Thermal expansion

Thermal expansion can be three types:

Linear expansion

$$\alpha_l = \frac{1}{\Delta T} \frac{\Delta l}{l}$$

Area expansion

$$\alpha_a = \frac{1}{\Delta T} \frac{\Delta A}{A}$$

Volume expansion

$$\alpha_v = \frac{1}{\Delta T} \frac{\Delta V}{V}$$