Waals, Johannes Diderik van Der
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
Johannes Diderik van der Waals
Johannes Diderik van der Waals
The Dutch physicist Johannes Diderik van der Waals (1837-1923) did pioneering studies on the equation of state of liquids and gases, for which he received the Nobel Prize for physics in 1910.
Johannes van der Waals was born on Nov. 23, 1837, in Leiden, the son of Jacobus van der Waals and Elizabeth van den Burg. His life is a classic illustration of the fact that lack of proper educational opportunities is not an insurmountable obstacle to greatness in science, provided one's potential is matched by one's determination. Following the completion of his elementary and secondary education, he taught elementary school in Leiden with his mind fixed on much higher goals. His thirst for knowledge had at first to be satisfied with reading in his spare time, but during the years 1862-1865 he followed courses at the University of Leiden and obtained the certification to teach mathematics and physics in high schools. In 1864 he married Anna Magdalena Smit, who soon died, leaving him with four small children.
While Van der Waals served as director of a high school in The Hague, a new law removed classical languages from the list of compulsory courses for science students at universities, and he passed in 1873 the examinations for doctor's degree in physics. His dissertation, On the Continuity of the Gaseous and Liquid States, revealed him at one stroke as a most original master of physics. In fact James Clerk Maxwell remarked, when he learned of the dissertation's contents, "The name of Van der Waals will soon be among the foremost in molecular science."
Van der Waals argued that R. J. E. Clausius's derivation of Robert Boyle's gas law from statistical mechanics had to be supplemented by new considerations if it was to hold for real gases and their transformation into liquids. The new consideration was the "principle of continuity, " by which Van der Waals meant that from the viewpoint of statistical mechanics there could be no basic difference between the gaseous and the liquid states. In addition he noted the need for considering two factors, the volume of molecules and their mutual attraction. He succeeded in relating these two factors to the critical temperature, pressure, and volume, or the critical point. It therefore followed that the equation of state could be expressed in a form independent of any particular gas or liquid.
This in turn led to the most momentous part of Van der Waals's research, the law of corresponding states, formulated in 1880. According to it, the whole range of behavior of a substance can be predicted once its critical point has been ascertained. This result played a crucial role in the efforts leading to the liquefaction of hydrogen (1898) and of helium (1908). His other principal achievement consisted in the combination of the law of corresponding states with the second law of thermodynamics, which he outlined in 1890 in his first treatise on the theory of binary solutions.
In 1876 Van der Waals became the first professor of physics at the newly established University of Amsterdam. His son, Johannes Diderik, Jr., was the next occupant of the chair. Van der Waals died in Amsterdam on March 8, 1923.
Further Reading
Biographical information on Van der Waals and accounts of his work are in N. de V. Heathcote, Nobel Prize Winners in Physics, 1901-1950 (1953), and Nobel Foundation, Nobel Lectures: Physics, 1901-1921 (1967). □