# Thermal Expansion Formula

Thermal expansion describes the tendency of an object to change in its area, volume and shape to a shift in temperature through a transfer of heat. Heat is a consistently decreasing function of the average molecular kinetic energy of an object. Heating up a substance increases its kinetic energy.

Since thermal expansion leads to changes in dimension either in length or volume, therefore, there are three types of thermal expansion namely – Linear expansion, Area expansion, and Volume expansion.

1.    Linear expansion occurs when there is a change in the length. 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.

1.     Volume expansion occurs when there is a 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.

1.     Area expansion occurs when there is any 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 area,

αA = area expansion coefficient,

ΔT = temperature difference,

A0 = expanded area.

Example 1

A 5m long rod is heated to 40oC. If the length of the rod expands to 7m after some time, calculate the expansion coefficient. Given room temperature is 30o 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 = 40o C – 30o  = 10o C

= 283 K

The linear expansion formula is given by,

ΔL / Lo = αL Δ T

Length expansion coefficient is given by,

αL = ΔL / Lo×ΔT

= 2 / 5 x 283

αL = 14 × 10-4 K-1.

Example 2:

A volume of a balloon changes from 4 cm to 10 cm. Determine the change in its volume.

Solution:

Given:

Original volume Vo = 4 cm,

Volume expansion V = 10 cm

The change in volume is given by

Δ V = V – Vo

= 10 – 4

= 6 cm.