Explain relative expansion through particle motion and arrangement
Compare the usual solid, liquid and gas expansion order under matched conditions.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Describe particle arrangement and motion in all three states.
- Describe free thermal expansion at constant pressure.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which samples make the intended relative-volume comparison?
What you will learn
- Explain the usual qualitative order: solids least, liquids more, gases most.
- Keep particle size distinct from average separation and retain comparison controls.
Match the comparison before ranking it
The usual qualitative comparison is solids expanding least, liquids more and gases most for comparable starting volumes and temperature increases at constant pressure, without a state change. This refers to relative volume changes under matching conditions, not a ranking of unrelated total lengths. A long solid bar and a tiny gas sample cannot be compared by raw length and volume numbers as if they were the same quantity.
This is the syllabus's broad particle-model comparison, not a numerical coefficient for every substance or temperature range. The diagram uses qualitative rank words rather than calibrated percentage bars. To calculate actual expansion, a problem would need additional material data and conditions; the selected requirement does not ask for an expansion-coefficient formula.
Explain motion and arrangement together
In the usual solid examples, increased vibration together with particle interactions permits a small increase in mean separation while relative positions are retained. Close liquid particles move more energetically and can rearrange, giving a larger usual change in occupied volume. The particles themselves do not need to become larger: expansion concerns the sample's arrangement and average separation.
Gas particles are widely separated. At constant pressure with room to expand, faster average motion is accompanied by increased accessible volume and separation, rather than the fixed-volume pressure rise. The usual gas expansion is greatest in this matched qualitative comparison. A rigid gas vessel instead prevents volume change, so it does not test the constant-pressure free-expansion ranking.
Sources for this lesson
Pause and explain
Why does a rigid heated gas not test the stated free-expansion ranking?
Worked example
Compare equal initial volumes of solid, liquid and gas for the same temperature rise at constant pressure in the usual qualitative model. Explain whether individual particles grow.
Show the worked solution
- Use matched starting volumes, temperature changes and pressure conditions.
- The usual relative expansion order is solid least, liquid more and gas most.
- Changes in motion, arrangement and average separation explain it; particle growth is unnecessary.
Answer Usual order: solid least, liquid more, gas most; particles do not need to grow.
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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.
Give the usual relative expansion order for matched solid, liquid and gas volumes at equal temperature rise and constant pressure.
Give me a hint
State the controls before the qualitative order.
Compare my reasoning
- Initial volumes and temperature changes match.
- Samples can respond at constant pressure without a phase change.
- The usual qualitative order is solid least, liquid more, gas most.
Solid least; liquid more; gas most under the stated matched conditions.
Look for these in your work
- Include the conditions.
- Use a qualitative order rather than invented coefficients.
Explain the usual order using particle motion, separation and arrangement; state whether particles themselves must grow.
Give me a hint
Use close interactions for solids and liquids and the available-space response for gas.
Compare my reasoning
- Solid particles vibrate near retained relative positions with a small usual mean-separation increase.
- Liquid particles are close but can rearrange, while gas particles are widely separated and can occupy more space at constant pressure.
- Changed motion and separation account for expansion without enlarged individual particles.
The different arrangements and permitted separation changes explain the usual order; particle growth is unnecessary.
Look for these in your work
- Connect all three states.
- Keep gas pressure conditions explicit.
A large solid bar lengthens 2 mm while a small gas sample expands by 1 cm³. A student calls this proof that solids expand more than gases. Evaluate it.
Give me a hint
The numbers have different dimensions and the sample conditions are unmatched.
Compare my reasoning
- A length change and a volume change are not directly comparable magnitudes.
- Initial sample amounts, temperature rises and pressure controls are not matched.
- The result does not test the stated relative-volume comparison or overturn it.
The unmatched length and volume changes do not establish the relative expansion ranking.
Look for these in your work
- Compare like quantities.
- Identify missing controls.
Common mistakes
- Match starting volume and temperature rise.
- Compare like quantities, not solid length against gas volume.
- A rigid gas sample is not a free constant-pressure comparison.
What can you explain now?
What microscopic change should not be used as the explanation of thermal expansion?
Compare with the explanation
Growth of the individual particles.
The model concerns motion, arrangement and average separation instead.
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Make it stick
Explain the usual matched expansion order using particles and recognise constraints or incomparable measurements.
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.