# Thermal Expansion

When heat is added to most materials, the average amplitude of the atoms' vibrating within the material increases. This, in turn, increases the separation between the atoms causing the material to expand. If the material does not go through a phase change, the expansion can be easily related to the temperature change. The linear coefficient of thermal expansion (α) describes the relative change in length of a material per degree temperature change. As shown in the following equation, a is the ratio of change in length (Δl) to the total starting length (li) and change in temperature (ΔT).

$\alpha=\frac{\Delta l}{l_{i}\Delta T}$

By rearranging this equation, it can be seen that if the linear coefficient of thermal expansion is known, the change in components length can be calculated for each degree of temperature change. This effect also works in reverse. That is to say, if energy is removed from a material then the object's temperature will decrease causing the object to contract.

Thermal expansion (and contraction) must be taken into account when designing products with close tolerance fits as these tolerances will change as temperature changes if the materials used in the design have different coefficients of thermal expansion. It should also be understood that thermal expansion can cause significant stress in a component if the design does not allow for expansion and contraction of components. The phenomena of thermal expansion can be challenging when designing bridges, buildings, aircraft and spacecraft, but it can be put to beneficial uses. For example, thermostats and other heat-sensitive sensors make use of the property of linear expansion.

## Linear Coefficient of Thermal Expansion for a Few Common Materials

 Material $\alpha$ (m/m/oK) $\alpha$ (mm/m/oK) Aluminum 23.8 x 10-6 0.0238 Concrete 12.0 x 10 -6 0.011 Copper 17.6 x 10 -6 0.0176 Brass 18.5 x 10 -6 0.0185 Steel 12.0 x 10 -6 0.0115 Timber 40.0 x 10 -6 0.04 Quartz Glass 0.5 x 10 -6 0.0005 Polymeric Materials 40-200 x 10 -6 0.040-0.200 Acrylic 75.0 x 10 -6 0.075