Generated ERQ

✓ passed A.1 Kinematics × B.3 Gas laws 12 marks HL 3 passes 121.08s $0.8080

``` ## ERQ · 12 marks · Topics: A.1 Kinematics + B.3 Gas laws · Archetype: theory_application **Integration:** primary=A.1 Kinematics, secondary=B.3 Gas laws (strength: supporting) **Stem.** A vertical, frictionless cylinder of internal cross-sectional area 4.50 × 10⁻⁴ m² is closed at the bottom and sealed at the top by a light piston of mass 0.180 kg that slides freely. Beneath the piston is trapped 2.40 × 10⁻³ mol of an ideal monatomic gas. Atmospheric pressure outside the cylinder is 1.013 × 10⁵ Pa. Initially the gas is in thermal and mechanical equilibrium with the surroundings at 295 K. A small electrical heater inside the gas is switched on at time t = 0 and delivers thermal energy at a constant rate, causing the piston to rise. A motion sensor records that the piston, starting from rest, reaches a steady upward speed of 6.85 × 10⁻³ m s⁻¹ after a brief acceleration phase lasting 0.40 s, and then continues at this speed for a further 7.60 s before the heater is switched off. Take g = 9.81 m s⁻². ### Part (a) Show that [2 marks] · AO2 · Topic: B.3 Gas laws Show that the pressure of the gas trapped beneath the piston during the heating, while the piston moves freely, is approximately 1.05 × 10⁵ Pa. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: A.1 Kinematics Using the kinematic data from the motion sensor, calculate the total vertical displacement of the piston from t = 0 until the heater is switched off at t = 8.00 s. Assume constant acceleration during the initial 0.40 s phase. ### Part (b)(ii) Determine [3 marks] · AO2 · Topic: A.1 Kinematics + B.3 Gas laws Determine the final temperature of the gas at the instant the heater is switched off. Take the initial volume of trapped gas to be 5.40 × 10⁻⁵ m³. ### Part (c) Explain [2 marks] · AO3 · Topic: A.1 Kinematics + B.3 Gas laws During the 7.60 s phase of constant piston velocity, the gas continues to receive thermal energy and to expand, yet the piston has zero acceleration. Explain how this is consistent with Newton's second law applied to the piston. ### Part (d) Discuss [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR A student claims: "Because the motion sensor records a brief acceleration phase, the gas process cannot truly be at constant pressure — the model used in (a) and (b)(ii) must be wrong." Discuss whether the isobaric (quasi-static) treatment of this process is appropriate. --- ## Mark Scheme ### Part (a) [2 marks] — Show that - M1: Force balance on piston in equilibrium (or constant velocity): P_gas · A = P_atm · A + m·g ⇒ P_gas = P_atm + mg/A [no ECF] - M2: Substitution P_gas = 1.013 × 10⁵ + (0.180 × 9.81)/(4.50 × 10⁻⁴) = 1.013 × 10⁵ + 3924 ≈ 1.052 × 10⁵ Pa [no ECF; Show-that target 1.052 × 10⁵ Pa given to 4 sf; student-derived 1.05 × 10⁵ Pa acceptable] ### Part (b)(i) [3 marks] — Calculate - M1: Displacement during acceleration phase: s₁ = ½ × v × t = ½ × 6.85 × 10⁻³ × 0.40 = 1.37 × 10⁻³ m (using ½(u+v)t with u=0) [no ECF] - M2: Displacement during constant-velocity phase: s₂ = v × t = 6.85 × 10⁻³ × 7.60 = 5.206 × 10⁻² m [no ECF] - M3: Total displacement s = s₁ + s₂ = 1.37 × 10⁻³ + 5.21 × 10⁻² = 5.34 × 10⁻² m (accept 5.3 × 10⁻² m to 5.4 × 10⁻² m) [ECF from M1, M2] ### Part (b)(ii) [3 marks] — Determine - M1: Volume change ΔV = A · s = 4.50 × 10⁻⁴ × 5.34 × 10⁻² = 2.40 × 10⁻⁵ m³; final volume V_f = 5.40 × 10⁻⁵ + 2.40 × 10⁻⁵ = 7.80 × 10⁻⁵ m³ [ECF from (b)(i)] - M2: Apply isobaric law V_i/T_i = V_f/T_f ⇒ T_f = T_i × (V_f/V_i) = 295 × (7.80 × 10⁻⁵ / 5.40 × 10⁻⁵) [use P = 1.05 × 10⁵ Pa from (a) as given Show-that value] - M3: T_f = 295 × 1.4444 ≈ 426 K (accept 420–430 K) [ECF from M1] ### Part (c) [2 marks] — Explain (causal chain per §4.4.1) - M1: During the constant-velocity phase the piston has zero acceleration, therefore by Newton's second law the net force on the piston is zero — the upward gas pressure force exactly balances atmospheric pressure force plus piston weight. - M2: Since the force balance fixes P_gas at the value found in (a), continued heating must increase T and V proportionally (isobaric expansion) which means the piston translates upward at constant velocity without requiring any net force — energy input goes into raising internal energy of the gas and doing work against (P_atm + mg/A), not into accelerating the piston. ### Part (d) [2 marks] — Discuss (paired competing perspectives per §4.4.1) - M1: Judgement in favour of the student: real pistons possess inertia; the observed finite displacement (~5.3 cm) achieved in finite time (8.0 s) cannot occur at truly infinitesimal velocity, so during the initial 0.40 s phase a non-zero net force (and hence pressure imbalance, P_gas ≠ P_atm + mg/A) must exist — strictly the process is not isobaric throughout. - M2: Judgement in favour of the model: the acceleration phase (0.40 s) is short compared with the dominant constant-velocity phase (7.60 s), during which the force balance holds and the pressure is fixed at 1.05 × 10⁵ Pa; the displacement contribution from the non-isobaric phase (~1.4 mm) is < 3% of the total, so the quasi-static isobaric treatment introduces negligible error and is justified for calculating T_f. ### Marker notes - Alternative method for (b)(i): treat as v_avg × t_total with appropriate averaging during acceleration phase; accept 5.3 × 10⁻² to 5.4 × 10⁻² m. - (b)(ii) ECF: candidates using their own (b)(i) displacement should obtain T_f via V_f/V_i ratio; award full marks if method correct. - (c) accept equivalent wording: "thermal energy input drives expansion at fixed pressure, so volume and temperature rise together while the piston drifts at terminal velocity." - (d) accept any genuine paired discussion contrasting realism (inertia/finite acceleration ⇒ pressure transient) against tractability (short transient phase ⇒ isobaric approximation valid for the bulk of the process). Do NOT award two marks for two statements that both support the same side. - Show-that target in (a): 1.052 × 10⁵ Pa given to 4 sf; student-derived 1.05 × 10⁵ Pa acceptable. Subsequent parts use 1.05 × 10⁵ Pa. ```

Critic verdicts

Iteration 0 — failed

ao_ladder fail

The cognitive ladder is broken. Parts (a), (b)(i), (b)(ii), and (c) are all AO2 (Calculate/Show that/Determine), violating the requirement that middle parts must progress through AO2/AO3 and that the final part must be AO3. Part (d) is correctly AO3 (Discuss), but without proper AO2→AO3 progression in the middle tiers, the scaffold fails.

FIX: Restructure as follows: (a) AO1/AO2 State/Define/Outline [2 marks] — define equilibrium condition for piston; (b) AO2 Calculate [3 marks] — find P_gas and L₂; (c) AO2 Calculate [2 marks] — find v_avg and a_avg; (d) AO3 Explain [3 marks] — explain why the constant-force model is unrealistic and discuss the quasi-static isobaric process instead. This creates a proper AO1/AO2 → AO2 → AO3 ladder within the 12-mark budget.
command_structure fail

Part (d) violates §4.4.1 AO3 Discuss structure. The mark scheme provides two perspectives (M1 supporting, M2 limiting), but M1 does NOT constitute a genuine second perspective—it merely restates the model's assumptions rather than presenting a contrasting viewpoint or trade-off. A valid Discuss structure requires at least two genuinely independent perspectives (e.g., 'the model is reasonable because X' vs. 'the model fails because Y'), not an assumption plus a critique. M2 correctly identifies physical limitations, but M1 lacks intellectual opposition.

FIX: Rewrite Part (d) M1 to present a genuinely alternative or competing perspective, such as: 'M1 (supporting perspective): the constant-force kinematic model is an acceptable simplification because the displacement (3.7 cm) is indeed small, the process is quasi-static so transient effects are negligible, and averaging obscures fine structure that is experimentally undetectable given measurement precision.' Then M2 remains the limiting critique. Alternatively, restructure to offer two trade-offs: e.g., M1 = 'mathematical tractability of constant-force model vs. physical realism' and M2 = 'quasi-static assumption masks actual isobaric dynamics.' Ensure the two bullets address genuinely separate considerations that an examiner must weigh.
cross_theme fail

Parts (a) and (b) are entirely segregated by topic: (a) uses only A.1 kinematics with a constant force, while (b)(i)–(b)(ii) use only B.3 gas laws (equilibrium pressure and isobaric expansion). Part (c) nominally combines both topics, but does so artificially by treating the gas-law result (new length) as input to a kinematic calculation without genuine physical integration—the constant-force model contradicts the actual isobaric process. Part (d) acknowledges this contradiction rather than resolving it, revealing that the two topics are never authentically blended in the solution method.

FIX: Restructure the question so that kinematics and gas laws are mutually dependent throughout. For example: (i) calculate the work done by the expanding gas during heating using the isobaric process and PV work; (ii) equate this work to kinetic energy and gravitational potential energy changes to derive the piston's motion profile; or (iii) derive the piston's acceleration directly from the pressure–volume–temperature dynamics, showing how the quasi-static heating rate constrains the instantaneous kinematic behaviour. This way, both topic letters (A and B) genuinely contribute to each step of the solution.
discriminator pass

Part (d) explicitly asks students to 'Discuss whether the kinematic treatment in part (c)…is a physically reasonable description of the actual motion.' This is a genuine model-critique question that requires evaluation of assumptions (constant net force, kinematic profiles) against the physical reality (quasi-static isobaric process, net force ≈ 0). The mark scheme confirms balanced discussion is expected.
rule_of_one pass

All parts comply with the mark–criterion matching requirement. Part (a) [2 marks] has 2 criteria (acceleration, speed); (b)(i) [2 marks] has 2 criteria (equilibrium condition, calculation); (b)(ii) [3 marks] has 3 criteria (isobaric law, substitution, answer); (c) [3 marks] has 3 criteria (displacement, average velocity, average acceleration); (d) [2 marks] has 2 criteria (supporting and limiting perspectives). No divergence exceeds 1.
topic pass

The ERQ authentically integrates both topics. Part (a) requires kinematic analysis (constant force, acceleration, kinematics equations); parts (b)(i)–(b)(ii) require gas law reasoning (equilibrium condition, isobaric process, ideal gas law). Critically, part (c) and especially part (d) demand genuine synthesis: students must connect the kinematic displacement from gas laws to kinematic quantities, then critically evaluate whether constant-force kinematics is physically appropriate for an isobaric heating process—a non-trivial conceptual bridge between A.1 and B.3.

Iteration 1 — failed

ao_ladder pass

The ERQ correctly follows the cognitive ladder: Part (a) is AO1 (State), parts (b) and (c) are AO2 (Show that/Determine), and part (d) is AO3 (Discuss). The progression from foundational definitions through calculation to critical evaluation meets IB criteria.
command_structure fail

Part (d) mark scheme fails §4.4.1 Discuss structure. While M1 and M2 present two perspectives, M3 does not constitute a genuine 'trade-off' or second competing perspective—it is merely a reconciliation/judgement that acknowledges the idealisation. A proper Discuss requires at least two substantive, competing viewpoints on the same question (e.g., 'the model is valid because...' vs. 'the model is problematic because...'), not a narrative that the perspectives are both correct under different assumptions. The current M3 sidesteps rather than discusses the genuine tension.

FIX: Restructure part (d) M3 to present an explicit competing perspective on *whether the quasi-static model is appropriate for this scenario*, rather than merely reconciling the two views. For example: M3 could be 'Judgement in favour of the student's claim: real pistons exhibit inertia; the finite 2.74 cm displacement in finite time 8.0 s *cannot* occur at truly infinitesimal velocity, so a non-zero net force (and acceleration) must exist during the real process, contrary to the idealised model's prediction.' Then add M4: 'Judgement in favour of the model: the quasi-static approximation is valid *provided* the displacement timescale is much longer than the inertial timescale (acceleration/deceleration phases); the dominant phase of the heating exhibits near-zero acceleration, justifying the isobaric treatment.' This presents a genuine trade-off (realism vs. tractability) and satisfies §4.4.1.
cross_theme pass

The ERQ genuinely integrates both A.1 (Kinematics) and B.3 (Gas laws) throughout. Kinematics appears in (a)–(d) via equilibrium forces, displacement, velocity, and acceleration; Gas laws appear in (a)–(d) via pressure equilibrium, ideal gas law, isobaric process, and volume–temperature relations. Part (d) explicitly reconciles kinematic and thermodynamic viewpoints, ensuring neither topic is filler.
discriminator pass

Part (d) explicitly asks the student to discuss whether the student's claim is consistent with the quasi-static isobaric model, requiring critique of the model's assumptions and limitations. The mark scheme confirms this is a genuine model-critique question with three marks for (i) kinematic perspective, (ii) thermodynamic perspective, and (iii) reconciliation via the quasi-static idealisation—exactly the dimension required.
rule_of_one pass

Each part's mark count matches the number of distinct award criteria. Part (a) [2 marks] has 2 bullets; (b) [3 marks] has 3 bullets; (c) [4 marks] splits as 2+2 with 2 bullets each; (d) [3 marks] has 3 bullets. All allocations align correctly with the arithmetic and logical structure.
topic pass

The ERQ genuinely integrates both A.1 Kinematics and B.3 Gas laws throughout. Part (a) requires the equilibrium condition (Newton's second law, kinematics) combined with gas pressure (gas laws). Part (b) uses the ideal gas law with the isobaric constraint from equilibrium. Part (c) applies the first law and kinematics (velocity, acceleration) to an isobaric process. Part (d) explicitly reconciles kinematic and thermodynamic viewpoints. Neither topic is superficial or merely nominal.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO2 with 'Show that' (command term appropriate for force-balance derivation). Parts (b)(i)–(b)(ii) are AO2 with 'Calculate'/'Determine' (procedural kinematics and gas-law application). Parts (c)–(d) are both AO3 with 'Explain'/'Discuss' (causal reasoning and competing perspectives). The progression from lower to higher order thinking is maintained throughout.
command_structure fail

Part (c) mark scheme fails the AO3 Explain structure requirement (§4.4.1): M1 and M2 together form a single causal chain (zero acceleration → zero net force → pressure fixed → isobaric expansion), not two independent explicit 'X therefore Y' marking points as required. The scheme should separate the causal logic into two distinct claims, each with its own warrant. Part (d) also has marginal clarity: while it nominally presents two perspectives, M1 and M2 read more like a single rebuttal sequence than two genuinely competing trade-offs with equal weight.

FIX: Part (c): restructure as M1: 'Zero acceleration during constant-velocity phase means net force = 0 (Newton's second law), therefore P_gas·A = P_atm·A + mg, so pressure remains constant at 1.05 × 10⁵ Pa.' M2: 'At constant pressure, continued thermal energy input increases T and V proportionally (ideal gas law at fixed P), therefore the piston rises at constant velocity with no acceleration needed — all energy goes into internal energy and boundary work, not kinetic energy.' Part (d): reframe M1 as 'Perspective supporting the student: the 0.40 s transient phase with measurable acceleration requires a pressure excess above equilibrium value; the process is strictly non-isobaric during this phase.' M2 as 'Perspective supporting the model: the transient phase contributes only ~1.4 mm (3% of total displacement); treating the dominant 7.60 s phase as isobaric is a justified quasi-static approximation with negligible impact on the calculated final temperature.' Ensure both perspectives carry equal explanatory weight.
cross_theme pass

The ERQ genuinely integrates A.1 Kinematics (primary, theme letter A) and B.3 Gas laws (secondary, theme letter B) throughout. Kinematics is used in parts (b)(i) and (c) to analyze piston motion; gas laws are used in parts (a) and (b)(ii) to determine pressure and final temperature via the isobaric relation. Part (b)(ii) is the critical synthesis point: the displacement from kinematics directly feeds into the volume calculation, which then uses the ideal gas law and isobaric process to find final temperature. Neither topic appears as name-check filler; both are essential to the solution.
discriminator pass

Part (d) explicitly asks the student to 'Discuss whether the isobaric (quasi-static) treatment of this process is appropriate,' which is a genuine model-critique task. The mark scheme requires a paired discussion of competing perspectives (realism vs. tractability), directly evaluating the validity and limitations of the constant-pressure model assumption used in earlier parts.
rule_of_one pass

All four parts have mark counts that align appropriately with their award criteria. Part (a) [2 marks] has 2 bullets (force balance + substitution); (b)(i) [3 marks] has 3 bullets (two displacement calculations + total); (b)(ii) [3 marks] has 3 bullets (volume change + isobaric relation + final temperature); (c) [2 marks] has 2 bullets (force balance reasoning + energy interpretation); (d) [2 marks] has 2 bullets (paired competing perspectives). No divergence exceeds 1.
topic pass

The ERQ genuinely integrates both A.1 Kinematics and B.3 Gas laws throughout. Part (a) requires gas law reasoning (force balance and ideal gas pressure); part (b)(i) is pure kinematics (displacement calculation); part (b)(ii) explicitly combines kinematic displacement with the ideal gas law (isobaric process); part (c) explains the kinematic observation (zero acceleration) using both Newton's second law and gas expansion principles; part (d) critically examines the validity of the isobaric model in light of the observed kinematic behaviour. Neither topic is superficial or merely nominally invoked—both are essential to solving the problem and understanding the physics.

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