For a fixed amount of gas at constant temperature, pressure and volume vary inversely. This empirical relation is Boyle's law:

$$pV=\text{constant}.$$

For two equilibrium states of the same gas sample at the same temperature,

$$\boxed{p_1V_1=p_2V_2}.$$

If the volume is reduced, the same gas particles occupy less space and collide with the container walls more frequently, so pressure rises. Doubling the volume at constant temperature halves the pressure in the ideal-gas limit.

Example

A gas occupies $2.40,\mathrm L$ at $100,\mathrm{kPa}$. It is compressed isothermally to $1.60,\mathrm L$. Assuming ideal behavior,

$$p_2=\frac{p_1V_1}{V_2} =\frac{(100,\mathrm{kPa})(2.40,\mathrm L)}{1.60,\mathrm L} =150,\mathrm{kPa}.$$

Only absolute pressures should be used in gas-law calculations.

Boyle's law applies when the amount of gas and temperature remain fixed. If gas leaks from the container or its temperature changes during compression, the simple relation $pV=\text{constant}$ no longer isolates the actual change.

The law is not a separate fundamental equation from the ideal-gas law. It is the constant-$n$, constant-$T$ consequence of the more general relation among pressure, volume, amount and absolute temperature.