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, the relative order of magnitudes of the expansion of solids, liquids and gases as their temperatures rise.

Key Concepts

• All matter expands when heated because its particles gain kinetic energy.
• The amount of expansion depends on how freely the particles can move apart.
• Solids, liquids and gases have different particle arrangements, leading to different expansion behaviours.

Particle‑Level Explanation

Solids

In a solid the particles are packed closely in a regular lattice and vibrate about fixed equilibrium positions. When temperature increases, the amplitude of these vibrations increases, pushing neighbouring particles slightly further apart. Because the particles are already tightly bound, the increase in average separation is small.

Liquids

Liquid particles are still close together but are not in a fixed lattice; they can slide past one another. Heating increases the kinetic energy, causing the particles to move more vigorously and to overcome some of the intermolecular attractions. The average distance between particles therefore increases more than in a solid, but less than in a gas.

Gases

Gas particles are far apart and interact only through occasional collisions. Their kinetic energy is directly related to temperature. When heated, the particles move faster and, because there is little attractive force holding them together, the average separation increases dramatically. This leads to the greatest expansion among the three states of matter.

Comparative Summary

Why the Order of Magnitude Differs

1. Inter‑particle forces: Strong in solids (ionic, metallic, covalent bonds) → limited separation change.
2. Freedom to move: Liquids have weaker van der Waals forces, allowing greater separation when kinetic energy rises.
3. Density of particles: Gases have low density; a small increase in kinetic energy leads to a large increase in average separation.
4. Equation of state: For an ideal gas, \$pV = nRT\$ gives \$V \propto T\$ at constant pressure, showing a direct proportionality between temperature and volume.

Practical Implications

• Metal bridges and railway tracks (solids) require expansion joints to accommodate small but predictable length changes.
• Thermometers use liquids (e.g., mercury) because their expansion is larger than solids but still linear over a useful range.
• Hot‑air balloons rise because heated air (gas) expands, decreasing its density relative to the surrounding cooler air.

Key Take‑away

The magnitude of thermal expansion follows the order gas > liquid > solid because the particles in gases are the least constrained, allowing the greatest increase in average separation when temperature rises. This behaviour is rooted in the fundamental differences in particle motion and arrangement for each state of matter.