Method for constructing fundamental equation of state that satisfies the scaling theory and applicable for substances insufficiently explored in the critical point vicinity

Abstract

Here, the authors discuss the problem of describing the equilibrium properties of a substance in the vicinity of the critical point on the basis of the fundamental equation of state (FEoS) of a liquid and a gas in the absence of experimental information about the calorific properties of a given substance in this field of state parameters. FEoS has the following characteristics: in the region of low densities, FEoS transforms to the virial equation of state; in the asymptotic vicinity of the critical point, FEoS meets the requirements of the scaling theory of critical phenomena. The method is based on a new representation of the scaling hypothesis based on the Scofield–Litster–Ho linear model (LM), the Benedek hypothesis and the Lysenkov–Rykov ratio (LR) which establishes the relationship between LM parameters and the real liquid using the Pokrovsky transformations. Testing of the proposed method for constructing FEoS has been carried out using the example of describing the equilibrium properties of argon. It has been ascertained that the use of the LR ratio has allowed, firstly, reducing the number of individual FEoS parameters and, secondly, excluding the data about isochoric heat capacity CV related to the critical point wide vicinity from the calculation scheme.