Formula and Derivation

As per Boyle’s law, any change in the volume occupied by a gas (at constant quantity and temperature) will result in a change in the pressure exerted by it. In other words, the product of the initial pressure and the initial volume of a gas is equal to the product of its final pressure and final volume (at constant temperature and number of moles). This law can be expressed mathematically as follows:

P₁V₁ = P₂V₂

Where,

• P₁ is the initial pressure exerted by the gas
• V₁ is the initial volume occupied by the gas
• P₂ is the final pressure exerted by the gas
• V₂ is the final volume occupied by the gas

This expression can be obtained from the pressure-volume relationship suggested by Boyle’s law. For a fixed amount of gas kept at a constant temperature, PV = k. Therefore,

P₁V₁ = k (initial pressure * initial volume)

P₂V₂ = k (final pressure * final volume)

∴ P₁V₁ = P₂V₂

This equation can be used to predict the increase in the pressure exerted by a gas on the walls of its container when the volume of its container is decreased (and its quantity and absolute temperature remain unchanged).