**Thermal Expansion Formula**

When the temperature operates on the body, the length, width, height, and volume of the material change. Thermal expansion is visible in solids because the atoms are densely packed.

Thermal expansion is the tendency of an item to change its area, volume, and form in response to a change in temperature caused by heat transfer.

**Linear expansion**

The change in length caused by heat is known as linear expansion. Linear expansion formula is given as,

ΔL / Lo= LΔT

Where,

Lo= original length,

L = expanded length,

= length expansion coefficient,

ΔT = temperature difference,

ΔL = change in length

**Solved Examples:**

**Q.1: A 4m long rod has been heated to 40°C. Calculate the thermal expansion coefficient for length if the rod’s length extends to 6m after some time. The temperature in the room is 30 degrees Celsius.**

Given: L0 = 4m is the rod’s initial length.

L = 6 m is the rod’s expanded length.

ΔL = 6–4 = 2m is the change of length.

ΔT is the temperature difference.

= 40°C – 30°C = 10°C

= 10°C + 273°K

= 283 K

The linear expansion formula is given by,

ΔL/ Lo=LΔT

To get the length expansion coefficient, rearrange the above formula: we obtain,

L=ΔL /Lo ×ΔT

= 2/4 X 283

= 1/566

= 0.0017 K^{-1}

As a result, the length thermal expansion coefficient will be 0.0017 K^{-1}

**Q.2: 1. A 40°C-heated rod measuring 5 metres in length. After a while, the length reaches 7 metres. Find the expansion coefficient. The temperature in the room is 30°C.**

Ans: Initial length Lo= 5m

Expanded length L = 7 m are given.

L = 7 – 5 = 2 m is the length difference.

T = 40°C – 30°C = 10°C temperature difference

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

Length expansion coefficient is given by,

= 2 / (5 283)

=14×10^{-4}k^{-1}