Why does the volume of a gas decrease when its pressure is doubled at constant temperature?

The volume of a gas decreases when its pressure is doubled at a constant temperature because of the relationship described by Boyle’s law. This empirical law states that the pressure ($p$) of a given quantity of gas is inversely proportional to its volume ($v$) when the temperature remains constant.12

Mathematically, this is expressed as $pv=k$, where $k$ is a constant. Because the product of pressure and volume must remain constant at a fixed temperature, increasing the pressure by a factor of two necessitates that the volume decreases by one-half to maintain that equality.12

This behavior is a fundamental characteristic of ideal gases, which are described by the ideal gas equation of state. While real gases may show slight deviations from this behavior at higher pressures, they generally follow this inverse relationship under conditions of lower density.21