Thermal expansion

Thermal expansion is a change in the size or volume of a system caused by a change in temperature. In many materials, heating increases the average separation between atoms or molecules. In solids, this can be understood from the asymmetry of the interatomic potential: as atomic vibrations become more energetic, the average spacing between neighboring atoms tends to increase. The magnitude of this response varies among materials because their bonding and structure differ. Most materials expand when heated under ordinary conditions, but this is not universal; water, for example, has an unusual density maximum near 4 °C at atmospheric pressure.

For a small temperature interval and a material whose coefficient is approximately constant, linear expansion is described by ΔL ≈ αL₀ΔT. Here L₀ is the initial length, ΔL the length change, ΔT the temperature change, and α the coefficient of linear expansion. The coefficient represents fractional length change per unit temperature interval and is commonly expressed in K⁻¹ or °C⁻¹; the numerical values are the same because a temperature interval of one kelvin equals one degree Celsius. For volume change, ΔV ≈ βV₀ΔT, where V₀ is the initial volume and β the coefficient of volume expansion. For an isotropic solid and sufficiently small changes, β is approximately three times α. These simple forms are approximations; coefficients may vary with temperature, and some crystals expand differently in different directions.

Solids can change length, area and volume when heated, while a liquid’s linear dimensions depend on its container, so liquids are generally described by volume expansion. Gases also change volume with temperature, but their behavior depends on pressure and other constraints. In solids that are free to expand, temperature changes usually alter size without changing shape if the material is isotropic. If expansion or contraction is constrained, thermal stresses can develop; in sufficiently severe cases these stresses may damage a component.

Expansion joints in bridges and railway tracks provide space for components to change length as temperatures vary. A bimetallic strip bends when its bonded layers expand by different amounts, a principle used in some temperature-sensitive switches and thermostats. The design of concrete and steel structures, precision instruments, electronic devices and other assemblies must account for thermal expansion to reduce unwanted deformation or stress. Measurement of expansion coefficients is also useful for selecting materials that will remain compatible as temperatures change.