75-Archetype SyllabusPhysics • ARCH-P-15 • Spec P4

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: P4 (Thermal physics)ASSUMED MATHS 1 PREREQUISITE: M3.4FREQUENCY: HIGH

Thermal Conduction Rod Scaling (Q̇ ∝ AΔT/L), Convection Density Currents & Radiative Power (P ∝ R^2 T^4)

Deconstructed from 13 past UAT-UK questions (5.58% of all historical Physics papers). Students using standard A-Level classroom methods spend an average of 135s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 35s (saving 100s per question).

Historical Frequency

13 Past Qs

5.58% of Physics

Classroom Trap Time

135s

+45s over 90s budget

Sub-90 Target Time

35s

Banks +100s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M3.4

Card 1 & Card 2 Preview: The Classroom Time Trap vs. Sub-90 2-Line Rule

Excerpted from our interactive 6-Step Topic Lesson for ARCH-P-15.

Launch All 6 Active-Recall Cards

CARD 1 OF 6 • THE CLASSROOM TIME TRAP (135s)

Why Students Bleed Time:

By Fourier's conduction law,

\dot{Q} = \frac{k A \Delta T}{L} = \frac{k (\pi d^2 / 4) \Delta T}{L}

. Taking ratios gives

\frac{\dot{Q}_2}{\dot{Q}_1} = \left(\frac{d_2}{d_1}\right)^2 \left(\frac{\Delta T_2}{\Delta T_1}\right) \left(\frac{L_1}{L_2}\right) = 2^2 \times 1 \times \frac{1}{2} = 2

. Thus

\dot{Q}_2 = 20 \times 2 = 40\text{ W}

(~120s).

In 13 past UAT-UK questions (5.58% of Physics), candidates lose 100s by doubling cylinder diameter quadruples cross-sectional area a, multiplying thermal conduction rate by 4. Instead, apply P4 with Maths 1 skill M3.4.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<35s)

**Line 1 (Conduction Scaling

\dot{Q} \propto d^2 \Delta T / L

):** Square the diameter factor (

2^2 = 4

) and invert the length factor (

1/2

Line 2 (Multiply):

\dot{Q}_2 = 20 \times \frac{4 \times 1}{2} = 40\text{ W}

(25s).

Sanity & Limit Check: Verify units/signs against factor_of_two_or_stoichiometry_trap (Scaling cylindrical rod conduction rate linearly with diameter d (×2) instead of cross-sectional area A = πd²/4 (×4)) and sign_or_direction_flip (Multiplying by rod length L instead of dividing by L in thermal conduction rate Q̇ ∝ A*(T₂ - T₁) / L).

Examiner Distractor Blueprint for ARCH-P-15

FOIL #1factor_of_two_or_stoichiometry_trap

Scaling cylindrical rod conduction rate linearly with diameter d (×2) instead of cross-sectional area A = πd²/4 (×4)

Doubling cylinder diameter quadruples cross-sectional area A, multiplying thermal conduction rate by 4.

Open Factor-of-2 / Stoichiometry Clinic

FOIL #2sign_or_direction_flip

Multiplying by rod length L instead of dividing by L in thermal conduction rate Q̇ ∝ A*(T₂ - T₁) / L

A longer bar has a smaller temperature gradient ΔT/L and therefore a lower rate of heat transfer.

Open Sign / Direction Flip Clinic

FOIL #3multi_statement_linchpin_foil

Claiming shiny/dull surface finish alters the rate of CONVECTION directly, or that individual air molecules expand when heated

Surface emissivity (dull black vs shiny) governs thermal RADIATION; convection depends on bulk fluid density decrease (molecules move further apart, molecules themselves do not expand).

Open Multi-Statement Linchpin Foil Clinic

FOIL #4fence_post_or_domain_trap

Raising temperature factor to power 2 instead of power 4 in Stefan-Boltzmann radiative power P = k * R² * T⁴

Halving surface temperature T reduces radiative power by 2⁴ = 16.

Open Fence-Post / Domain Trap Clinic

Try 1 Live Sample Question Under the 90-Second Stopwatch

Press W to open the 2-line dry-wipe scratchpad, select A–E, and lock in to reveal the Dual-View solution.

Full 6-Card Lesson Launch All 15 Questions (ARCH-P-15)

ARCH-P-15: Thermal Conduction Rod Scaling (Q̇ ∝ AΔT/L), Convection Density Currents & Radiative Power (P ∝ R^2 T^4) (Sample)Physics

00:00.0

SUB-90 ZONE (<35S)

0.0s35s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-P-15 (6-Card Lesson)Format: Standard 5-Option

Right-click any option to cross out • Keys A–E + Enter

Question 1 of 1 • 90s Target

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The question stem, diagram, and answer options are hidden behind this pre-start gate. When you click below, the question will reveal and your 90-second split stopwatch will immediately begin ticking.

Physics•ARCH-P-15•Standard 5-Option

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