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. Â
- Â Â Â Linear expansion occurs when there is a change in the length. Linear expansion formula is given as,
Where,
L0 = original length,
L = expanded length,
α = length expansion coefficient,
ΔT = temperature difference,
ΔL = change in length.
- Â Â Â Â Volume expansion occurs when there is a change in volume due to temperature. Volume expansion formula is given as
Where,
V0 = original volume,
V = expanded volume,
αv = volume expansion coefficient,
ΔT = temperature difference,
ΔV = change in volume after expansion.
- Â Â Â Â Area expansion occurs when there is any change in area due to temperature change. Area expansion formula is given as,
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. Â
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.
