**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 â€“ 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,

Î± = length expansion coefficient,

Î”T = temperature difference,

Î”L = 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,

Î±v = volume expansion coefficient,

Î”T = temperature difference,

Î”V = 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,

Î”A = change in area,

Î±A = area expansion coefficient,

Î”T = temperature difference,

A0 = expanded area.

**Example 1**

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

**Solution:**

Given:

Initial length Lo = 5 m,

Expanded length L = 7 m

Change in length Î” L = 7 – 5 = 2 m

Temperature difference Î” T = 40o C – 30o Â = 10o C

Â Â = 283 K

The linear expansion formula is given by,

Î”L / Lo = Î±L Î” T

âˆ´ Â Length expansion coefficient is given by,

Î±L = Î”L / LoÃ—Î”T

Â Â Â = 2 / 5 x 283

Â Â Â Î±L = 14 Ã— 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

Î” V = V – Vo

Â = 10 – 4

Â = 6 cm.