Thermal expansion is one of the phenomenons that shows temperature and atomic structure are related to each other. For example, in a crystalline solid, atoms are seperated from each other by chemical bonds that vibreate about their equilibrium positions, and when temperature goes up, these vibrations becomes more energetic so that departures from the equilibrium positions become more pronounced. And these motions mean that each atom will need more space for its motion. As a result, the size of the whole crystalline solid increases. The tendency for a heated object to expand is expressed in terms of coefficient of linear expansion. It relates the length L of a material at centain temperature to its length L' at another temperature. In formula it is written as:

L'=L(1+αΔT)

ΔT refers to temperature change, and α is the coefficient of thermal expansion, a number that varies from material to material.

The formula is also equivalent to:

(L'-L)/L=αΔT