The area of a solid is increased with an increase of temperature. It is called superficial expansion. Whenever there is an increase in the size of a body due to heating, then the body is said to be expanded and the fact is known as expansion.

Let the initial surface area of a solid at **θ _{1}** temperature = A

_{1}

When the temperature is increased to **θ _{2}** the final surface area =A

_{2}

So, Increase in temperature = **θ _{2} – θ_{1}**

And the increase in area = **A _{2} – A_{1}**

The coefficient of superficial expansion is expressed by the symbol β (beta). The amount by which unit area of a material increases when the temperature is raised by one degree is called the coefficient of superficial (i.e. area) expansion and is represented by β (Greek beta).

Superficial expansion, **β = [(A _{2} – A_{1}) / A_{1}(θ_{2} – θ_{1})] ….. ………. ………(1)**

**[Increase in surface area / (Initial area x increase of temperature)]**

In equation (1) if the surface area, A_{1} = 1 m^{2} and the increase of temperature (**θ _{2} – θ_{1})** = 1K is considered, then the increase in surface area, β (beta) =

**A**= increase in surface area. If the temperature increases, then the volume of the substance also increases. Usually, this is known as thermal expansion.

_{2}– A_{1 }Superficial Expansion of Solids: The coefficient of superficial expansion is defined as the ratio of increase in area to its original area for every degree increase in temperature.

Coefficient of superficial expansion = Increase in area / (Initial area – Rise in temp) (°C) = 2 × coefficients of linear expansion.

So, the increase in surface area of 1 m^{2} surface area of a solid for the rise of temperature 1K is called the coefficient of superficial expansion of the material of that solid. In case of expansion of a solid, normally linear expansion coefficient is generally employed. Its unit is K^{-1}. The coefficient of superficial expansion of copper is **33.4 x 10 ^{-6} K^{-1}**. We can express it in this method that it is the fractional change in length or volume per unit change in temperature. It means that if the temperature of a copper body is increased through 1K, then the increase in surface area of copper is

**33.4 x 10**

^{-6}m^{2}.