Section I.

1. He does not assume that the space actually occupied by the elastic spheres representing the molecules is negligibly small compared to the total volume of the gas;

2. He assumes that, in addition to the elastic forces acting for a vanishingly short time only during collisions, there is also an attractive force active between the molecules. This force acts in the direction of their center line, and its intensity is a function of the distance between their centers. We call this attractive force the van der Waals cohesive force. Named after Johannes Diderik van der Waals, who formulated the equation of state for gases and liquids in 1873.

The necessity of assuming an attractive force between molecules follows directly from the fact—now proven for all gases—that they can be liquefied. The simultaneous coexistence of a liquid phase and a vapor phase of the same substance, at the same temperature and pressure within the same vessel, can only be explained if there are attractive forces active between the molecules alongside the force that causes them to bounce apart during collisions.

These attractive forces could be directly demonstrated by the following experiment. Suppose one suddenly connects a vessel filled with a compressed gas to another vessel containing the same gas in a more diluted state. During the overflow, the gas in the first vessel performs work by overcoming the pressure and thus cools down; in the second vessel, visible currents are initially created, which over time are converted into heat through friction. If only collision forces were active between the molecules, the heat ultimately generated by this process would have to be completely equivalent to the cooling in the first vessel. If, on the other hand, there are also attractive forces active between the molecules that extend over somewhat larger distances, this equivalence is not complete. Instead, a small total loss of heat occurs, since the average distances between the molecules have increased, and therefore a certain amount of heat had to be expended to overcome their attraction. This describes the Joule-Thomson effect, where a real gas changes temperature when expanding without performing external work.

Molecules, attractive force, van der Waals cohesive force, collisions, gas, liquefaction, heat loss