Thermal expansion in solids is of three types –

1. Linear Expansion
2. Surface or Superficial Expansion
3. Volume or Cubical Expansion
The thermal expansion of different solids for the same rise in temperature is different. For example, copper undergoes a greater thermal expansion than iron, for the same rise in temperature with respect to their initial length, surface, or volume.
Coefficient of Linear Expansion:
Experimentally, it is observed that the linear expansion of a metal rod on heating is directly proportional to the initial length of the rod and the rise in temperature of the rod.
The increase in length for the unit rise in temperature for a unit length of a solid is called the coefficient of linear expansion of the material of the solid. The coefficient of linear expansion is denoted by α.
Unit of Coefficient of Linear Expansion:
α = unit of length / unit of length x unit of temperature
= 1 / unit of temperature
Coefficient of Surface Expansion:
The increase in surface area for a unit rise in temperature for a unit surface area of a solid is called the coefficient of surface expansion of the material of that solid. The coefficient of surface expansion is denoted by β.
Unit of Coefficient of Surface Expansion:
β = increase in area / initial area x rise in temperature
Coefficient of Volume Expansion:
The increase in volume for the unit rise in temperature for a unit volume of a solid is called the Coefficient of Volume Expansion of the material of that solid. The coefficient of volume expansion is denoted by γ.
γ = increase in volume / initial volume x rise in temperature