WAALS, JOHANNES DIDERIK VAN DER

(b. Leiden, Netherlands, 23 November 1837: d. Amsterdam, Netherlands, 8 March 1923), Physics.

The son of a carpenter, van der Waals became a primary-school teacher. After training for secondary-school teaching (1866), while a headmaster in The Hague, he studied physics at the University of Leiden. On the basis of his knowledge of the work of Clausis and other molecular theorists, he wrote his dissertation, Over de continiteit van den gasen vloeisotoftoestand (1873). As Maxwell said, “this at once put his name among the foremost in science.” Using rather simple mathematics, the dissertation gave a satisfactory molecular explanation for the phenomena observed in vapors and liquids by Thomas Andrews and other experimenters, especially the existence of a critical temperature, below which a gas can be condensed to a two-phase system of vapor and liquid; while above it there can be only a homogeneous vapor phase. This was one of the first descriptions of a collective molecular effect, although the kinetic theory of gases was already well known.

The law of corresponding states, which van der Waals developed some years later, allows a somewhat better fit with experimental data and in succeeding years was a useful guide in the work on liquefaction of the “permanent” gases. In 1875 he was elected to the Royal Netherlands Academy of Sciences and Letters; and two years later, after the Amsterdam Athenaeum had become the University of Amsterdam, he occupied the chair of physics. As a teacher van der Waals was much admired, and he inspired his pupils to do both experimental and theoretical work. His scientific publications were mostly on molecular physics and thermody

namics. He retired in 1907 and was succeeded by his son, who was named for him. In 1910 he was awarded the Nobel Prize for physics.

The van der Waals equation of state links the pressure P, absolute temperature T, and volume V, using three constants a, b, and R (the last four quantities being proportional to the amount of substance or its square):

The term a/V² accounts for the molecular attraction, determined by integrating over the “attraction sphere” (Figure 1). It is supposed (and at medium densities it is sufficiently true) that in the average over time the attraction sphere, outside its central part, is filled rather homogeneously will molecules with a local density equal to the overall density. With very close packing a would no longer remain constant, but gradually increase (by less than a factor of 2). Likewise b, accounting for the non-overlapping of molecules, is equal at low density to four times the “proper” volume of all molecules together, but gradually decreases (by a factor not smaller than 0.5) for very close packing. Moreover, the temperature also affects a and b, since it influences the radial distribution of the molecules around an arbitrary one.

These detailed and, even for modern methods, rather difficult complications were rightly disregarded by van der Waals, although he was aware of them. With constant a and b, the isotherms may be calculated (see Figure 2), giving for the critical point

Below the critical point the assumption of one homogeneous phase no longer holds, except perhaps for very short moments. Energy relations are such that it is more favorable here for some of the molecules to move closer together (liquid), leaving the other molecules to fill the rest of the volume in a much sparser distribution (vapor). This two-phase system is represented by horizontal line tracks in Figure 2. Most thermodynamic quantities can now be calculated: saturated vapor pressure curve, Joule-Kelvin effect, supercooling, and so on. The comparison with experiment is given in Figures 3 and 4 for noble and pseudo-noble gases (hydrogen, carbon monoxide, nitrogen). The falling of all experimental points for these different substances, in reduced variables, on the same curve is an expression of the law of corresponding states. For other kinds of molecules the divergences from van der Waals’s findings may be smaller or larger.

Van der Waals scarcely could have had adequate ideas about the nature of the attractive forces between molecules, so it is historically rather inexact that the London forces (energy proportional to r^-6) should often be called “van der Waals forces.” It would be somewhat more reasonable to give this name to all forces not of ionic origin, but so loose a terminiology would not be useful.

BIBLIOGRAPHY

I. Original Works. Van der Waals’s writings include Over de continuiteit van den gas- en vloeistoftoestand (Leiden, 1873), his dissertation: articles in Versl. kon. Akademie van Wetenschappen: and Lehrbuch der Thermodynamik (Leipzig, 1912), written with P. A. Kohnstamm. See also “The Equation of State for Gases and Liquids,” in Nobel Lectures in Physics, 1901-1921 (Amsterdam, 1967), which also contains a biography.

II. Secondary Literature. See an article in physics (Amsterdam), 4 (1937); S. G. Brush, Nobel Prizes in physics (Milan, 1970); W. Leendertz, “J. D. van der Waals,” in Gids, 87 (1923), 151.

J. A. Prins