What is the relationship between the pressure and volume of a fixed mass of gas at constant temperature?

The relationship between the pressure and volume of a fixed mass of gas at constant temperature is described by Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure when the temperature is held constant. This means that if the volume of the gas decreases, the pressure increases, and vice versa, assuming no change in temperature and amount of gas present. Mathematically, this can be expressed as ( P \propto \frac{1}{V} ), or more commonly used in the equation form ( PV = k ), where ( k ) is a constant.

This relationship highlights that as gas particles are compressed into a smaller volume, they collide with the walls of the container more frequently, leading to an increase in pressure. Conversely, if the gas expands, the frequency of collisions decreases, resulting in a lower pressure. Thus, the inverse correlation between volume and pressure is a fundamental principle in understanding gas behavior under varying conditions, particularly in the context of ideal gases.