p. 211, Paris, 1869) proposed an equation of the form (p+po)(v - b) =RO, in which the effect of the size of the molecules is represented by subtracting a quantity b, the " covolume," from the volume occupied by the gas, and the effect of the mutual attractions of the molecules is represented by adding a quantity po, the internal pressure, to the external pressure, p. This type of equation, was more fully worked out by van der Waals, who identified the internal pressure, po, with the capillary pressure of Laplace, and assumed that it varied directly as the square of the density, and could be written a/v 2 .

00According to van der Waals, assuming spherical molecules, it should be four times; according to O.

00Van der Waals's Equation.

00Van der Waals, in a famous monograph, On the Continuity of the Liquid and Gaseous States (Leiden, 1873), has shown that the imperfections of equation (14) maybe traced to two_causes: (i.) The calculation has not allowed for the finite size of the molecules, and their consequent interference with one another's motion, and (ii.) The calculation has not allowed for the field of inter-molecular force between the molecules, which, although small, is known to have a real existence.

00To allow for the first of these two factors, Van der Waals finds that v in equation '04) must be replaced by v - b, where b is four times the aggregate space occupied by all the molecules, while to allow for the second factor, p must be replaced by p +a/v 2 .

00Thus the pressure is given by the equation (p+a/v 2) (v - b) =RNT, which is known as Van der Waals's equation.

00The variation of gases from Boyle's law is represented in the equation of Van der Waals by subtracting a constant b from the total volume to represent the effect of the volume of the molecules themselves.

00Perhaps a satisfactory point of view may be here obtained by applying the van der Waals' equation A(P-{-a/V2)(V-b)=2T, which connects volume V, pressure P and temperature T (see Condensation Of Gases).

00In fact, the quantity 41rp 2 K, which we may call with van der Waals the molecular pressure, is so great for most liquids (5000 atmospheres for water), that in the parts near the surface, where the molecular pressure varies rapidly, we may expect considerable variation of density, even when we take into account the smallness of the compressibility of liquids.

00Van der Waals, G.

00

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