2.2.1 Thermal Expansion of Solids, Liquids and Gases
Learning objective
Explain, in terms of the motion and arrangement of particles, why the magnitude of thermal expansion follows the order gas > liquid > solid when the temperature of a material is increased at constant external pressure. Include everyday examples and the basic quantitative relationships required by the Cambridge IGCSE/A‑Level syllabus.
Key ideas (syllabus requirements)
- All matter expands on heating because its particles gain kinetic energy.
- The amount of expansion depends on how freely the particles can move apart and on the strength of the inter‑particle forces.
- Solids, liquids and gases have distinct particle arrangements, giving very different expansion coefficients.
- All descriptions assume the pressure of the surroundings remains unchanged (the condition stated in the syllabus).
Particle‑level description of each state
| State | Particle arrangement & forces | Effect of heating (constant p) | Typical expansion coefficient
(order of magnitude) | Everyday example |
|---|
| Solid | - Particles fixed in a regular lattice.
- Strong ionic, metallic or covalent bonds keep neighbours at a well‑defined equilibrium distance.
- Each particle vibrates about its lattice point.
| - Temperature rise → higher kinetic energy → larger vibrational amplitude.
- Because the bonds are stiff, the average separation increases only slightly.
- Result: a small linear increase in dimensions.
| α ≈ 10⁻⁵ K⁻¹ (linear) | - Railway tracks expanding in summer → need expansion joints.
- Bimetallic strips in thermostats.
|
| Liquid | - Particles are close‑packed but not in a fixed lattice; they can slide past one another.
- Inter‑molecular forces are weaker (van der Waals, hydrogen bonding).
- No long‑range order.
| - Extra kinetic energy lets particles overcome part of the attractive forces.
- Average intermolecular distance increases more than in a solid.
- Volume therefore expands noticeably, though the particles remain relatively close.
| β ≈ 10⁻⁴ K⁻¹ (volumetric) | - Hot‑water tank level rises in summer.
- Thermometer liquid (e.g., mercury) rising in a glass tube.
- Water’s anomalous expansion near 4 °C (used in lake‑ice formation).
|
| Gas | - Particles are far apart; interactions occur only during brief collisions.
- Negligible attractive forces under ordinary conditions.
- Behaviour well described by the ideal‑gas model.
| - Higher temperature → faster particle speeds.
- Because there is essentially no “bond” holding them together, the average separation grows dramatically.
- At constant external pressure the gas expands until the pressure of the gas again equals the external pressure.
| β ≈ 10⁻³ K⁻¹ (volumetric) – for an ideal gas β = 1/T | - Balloon inflates when heated.
- Tyre pressure rises on a hot day.
- Hot‑air balloons rise because the heated air expands and becomes less dense.
|
Why the order of magnitude differs – linking back to particle behaviour
- Strength of inter‑particle forces – Strong bonds in solids give a very small change in average separation (Δr), hence a tiny linear coefficient α.
- Freedom of movement – Liquids have weaker forces; particles can move a little farther apart when kinetic energy rises, giving a moderate volumetric coefficient β.
- Particle density – Gases are very low‑density; a modest increase in kinetic energy produces a large increase in average spacing, so the volumetric coefficient is an order of magnitude larger than for liquids.
- Equation of state – For an ideal gas, pV = nRT. At constant pressure, V/T = constant, so ΔV/V = ΔT/T. This linear relationship makes the expansion of gases appear much larger on the same temperature interval.
Quantitative relationships (useful for revision)
- Solids (linear expansion)