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The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is named after Dutch physicist Johannes Diderik van der Waals . It is an equation of state that relates the pressure , temperature , and molar volume in a fluid .
According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. [1] [2]
The van der Waals equation predicts that at low temperatures liquids sustain enormous tension---a fact that has led some authors to take the equation lightly. In recent years measurements have been made that reveal this to be entirely correct. [43]
His new formula revolutionized the study of equations of state, and was the starting point of cubic equations of state, which most famously continued via the Redlich–Kwong equation of state [5] and the Soave modification of Redlich-Kwong. [6] The van der Waals equation of state can be written as
The van der Waals equation of state may be written as (+) =where is the absolute temperature, is the pressure, is the molar volume and is the universal gas constant.Note that = /, where is the volume, and = /, where is the number of moles, is the number of particles, and is the Avogadro constant.
A second major discovery was the 1880 the law of corresponding states, which showed that the Van der Waals equation of state can be expressed as a simple function of the critical pressure, critical volume, and critical temperature. This general form is applicable to all substances (see Van der Waals equation [broken anchor].)
Critical isotherm for Redlich-Kwong model in comparison to van-der-Waals model and ideal gas (with V 0 =RT c /p c) The Redlich–Kwong equation is another two-parameter equation that is used to model real gases. It is almost always more accurate than the van der Waals equation, and often more accurate than some equations with more than two ...
Configuration integral – Function in thermodynamics and statistical physics; Dynamic pressure – Kinetic energy per unit volume of a fluid; Gas laws; Internal energy – Energy contained within a system; Van der Waals equation – Gas equation of state which accounts for non-ideal gas behavior