Challenge agreement between two energy measurements before defending a capstone

Select the evidence

Two methods agreeing is useful evidence, but it does not prove that either is correctly calibrated. The original packet compares energy inferred from capacitor voltage with energy inferred from a temperature rise. The hidden generator uses C=0.020 F and heat capacity H=0.10 J/K, with all stored capacitor energy entering that heat capacity. Hidden truth is disclosed to teach an inference failure; it is not an independent measurement available in a real investigation.

Derive the relation

Let a be a multiplicative voltmeter scale and b a multiplicative temperature-rise scale. The electrical estimate is C(aV)²/2=a²Etrue. The thermal estimate is H(bΔT)=bEtrue. Their ratio is a²/b. A perfect ratio of one establishes b=a² within this model, not a=b=1. Taking more voltages improves the visible trend but leaves that same ambiguity because every row shares the same scale errors.

Work the contrast

With a=1.1 and b=1.2, the ratio is about 1.00833: agreement looks close although voltage is 10% high and temperature rise 20% high. Exact agreement in the continuous formula would occur at b=1.21, which is not on this control grid. The display does not claim its near-equal estimates are exactly equal. At true 8 V, generator energy 0.64 J is inferred as 0.7744 J electrically and 0.768 J thermally.

Challenge the inference

An independent voltage standard, independent thermometer calibration, or a justified additional observation can discriminate. Recomputing both methods from the same generator is not independent evidence. A temperature offset, heat leak, uncertain capacitance or changing heat capacity adds new hypotheses not covered by these two scale controls. Report that limitation rather than treating a precise ratio as proof of a unique cause.

Prepare independent review

The final course capstone requires the same discipline across all seven AP2 units: prior predictions, declared systems and references, raw evidence, signed calculations, competing explanations and changed-case tests. Preserve the first report, a criterion-specific human critique, one revision and a genuinely new frozen assignment with response. Public worked answers and a named reviewer are not authentication of independence. Actual supervised laboratory work remains a separate evidential requirement.

Worked original case

At voltage scale 1.1 and temperature-rise scale 1.2, every row has electrical/thermal ratio 1.21/1.2≈1.00833. For true 8 V, values 0.7744 and 0.768 J differ by only 0.0064 J, while both exceed generator 0.64 J substantially.

Prediction and retained investigation

Can five agreeing energy comparisons share the same calibration error? Compare scales 1,1; 1.1,1.2; and 0.8,0.8. Predict the whole-table ratio before reading. Retain the first explanation, then propose an external calibration or new controlled observation that separates at least two hypotheses without using the disclosed generator truth as evidence.

Changed-case practice

A separate packet has voltage scale 0.9 and temperature-rise scale 0.81. Find the inferred-energy ratio and both estimates when true energy is 2 J. Explain what the agreement establishes.

Check after your attempt

Ratio 0.9²/0.81=1. Both estimates are 1.62 J, 19% below 2 J. Agreement is consistent with the shared scale relation, not a demonstration of accuracy or independent calibration.

Retain course-wide evidence

Use the AP Physics 2 course evidence workspace for the seven-unit synthesis responses and cumulative project for the first report, critique, revision and frozen fresh assignment. These are retained records, not automated mastery judgments.

What makes a changed assignment genuinely new rather than the same public problem with a different title?

Sources and safety

Original supplied cases checked 30 October 2026 against current AP2 scope, OpenStax capacitor energy and first-law processes. Entirely virtual; no electrical, thermal, pressure, light or radiation apparatus is requested. No simulated result substitutes for supervised measurement technique or independent learner evidence.