# Thermal Expansion

Thermal expansion is the change in specific volume of a material as it is heated. The linear coefficient of thermal expansion (a with units of inverse temperature) can be expressed as the change in length of an object, normalized by its original length, for a given temperature change (3): (3)

where AL is the change in length for a given temperature change (m), L is the original length (m), and AT is the change in temperature (K).

In general, all materials have a positive thermal expansion coefficient; that is they increase in volume when heated. Thermal expansion results from thermal excitation of the atoms that compose the material . At absolute zero, atoms are at rest at their equilibrium positions (i. e., at r0 in Fig. 1). As they are heated, thermal energy causes the atoms to vibrate around their equilibrium positions. The amplitude of vibration increases as heating is continued. Asymmetry in the shape of the potential well causes the average interatomic distance to increase as temperature increases, leading to an overall increase in volume .

The importance of considering thermal expansion cannot be underestimated. Ignoring thermal expansion or incorrectly accounting for thermal dilations can have serious consequences. Consider a vessel that is ~3 m (~10 ft) in diameter insulated with a zirconia refractory. Assuming a linear coefficient of thermal expansion of 13 ppm K-1, heating the lining from room temperature to 1600°C the inside surface of the lining would grow by about 5 cm (~2 in.). To compensate for expansion in large systems, it is common to leave expansion joints spaced at regular intervals. When temperature is increased, the refractory material will shift into the open space preventing potential problems.