Van Der Waals Law

Van der Waals law (Van-der-Waals), equation of state for real gases (see Aggregation state), that do not obey the laws of Boyle and Gay-Lussac (pv = RT), which is valid for ideal gases. If we denote the volume of a gas by v, the pressure by p, the absolute temperature by T, and the so-called gas constant, which also appears in the Boyle-Gay-Lussac equation, by R, then according to Van der Waals, (p + a/v²)(v - b) = RT. Here a and b are two constants that depend on the size of the molecules and the forces of interaction between them. As can be seen from the given equation of state, the pressure p in the case of a gas that differs in its properties from an ideal one increases by an additional term a/v², which is the greater the stronger the forces of intermolecular attraction (in the case of an ideal gas, such forces should not exist). The measure of these forces can therefore be the constant a. For different gases it is different. Thus, for H₂ it is close to zero, since this is the gas that most closely approaches the ideal in its properties. For air a = 0.0037, and for CO₂ it is even greater: a = 0.0115. The latter gas, as is known, shows particularly sharp deviations from the laws of Boyle and Gay-Lussac. The constant b enters into the other factor. It takes into account the volume occupied by the molecules themselves when it becomes impossible to neglect this volume. And this constant is small for H₂: it is equal to 0.00069 here. On the contrary, for air it reaches a value of 0.0026, and for CO₂ even 0.003. Van der Waals tried to apply his formula not only to gases but also to liquids. In the latter case, the term a/v² can be considered as the surface pressure experienced by a liquid, the surface of which, as is known, possesses a certain energy (see Adsorption). The magnitude of the surface pressure calculated in this way turns out to be for ether 1,300-1,400 atmospheres, for liquid CO₂ and for alcohol-about 2,200 atmospheres, for water-about 11,000 atmospheres.

V. Shuleikin.