From Van der Waals' equation to the scaling laws

From our present-day perspective, the most important results obtained by Van der Waals for thermodynamic behavior in the critical region of gases are: the cubic critical isotherm and quadratic coexistence curve; the continuity of slope of the vapor-pressure curve; the law of the rectilinear diameter and the law of corresponding states. The critical behavior of Van der Waals' equation is typical for equations of state that are regular at the critical point in a sense to be discussed; those equations are presently called "classical". The confrontation with experiment took place before 1900. At that time, the first power-law analyses of data were made and their results disproved classical theory convincingly. It took, however, another 65 years before classical theory was replaced by the scaling laws. The very limited validity of the law of corresponding states, however, never posed a serious threat to the classical equation. On the contrary, by generalizing this law in various ways, our insight into the relation between molecular interaction and thermodynamic behaviour has been deepend considerably. In a sense, the principle of universality may be considered the latest generalization of the law of corresponding states. The principle of continuity of slope of the vapor-pressure curve has been preserved; the direction of the vapor-pressure curve at the critical point is a very special one according to the thermodynamic theory of Wheeler and Griffiths and also in the theories of "extended scaling". The law of the rectilinear diameter, now under siege by theory, has not yet failed us experimentally. The lines from the past to the present are sketched in this contribution, and the modern concepts of scaling will be developed from the classical equation of state. The consequences of the scaling laws for the description of thermodynamic data of fluids in the critical region will be discussed and illustrated with experimental material. Universality of critical behaciour in fluids will be demonstrated.