Thermal Expansion

Finds the expansion as the coefficient of linear expansion × the original length × the temperature change. Enter the coefficient in units of 10⁻⁶/K: about 12 for steel and 23 for aluminium.

Explanation

Things grow when they are heated. How much they grow is proportional both to their original length and to the change in temperature.

\Delta L = \alpha L \Delta T

The coefficient $\alpha$ says what fraction of its length a material gains per kelvin. The numbers are tiny, so they are quoted in units of $10^{-6}$ /K.

Common coefficients (×10⁻⁶/K)

Steel — 12
Concrete — about 12
Aluminium — 23
Glass — 9
Invar alloy — around 1

Example

A 100 m rail warms by 30 K.

\Delta L = 12 \times 10^{-6} \times 100 \times 30 = 0.036\ \text{m} = 36\ \text{mm}

Nearly four centimetres. The gaps between rail sections exist to swallow exactly this. Without them the rail has nowhere to go and buckles sideways.

A 634 m tower moves $12 \times 10^{-6} \times 634 \times 40 = 0.30$ m over a 40 K swing: it stands a foot taller in summer than in winter.

Why reinforced concrete works at all

Steel and concrete have almost the same coefficient, both around 12.

That is a coincidence, but a decisive one. Were the values far apart, every change of temperature would shear the steel against the concrete and prise them apart. Modern construction rests on the fact that the two expand at the same rate.

Watch out

Since $\Delta T$ is a *difference*, it is the same number in Celsius or in kelvin. This is one place where you do not need absolute temperature.