Section I.

Fundamental Principles of van der Waals' Theory.

§ 1. General Views of van der Waals.

When the distance at which two gas molecules perceptibly act upon one another is negligibly small compared to the average distance from one molecule to its nearest neighbor—or, as one might also say, when the space occupied by the molecules (or rather, their spheres of action The "sphere of action" refers to the effective volume around a molecule within which it can influence another through physical forces.) vanishes in comparison to the space filled by the entire gas—then for each molecule, that portion of its path traveled during interaction with other molecules also vanishes when compared to the path of its center of mass traveled in a straight line or solely under the influence of external forces. In such a case, the Boyle-Charles Law Also known as the Ideal Gas Law, relating pressure, volume, and temperature. holds for the gas in question, whether its molecules are simple material points, rigid bodies, or arbitrarily complex aggregates. In all these cases, the gas in question is called an ideal gas.

The gases occurring in nature fulfill this condition of the ideal gas state only incompletely, and it is therefore highly desirable to have a theory that also takes into account the finite extent of the molecules' spheres of action.

Such a theory was provided by van der Waals, who otherwise—as we did at the beginning of the first part—imagines the molecules as elastic spheres that are negligibly deformable. However, he generalizes the theory in two ways: