# Thermal expansion

A2

As materials get hotter the particles oscillate (vibrate) more, so the average distance between them increases. This means that the material expands.

University

In 2D, the expansion is linear, and is given by the equation:

ΔL is the change in length, L0 is the original length, ΔT is the change in temperature, in Kelvin, K, and α is the coefficient of linear expansion, in K-1 (or the inverse of whichever temperature unit is used).

In 3D, the expansion is given by the equation:

ΔV is the change in length, V0 is the original length, ΔT is the change in temperature, in Kelvin, K, and β is the coefficient of volume expansion, in K-1 (or the inverse of whichever temperature unit is used).

We can work out how β is related to α using:

for a cube.

We can also use the chain rule, which says:

So we get:

because:

We know dL already from the equation for linear expansion, so we substitute it in, and equate what we get with the equation we already have for volume expansion:

This means:

Thermal stress is created when a material is held in position.

where F is force and A is area. For more about this, visit stress and strain.

Young’s modulus gives us:

For gases expanding freely:

(since W = pV, substitute p using the ideal gas equation)