Avogadro's law "P" are taken at standard conditions for temperature and pressure (STP), then "k"'=1/"n", where "n" is Loschmidt constant. Avogadro's hypothesis (as it was known originally) was formulated in the same spirit of earlier empirical gas laws like Boyle's law (1662), Charles's law (1787) and Gay-Lussac's law (1808). The hypothesis was first published by Amadeo Avogadro in 1811, and reconciled Dalton atomic theory with the "incompatible" idea of Joseph Louis Gay-Lussac that some gases were composite of different fundamental substances (molecules) in integer proportions. In 1814, independently from Avogadro, André-Marie Ampère published the same law with similar conclusions. As Ampère was
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