Gas dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature: In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature. In 1811, Amedeo Avogadro verified that equal volumes of pure
Kinetic theory of gases is an alternative approach developed by Grad based on moment expansions. In the other limit, for extremely rarefied gases, the gradients in bulk properties are not small compared to the mean free paths. This is known as the Knudsen regime and expansions can be performed in the Knudsen number. In kinetic model of gases, the pressure is equal to the force exerted by the atoms hitting and rebounding from a unit area of the gas container surface. Consider a gas of "N" molecules, each of mass "m", enclosed in a cube of volume "V" = "L". When a gas molecule