So far we have seen expansion of objects only in one direction. Practically, this method is applicable for objects whose width and thickness of the object are very small compared to its length. Now what if only the thickness of the object is very small compared to its length and width? In this case, we will deal with thermal expansion in two dimensions:-surface expansion.

Consider the plate of surface area A₀ at a temperature T₀, as shown in Figure 8. If the plate is heated until the temperature is increased by, ΔT, it expands in width and height such that the surface area is changed by AD. This change in area is directly proportional to the product of the original area and the change in temperature. Thus,

where the proportionality constant β is called the coefficient of surface (area) expansion, and it can be measured by the unit °C^-1, or k ^-1

If the final surface area at the new temperature, T, is A, then ∆ A = A - A ₀ . After some substitutions and rearrangements, we have

A = A0 (1 + β∆T)