The physical behaviour of a gas is described using four main variables :

- Temperature
- Pressure
- Volume
- Amount (mol number)

## Charles’s law

Charles’s law was formulated by the French scientist Jack Charle who was investigating the properties of gases in the 1780’s. This law describes the relation between the temperature and the volume of a gas at constant pressure and constant mole number.

After his experiment, Charles discovers that as the temperature of an enclosed gas increases, the volume increases, if the pressure is constant. So the volume of a fixed mass of gas is directly proportional to its temperature if the pressure is constant.

This relation is represented in the following graph.

A hot air balloon contains a propane burner onboard to heat the air inside the balloon. As the air is heated, the volume of the balloon increases. According to Charles’s law, as the temperature of the air increases, the volume of the balloon also increases.

Let’s consider a gas under two different conditions of temperature (T1 and T2) and volume (V1 and V2). Charles’s Law leads to the mathematical expression :

## Practice problem – Charles’s law

What is the temperature of a 2.3 L balloon if it shrinks to a volume of 0.632 L when it is dipped into liquid nitrogen at a temperature of 77 K?

## Solution

Given: V1= 2.3 L V2 = 0.632 L T2 = 77K T1 = ??

Charles’s Law : V1/T1 = V2/T2

T1 = (V1 x T2) / V2 = (2.3 x 77) / 0.632 = 280.22 K