The volume of a solid substance increases if its temperature is increased. It is called volume expansion. Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. The degree of expansion divided by the change in temperature is called the material’s coefficient of thermal expansion; it generally varies with temperature.

Let, the initial volume of a substance be V_{1} and the initial temperature is **θ _{1}**. When the temperature is raised to

**θ**, its volume becomes V

_{2}_{2}after being increased.

There increase in volume is V_{2} – V_{1} and increase of temperature = **θ _{2} – θ_{1}**

Now if the coefficient of volume expansion is represented by

**γ = [(V _{2} – V_{1}) / V_{1}(θ_{2} – θ_{1})] ….. ………. ………(1)**

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

[*Note that the volumetric expansion coefficient used in the calculator is constant. If you want to calculate volumetric change for a liquid over a temperature range where the volumetric expansion coefficient for the liquid changes a lot – interpolate the coefficient values, or split the calculation in the different temperature ranges.*]

In equation (1) if the initial volume V_{1} = 1 m^{3} and increase of temperature, **θ _{2} – θ_{1}** = 1K, then

**γ = V _{2} – V_{1 }= increase in volume.**

Therefore, the increase in the volume of a solid of volume 1 m^{3} for a rise of temperature 1K is called the coefficient of volume expansion of the material of the solid. The coefficient of volume expansion of copper is **50.1 x 10 ^{-4} m^{3}** means that if the temperature of a copper body with a volume of 1 m

^{3}increases through 1K then its volume will increase by

**50.1 x 10**.

^{-4}m^{3}**The relations among α, β, and γ are as follow: γ = 3α and β = 2α**

Example – water is a liquid where the volumetric expansion coefficient changes a lot with temperature. Water has its highest density and smallest volume at 4^{0}C (39.2^{0}F). The volumetric coefficient for water is negative below 4^{0}C and indicates that the volume decreases when the temperature moves from 0^{0}C (32^{0}F) to 4^{0}C.