Heat a solid and it grows. The atoms vibrate harder, and because the bond potential is not symmetric, their average separation increases. Over ordinary temperature ranges the effect is very close to linear.
α is the coefficient of linear expansion, in units of 1/K, usually quoted as micrometres per metre per kelvin. Steel’s 12 µm/m·K means a 1 metre steel bar grows 12 micrometres for each degree.
Area and volume
A plate expands in two directions and a solid in three, and to good approximation the coefficients simply multiply: area expansion is 2α and volume expansion is 3α. So the volume of an aluminium block grows about 0.007% per degree — small, but a 10,000 litre tank of fluid warming 20 degrees is a real overflow problem.
A hole in a plate expands too, and it expands as though it were made of the same material. This surprises people, but it follows from everything scaling uniformly. It is why heating a metal lid loosens it from a jar.
Coefficients
| Material | α (µm/m·K) |
|---|---|
| PVC | 70 |
| Lead | 29 |
| Aluminium | 23 |
| Copper | 17 |
| Steel | 12 |
| Concrete | 10.8 |
| Common glass | 9 |
| Borosilicate glass | 0.5 |
Concrete and steel sit close together at 10.8 and 12, which is the quiet reason reinforced concrete works at all. If the two expanded at noticeably different rates, every temperature swing would crack the concrete away from its rebar.
Consequences worth knowing
- Expansion joints. Bridges and rail track need gaps. A 100 m steel span moving through 50 °C changes length by 60 mm — enough to buckle track that has nowhere to go.
- Thermal shock. Pour boiling water into ordinary glass and the inside expands before the outside, and it cracks. Borosilicate barely expands at all, which is why laboratory glassware is made from it.
- Bimetallic strips. Bond two metals with different α and the strip curls when heated. This was the basis of mechanical thermostats for a century.
- Shrink fitting. Cool a shaft, warm the collar, assemble, let them equalise. The resulting interference fit needs no fasteners.
Where the model breaks
α itself varies with temperature, so this linear model degrades over wide ranges. Water is the famous anomaly: between 0 and 4 °C it contracts as it warms, which is why ice floats and lakes freeze from the top down. And near a phase change all bets are off — the volume jump on freezing or melting dwarfs ordinary thermal expansion.