# Thermal Expansion Formula

Thermal expansion describes the tendency of an object to change its dimension either in length, area or volume due to heat. Heating up a substance increases its kinetic energy. Depending on the type of expansion thermal expansion is of 3 types– Linear expansion, Area expansion, and Volume expansion.

Linear expansion is the change in length due to heat. Linear expansion formula is given as,

$\frac{\Delta&space;L}{L_{o}}\,&space;=\,&space;\alpha&space;_{L}\Delta&space;T$

Where,

L0 = original length,

L = expanded length,

α = length expansion coefficient,

ΔT = temperature difference,

ΔL = change in length

Volume expansion is the change in volume due to temperature. Volume expansion formula is given as

$\frac{\Delta&space;V}{V_{o}}\,&space;=\,&space;\alpha&space;_{V}\Delta&space;T$

Where,

V0 = original volume,

V = expanded volume,

αv = volume expansion coefficient,

ΔT = temperature difference,

ΔV = change in volume after expansion

Area expansion occurs is the change in area due to temperature change. Area expansion formula is given as,

$\frac{\Delta&space;A}{A_{o}}\,&space;=\,&space;\alpha&space;_{A}\Delta&space;T$

Where,

A = original area,

ΔA = change in the area,

αA = area expansion coefficient,

ΔT = temperature difference,

A0 = expanded area.

## Solved Examples

Example 1

A rod of length  5 m  heated to 40°C. If the length of increases to 7 m after some time. Find the expansion coefficient. Room temperature is 30°C.

Solution:

Given:

Initial length Lo = 5 m,

Expanded length L = 7 m

Change in length Δ L = 7 – 5 = 2 m

Temperature difference Δ T = 40°C – 30°C  = 10°C

Absolute temperature T = 10°C +273=283 K

The linear expansion formula is given by,

$\frac{\Delta&space;L}{L_{o}}\,&space;=\,&space;\alpha&space;_{L}\Delta&space;T$

Length expansion coefficient is given by,

$\alpha _{L}=\frac{\Delta L}{L_{0}\times \Delta T}$

= 2 / 5 x 283

$\alpha _{L}=14\times 10^{-4}K^{-1}$