Expansio

Meet Expansio, a steel rail who grows a little every time the sun warms her.

Heat a solid and its atoms vibrate more strongly, pushing slightly farther apart on average. The material grows. For modest temperature changes, the change in length is proportional to both the original length and the temperature change: ΔL = αLΔT, where α is the material's linear expansion coefficient.

For steel, α is about 12×10⁻⁶ per kelvin. A 100 m steel bridge warming by 30 K grows by about 12×10⁻⁶ × 100 × 30 ≈ 0.036 m, or 3.6 centimetres. That is why bridges have expansion joints and why long pipelines include loops.

Thermostats use bimetallic strips: two metals with different α bonded together bend as they warm. Glass that cracks when hot water is poured into it fails because one part expands faster than another.

α itself varies with temperature, so the formula is an approximation over modest ranges. Water is a famous exception: between 0 °C and 4 °C it contracts as it warms.