Physical Sciences and Mathematics Commons^™

The Van Der Waals Equation As A Cubic, Carl W. David

Chemistry Education Materials

The van der Waals (from his thesis of 1873) equation is a cubic in the molar volume. Since this is the first equation of state studied in chemistry more complicated than the ideal gas equation, it is noteworthy that the solution of this cubic is rarely if ever addressed. When (lowering the temperature) the two imaginary roots coalesce with the real root of the van der Waals equation we have the critical point. At Kelvin temperatures below Tc. the equation has three real roots; we explore obtaining those roots to aid in the Maxwell construction required to obtain the vapor …