What relationship exists between pressure and temperature in Kelvin for a gas?

The relationship between pressure and temperature in Kelvin for a gas is described by Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature (measured in Kelvin) when the volume is held constant. This means that as the temperature increases, the pressure also increases, provided there is no change in the volume of the gas.

This direct proportionality can be mathematically expressed as ( P \propto T ) or in the equation form ( \frac{P}{T} = k ), where ( k ) is a constant. Therefore, if the temperature of a gas in Kelvin doubles, the pressure will also double under constant volume conditions.

Understanding this relationship is critical in various applications, including understanding how gas behaves under different temperatures and pressures, which is applicable in fields ranging from meteorology to engineering and thermodynamics.