The volume of a solid substance increases if its temperature is increased. It is called volume expansion.
Let, the initial volume of a substance be V1 and initial temperature be θ1. When the temperature is raised to θ2, its volume becomes V2 after being increased.
There increase in volume is V2 – V1 and increase of temperature = θ2 – θ1
Now if the coefficient of volume expansion is represented by
γ = [(V2 – V1) / V1(θ2 – θ1)] ….. ………. ………(1)
[Increase in surface area / (Initial area x increase of temperature)]
In equation (1) if the initial volume V1 = 1 m3 and increase of temperature, θ2 – θ1 = 1K, then
γ = V2 – V1 = increase in volume.
Therefore, the increase in volume of a solid of volume 1 m3 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 m3 means that if the temperature of a copper body with a volume of 1 m3 increases through 1K then its volume will increase by 50.1 x 10-4 m3.
The relations among α, β, and γ are as follow: γ = 3α and β = 2α