# Thermal Expansion

Almost all solids are found to expand with rise in temperature. The thermal expansion of solids is of three types namely: linear expansion, superficial expansion and cubical expansion. In each type of expansion, the increase I dimension is observed to be proportional to the original dimension and the rise in temperature.

Solids are made up of atoms and molecules. At a given temperature, the atoms and molecules are located at some equilibrium distance. When heat is added to a solid, the amplitude of the vibrations of the atoms and molecules increases. Due to this, the effective interatomic separation increases, which results in expansion of the solids.

# Linear expansion

Suppose that a solid in the form of a rod of length is heated, till its temperature rises through  Δ T. . If the length of the rod becomes ', then it is found that increase in length is
1. directly proportional to its original length i.e.
2. directly proportional to rise in temperature of the rod i.e.

From the above equations, we have

Here, the constant of proportionality α is called the coefficient of linear expansion. Its value depends upon the nature of the material.
The coefficient of linear expansion of the material of a solid rod is defined as the change in length per unit length resulting from per unit change in its temperature.

Its unit is K-1 in S.I. The value of α for most of the solids is found to be between 10-6 K-1 to 10-5 K-1. Its value is found to be more for ionic solids than that for the non-ionic solids. It may be pointed that the value of coefficient of linear expansion of a solid rod does not depend upon the shape of the cross-section of the rod.

# Superficial expansion

If S is the initial surface area and S is the surface area of a solid, when temperature changes by Δ T, then as explained above, we have
(S - S) S
∝ Δ T
(S′ - S) = β S Δ T
S = S (1 + β Δ T)

Here, β is called the coefficient of superficial expansion.

The coefficient of superficial expansion is defined as the change in surface area per unit surface area per change in its temperature.

Its unit is also K-1 is SI.

# Cubical expansion

Again, if V is the initial volume and V, the volume of the solid, when temperature changes by ΔT; then as explained above
(V - v) α V

α Δ T
V - V = γ V ΔT
V = V(1+γ Δ T)

Here, γ is called the coefficient of cubical or volumetric expansion.

The coefficient of cubical expansion is defined as the change in volume per unit volume per unit change in its temperature.

Its unit is also as that of α or β i.e. K-1 in S.I.

The three coefficients of expansion are not constant for a given solid. Their values depend upon the temperature range in which they are measured. For example, the coefficient of cubical expansion of copper increases with increase in temperature. It has a constant value only above 500 K.
 Figure - Temperature vs Coefficient of cubical expansion