Explain, in terms of the motion and arrangement of particles, the relative order of magnitudes of the expansion of solids, liquids and gases as their temperatures rise

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

StateParticle arrangement & forcesEffect 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

  1. Strength of inter‑particle forces – Strong bonds in solids give a very small change in average separation (Δr), hence a tiny linear coefficient α.

  2. Freedom of movement – Liquids have weaker forces; particles can move a little farther apart when kinetic energy rises, giving a moderate volumetric coefficient β.

  3. 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.

  4. 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)