Thermal Expansivity

We have learnt in previous lessons that when heat is applied to most solids and liquids, they expand, that is, they increase in size. There may be an increase in length, area or volume of the solid. This is because according to kinetic theory, when an object is heated, the molecules gain more kinetic energy to move around and thus increasing their displacement about their mean positions.

Expansion in solids

Always remember that solids expand when heat is applied and

contract when cooled.

LINEAR EXPANSIVITY

Linear expansion occurs when solids increase in length over a degree rise in temperature of the body.

Linear Expansivity of a solid can be defined as the increase in length per unit length per degree rise in temperature of the solid.

Mathematically,

α = l₂ – l₁ / l₁ (θ₂ – θ₁)

where ; α = linear expansivity of the solid

                l₁=length of solid at temperature θ₁

                l₂ = length of solid at temperature θ₂

                θ₂ – θ₁ = change in temperature

                e = l₂ – l₁ = increase in length or expansion

We can also say that;

Linear expansivity, α = increase in length / original length x change in temperature

Note: The new length l₂ can be calculated from the formula above by making l₂ the subject of the formula thus;                            l₂ = l₁ (1 + αθ)

Also, linear expansivity differs from solid to solid. The linear expansivity of copper is 0.000017^oK, that of Iron is 0.000012^oK and Aluminium is 0.000023^oK etc. This implies that a unit of copper length expands by 0.000017units when its temperature increases by 1K.

AREA EXPANSIVITY

As solids increase in length when heated, there is also an increase in breadth and height. Therefore this also results to an increase in area of the solid. This increase is known as area or superficial expansion.

Area expansivity, β can be defined as the increase in area of the solid per unit area per degree rise in temperature of the substance.

Mathematically,

Area expansivity, β = change in area / original area x change in temperature

                                   β = A₂ – A₁ / A₁ (θ₂ – θ₁)

where; β = Area expansivity of the solid

                A₁= Area of solid at temperature θ₁

                A₂ = Area of solid at temperature θ₂

                θ₂ – θ₁ = change in temperature

                e =A₂ – A₁ = increase in area or expansion            A₂ = A₁ (1 + αθ)

VOLUME EXPANSIVITY

The increase in length, breadth and volume of a solid will result in an increase in the volume of the solid known as cubic expansivity.

Cubic expansivity is defined as the increase in volume per unit volume per degree rise in temperature.

Cubic expansivity, ϒ = change in volume / original volume x change in temperature

                                     ϒ = V₂ – V₁ / V₁ (θ₂ – θ₁)

where; ϒ = Cubic expansivity of the solid

                V₁= Volume of solid at temperature θ₁

                V₂ = Volume of solid at temperature θ₂

                θ₂ – θ₁ = change in temperature

                e =V₂ – V₁ = increase in volume                 V₂ = V₁ (1 + αθ)

Relationship between Linear, Area and Cubic Expansivity

Area expansivity, β = 2 x linear expansivity

                                   β = 2α

Cubic expansivity, ϒ = 3 x linear expansivity

                                    ϒ = 3α