Check pressure-volume data and model conditions
Compare supplied products and judge consistency without claiming proof of hidden controls.
Section P2.1.3 · Gases and the absolute scale of temperature
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Calculate pV with absolute pressure and common units.
- Identify what a supplied tolerance or uncertainty does and does not mean.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 3% of 12 000?
What you will learn
- Use pV products to check supplied states against a constant-product model.
- Distinguish numerical consistency from proof of fixed mass, temperature or experimental quality.
Calculate the product for each supplied row
An illustrative table lists A: 120 kPa and 100 cm³; B: 200 kPa and 60 cm³; C: 150 kPa and 85 cm³. Their products are 12 000, 12 000 and 12 750 kPa cm³. A and B match the proposed 12 000 product exactly; C is 750 above it, or 6.25% of the reference. These are supplied teaching values, not measurements recorded by this website.
If a question explicitly allows products within ±3% of 12 000, its acceptance interval is 11 640 to 12 360 kPa cm³. Row C is outside that supplied interval. Without a stated tolerance or measurement uncertainty, do not invent an experimental confidence claim or call every small numerical difference a proven temperature change.
A consistency check is not proof of every condition
Matching pV values are consistent with a fixed-mass, constant-temperature gas model, but they do not independently prove that mass and temperature were controlled. Evidence about apparatus, leaks and temperature is separate. A failed product check indicates a mismatch with the stated model and tolerance; it does not uniquely identify which measurement or control caused it.
Use positive absolute pressures and volumes before testing the product. Mixing gauge and absolute readings or incompatible units can create an artificial disagreement. First check the data's meanings, then calculate products and compare with the supplied acceptance rule. Written analysis of a table does not establish supervised practical competence.
Sources for this lesson
Pause and explain
A row's product is 12 750 against 12 000 ±3%. What conclusion is justified?
Worked example
Check A = 120 kPa × 100 cm³, B = 200 kPa × 60 cm³ and C = 150 kPa × 85 cm³ against 12 000 kPa cm³ with a supplied ±3% product tolerance.
Show the worked solution
- The products are 12 000, 12 000 and 12 750 kPa cm³.
- The tolerance is ±360, giving 11 640 to 12 360 kPa cm³.
- A and B pass this numerical check; C fails it, without proving a unique cause.
Answer A and B are within tolerance; C is outside at 12 750 kPa cm³.
Try a topic test
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Check the three supplied rows A: 120 × 100, B: 200 × 60 and C: 150 × 85 in common kPa and cm³ units against 12 000 ±3%.
Give me a hint
Calculate products and the explicitly supplied acceptance interval.
Compare my reasoning
- Products are 12 000, 12 000 and 12 750 kPa cm³.
- The interval is 12 000 ±360, or 11 640 to 12 360.
- A and B fit it; C does not.
A and B pass the supplied product check; C fails.
Look for these in your work
- Calculate all rows.
- Use the stated tolerance.
A table lists products 11 800, 12 200 and 12 400 kPa cm³. Which fit 12 000 ±3%, and what is the percentage excess of the last row over the reference?
Give me a hint
Apply the same interval and divide the excess by the reference.
Compare my reasoning
- The accepted interval remains 11 640 to 12 360.
- 11 800 and 12 200 fit; 12 400 does not.
- The excess is 400/12 000 × 100 ≈ 3.33%.
11 800 and 12 200 fit; 12 400 is outside at about 3.33% excess.
Look for these in your work
- Compare with both interval boundaries.
- Use the reference denominator.
Two rows have equal pV products, but no evidence of temperature control or constant gas mass is supplied. May the table prove both controls were maintained? Explain.
Give me a hint
Separate a numerical invariant from independent evidence of experimental conditions.
Compare my reasoning
- Equal products are consistent with the proposed model.
- The table does not independently establish fixed mass or temperature.
- Check the controls separately rather than claiming experimental proof from the product alone.
No; equal products show numerical consistency, not independent proof of both controls.
Look for these in your work
- Distinguish consistency and proof.
- Name the missing control evidence.
Common mistakes
- Use the supplied tolerance rather than inventing one.
- Matching products do not prove hidden controls.
- A failed model check does not uniquely identify a fault.
What can you explain now?
Does matching pV alone prove both constant mass and temperature?
Compare with the explanation
No.
It supports numerical consistency; independent evidence is needed for the controls.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Check products and stated tolerance, then separate numerical agreement from evidence of conditions and practical competence.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.