Summarizing Thermal Expansion of Solids and Liquids

Summary

• Thermal expansion is the increase, or decrease, of the size (length, area, or volume) of a body due to a change in temperature.
• Thermal expansion is large for gases, and relatively small, but not negligible, for liquids and solids.
• Linear thermal expansion is

  \(\text{Δ}L=\mathrm{\alpha L}\text{Δ}T,\)

  where \(\text{Δ}L\) is the change in length \(L\), \(\text{Δ}T\) is the change in temperature, and \(\alpha \) is the coefficient of linear expansion, which varies slightly with temperature.
• The change in area due to thermal expansion is

  \(\text{Δ}A=2\mathrm{\alpha A}\text{Δ}T,\)

  where \(\text{Δ}A\) is the change in area.
• The change in volume due to thermal expansion is

  \(\text{Δ}V=\mathrm{\beta V}\text{Δ}T,\)

  where \(\beta \) is the coefficient of volume expansion and \(\beta \approx 3\alpha \). Thermal stress is created when thermal expansion is constrained.

Glossary

thermal expansion

the change in size or volume of an object with change in temperature

coefficient of linear expansion

\(\alpha \), the change in length, per unit length, per \(1\text{º}\text{C}\) change in temperature; a constant used in the calculation of linear expansion; the coefficient of linear expansion depends on the material and to some degree on the temperature of the material

coefficient of volume expansion

\(\beta \), the change in volume, per unit volume, per \(1\text{º}\text{C}\) change in temperature

thermal stress

stress caused by thermal expansion or contraction