Escutcheons of Science
 van der Waals

Johannes Diderik van der Waals (1837-1923)
Dutch Physicist. Nobel Prize for Physics in 1910

Per fess wavy Azure and Argent, three swans Or naiant in fess overall.
Crest  A swan Or.   Mantling  Azure and Or.

frame  Alternate tinctures frame  
   Dutch postage stamp

The above  van der Waals  coat-of-arms has also been rendered in the different set of tinctures shown at left  (where the birds are  definitely  swans).  Both  renditions appear as  "family arms"  (Familiewapen)  in a  Dutch site  about the  Van der Waals  surname.

Per fess wavy Or and Azure, three swans Sable naiant in fess overall.
Crest  A swan Sable.   Mantling  Sable and Or.

Johannes Diderik van der Waals was born in Leyden  (Netherlands)  on November 23, 1837  and became a schoolteacher without ever acquiring any knowledge of the classical languages.  This meant he could not sit for formal university examinations at Leyden.  He could merely attend classes in his spare time  (from 1862 to 1865)  and obtain teaching certificates in mathematics and physics.

When the classical languages requirements were finally lifted for students in Science, van der Waals could move on with an academic career and obtain a doctorate in 1873  (he was 36 years of age by then)  His doctoral dissertation was entitled Over de Continuïteit van den Gas en Vloeistoftoestand  (On the Continuity of the Gas and Liquid State).  It was so remarkable that the great  James Clerk Maxwell  himself gave it one of the highest compliments ever paid by one scientist speaking about the work of another:

"It has certainly directed the attention of more than one inquirer to the study of the [Dutch] language in which it is written."

In that masterpiece of his, van der Waals introduced the famous  equation of state,  now named after him, which relates the pressure, volume and absolute temperature  (p, V, T)  of a  mole  of some fluid:

( p + a / V2 )  ( V-b )   =   RT

In this,  ab  and  R  are constant for a given fluid.  For an ideal gas,  a  and  b  would be zero and the above would reduce to the  Ideal Gas Law  for one mole  (n = 1)  of a "perfect" gas.  However, for a  "true"  van der Waals fluid  (for which  a  and  b  are nonzero)  the constant  R  need not be equal to the perfect gas constant  (of  8.31447 J/K).  It's just another parameter which can be adjusted for a best fit of the  van der Waals equation of state  to actual measurements of a real fluid.  In spite of what a few misguided comments may state, the  van der Waals equation of state  does feature  three  adjustable parameters  (ab  and  R).  In fact,  the three parameters of a perfect  van der Waals fluid  are best expressed in terms of the values of  p,  V  and  T  at its  critical point  (the "critical state" of a fluid was first chracterized by Cagniard in 1822).

a   =   3 pV 2           b   =   V / 3           R   =   8 pV / 3T

The parameter  b  (called molar  covolume)  is the nonzero volume that the fluid would occupy under a very large pressure.  Van der Waals argued that atoms and molecules had finite size  (see Van der Waals radius)  and that external pressure could not reduce the volume occupied by bouncing molecules when there are already almost "touching" each other.

The positive term  a / V 2  is called  inner pressure  or  internal pressure  and corresponds to an attraction between molecules.  (Technically, that  inner pressure  is always defined as the  isothermal  derivative of the internal energy  U  with respect to the volume  V.)  Qualitatively, Laplace and others had already observed that a column of water need not break apart when some of it is under a substantial  negative  pressure, indicating a resistance to pulling somewhat similar to that of a solid rod.  The interactions between the neutral molecules of a fluid are now called  Van der Waals forces.  In the main, the average interaction between two randomly oriented neutral molecules amounts to an attration inversely proportional to the inverse of the sixth power of the distance between them  (this magnitude is what the above Van der Waals  internal pressure  term states).  This is essentially due to the  electrical polarizability  of the molecules; a universal effect which would be investigated by another Nobel-prize-winning Dutchman: Peter Debye (1884-1966).

Van der Waals volume   |   Van der Waals forces
Van der Waals equation of state   |   Dutch Surname     van Der Waals
visits since April 13, 2009 Valid HTML
 (c) Copyright 2000-2014, Gerard P. Michon, Ph.D.