Thermal expansion

Most materials expand when they are heated and contract when they cool, because their particles vibrate more and move slightly further apart. Engineers leave gaps in railways and bridges for this, and thermometers and thermostats rely on it.

Key facts

  • Heating makes particles vibrate more and take up more space; the particles themselves do not grow.
  • Mass stays the same when something expands, so its density decreases.
  • Linear expansion: ΔL = αLΔT (α = linear expansivity, per °C).
  • Volume expansion: ΔV = βVΔT; liquids expand more than solids.
  • A bimetallic strip bends when heated: the metal that expands more ends up on the outside of the curve.
  • Water is unusual: it is densest at 4°C and expands when it freezes, so ice floats.

Worked examples

Example 1

Why are gaps left between sections of railway track?

  1. In hot weather the steel rails get longer.
  2. The gap closes up instead of the rails pushing each other and buckling.

Answer: to allow the steel to expand in hot weather without buckling

Example 2

A 30 m steel rail (α = 12 × 10⁻⁶ /°C) warms by 40°C. By how much does it expand?

  1. Each metre grows by α for each degree. Multiply by the length and the temperature rise. ΔL = 12 × 10^−6 × 30 × 40 = 0.0144 m
  2. Change to millimetres. 0.0144 m = 14.4 mm

Answer: 14.4 mm

Example 3

A steel ring of diameter 50.00 mm must fit over a 50.06 mm shaft. By how much must it be heated? (α = 12 × 10⁻⁶ /°C)

  1. Heating makes the hole bigger, just as if the ring were solid metal.
  2. Use ΔL = αLΔT with the diameter as the length. ΔT = 0.06 ÷ (12 × 10^−6 × 50) = 100°C

Answer: 100°C