How does the pressure of a gas change when its volume is decreased while temperature is constant?

When the volume of a gas is decreased while keeping the temperature constant, the pressure of the gas increases. This relationship is described by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. Mathematically, this can be expressed as ( P \propto \frac{1}{V} ) or ( PV = k ), where ( k ) is a constant.

As the volume ( V ) decreases, the product of pressure ( P ) and volume remains constant. Consequently, if the volume gets smaller, the pressure must increase in order to keep the product ( PV ) the same. This increase in pressure occurs because gas molecules have less space to move around, which results in more frequent collisions with the walls of the container, thereby increasing pressure.

Understanding this principle is fundamental in various applications, such as in breathing mechanics or in mechanical systems involving gases.