Chapter 2 - The Corresponding-States Principle from the Continuity of Vapor and Liquid States

Abstract

According to Regnault by a number of experiments except for hydrogen, no gas exactly complies with Boyle's law and the expansion coefficient of a real gas increases with the increase of pressure. Joule and Thomson discovered the Joule–Thomson effect, where the internal energy of a real gas changes during its expansion. Further, Mendeleev investigated the relationship between surface tension and temperature, and it was found that the vapor–liquid interface tension disappears at a specific temperature where the vapor and liquid phases become a single phase. The reaction deduced by Van-der-Waals is studied carefully in this chapter under different parameters and along with Maxwell's equal-area role, it can describe the vapor–liquid phase transition well, including the critical point. The Van der Waals' equation of state not only qualitatively explained the basic phenomena of the vapor–liquid phase transition such as the two-phase coexistence, critical point, supercooled and superheated states, but also could be used to quantitatively predict many properties of a substance near the critical point. Today, all who face the problem of predicting physical properties would agree with the statement by Guggenheim that the corresponding-states principle could safely be regarded as the most useful derivation of the Van der Waals' equation of state. The corresponding-states principle gradually became the basis to predict equilibrium properties of pure fluids and mixtures, reduced equation of state, and transport properties. The universal form of corresponding-states principle is discussed with modern theories of equation of state investigating the vital coefficients of the series expansion in the universal form of the corresponding-states principle, which may be considered as the basis of an understanding of the corresponding-states principle at the end of the chapter.