In 1662, Robert Boyle found that in a closed system with a fixed mass of gas, the pressure was inversely proportional to the volume, as shown:

• Mathematically (Fig 1)
• Graphically (Fig 2)

Applying this to a cylinder of gas, if the piston is driven inwards to halve the volume then the pressure doubles (Fig 3).

Select play to watch the animation.

The relationship of P and V for a gas in two different settings is therefore:

P₁V₁ = P₂V₂

Each side of the equation represents one of these two settings.

For a gas stored under pressure, this formula can be used to calculate the volume available for use.

Example: A 5 L cylinder containing oxygen at a pressure of 100 atmospheres provides a supply of 500 L at 1 atmosphere.