Equations of state for fluids: The Dieterici approach revisited

Abstract

In 1873, van der Waals proposed a simple equation of state that qualitatively described the phase behavior of fluids. Since then, the principles behind the van der Waals equation have been used and refined countless times in the quest for an accurate equation of state. Despite the enormous amount of work reported, the goal of a simple and accurate equation of state for even relatively simple systems, such as monatomic or polyatomic gases, has proved elusive. Therefore, the analysis of phase equilibria with equations of state is more often than not an exercise in data fitting rather than genuine prediction. In this work, we revisit the early work of Dieterici. When coupled with modern developments in equations of state, this little used approach has the potential of generating useful equations of state. To illustrate the usefulness of the Dieterici formula, we use it to derive a simple equation of state based on the Carnahan–Starling hard-sphere term and van der Waals interactions. This simple approach yields more accurate predictions of the phase co-existence of fluids than the traditional additive approach used to develop equations of state.