression does not allow sufficient time for heat transfer, so process becomes approximately adiabatic and T rises. Limiting: however, pV = nRT remains valid at each instant even if pV ≠ constant no longer holds.' This provides all three required elements for Evaluate per §4.4.1.
cross_theme fail

Part (c) uses both B.3 (gas laws/isothermal process) and A.3 (work, energy, first law of thermodynamics) genuinely in the warrant. However, parts (a), (b)(i), and (b)(ii) are purely B.3 Gas laws with no integration of A.3 concepts. Part (d) only mentions A.3 in the context of evaluating assumptions (adiabatic vs isothermal), but this is superficial name-checking. The secondary topic A.3 Work, energy and power is not truly blended throughout the question—it appears only in part (c)'s warrant and part (d)'s discrimination, not as an integral solving tool across the body of the ERQ.

FIX: Restructure part (b) to require students to apply energy conservation explicitly: e.g., ask them to calculate the heat transferred to the water jacket using the first law (Q = W_on_gas since ΔU = 0 for isothermal process), or modify part (c) to become a multi-part calculation where students must use both pV = nRT and the first law to estimate friction losses as (W_motor − 116 J). Alternatively, reframe the entire question to make A.3 (work, power, energy balance) the primary lens through which the gas compression is analysed, with B.3 as supporting context.
discriminator pass

Part (d) explicitly asks students to 'Evaluate the assumption that the gas remains at 295 K throughout the compression if the piston were instead driven inward rapidly.' This is a clear model-critique question requiring students to identify when and why the isothermal assumption breaks down, and to explain the physical mechanism (rapid compression prevents heat transfer, process becomes approximately adiabatic, temperature rises). The mark scheme confirms this evaluates the validity of the model rather than performing another calculation.
rule_of_one pass

Each part's mark allocation matches the number of distinct award criteria: (a) 2 marks/2 bullets (equation + symbols); (b)(i) 3 marks/3 bullets (formula, substitution, answer); (b)(ii) 4 marks/4 bullets (substitution, nRT evaluation, ln evaluation, final product); (c) 2 marks/2 bullets (proposal + warrant); (d) 1 mark/1 bullet (evaluation). All mark-to-criteria counts align within the acceptable tolerance.
topic pass

The ERQ genuinely integrates both topics. Part (b)(ii) and (c) require explicit application of the isothermal work formula from B.3 Gas laws, while part (c) critically invokes the first law of thermodynamics (ΔU = Q + W) from A.3 Work, energy and power to explain why motor work exceeds theoretical reversible work. The friction-dissipation mechanism fundamentally links mechanical work input to thermal energy, requiring both conceptual frameworks.

Planner output (stage 1)

Archetype: real-world device
Scenario: A gas-powered piston engine operates at constant temperature, compressing air from an initial volume of 500 cm³ at atmospheric pressure (101 kPa) to a final volume of 50 cm³. The piston moves at constant speed, and friction in the cylinder dissipates energy as heat. Students must apply the ideal gas law to find pressure changes, calculate work done on the gas, and evaluate how real-world energy losses affect the theoretical model's predictions.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State the ideal gas law in the form pV = nRT and define each symbol.
b(i)	3	AO2	Calculate the final pressure of the gas after isothermal compression from 500 cm³ to 50 cm³ at constant temperature.
b(ii)	3	AO2	Show that the work done on an ideal gas during isothermal compression is W = nRT ln(V₁/V₂), and calculate its numerical value for this process.
c	2	AO3	Suggest why the actual work input required by the piston exceeds the theoretical value calculated in part (b)(ii), referring to energy dissipation and the first law of thermodynamics.
d	2	AO3	Evaluate the assumption that the process remains isothermal. Discuss what happens to the gas temperature in practice and how this affects the validity of the ideal gas law model.

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