Method for constructing fundamental equation of state based on the relationships of similarity theory and scaling hypothesis

Abstract

On the basis of the new phenomenological theory of the critical point, the method for constructing fundamental equation of state (FEoS) of liquid and gas has been developed. Within the framework of the method proposed, a number of requirements are met: a) in the region of low densities, the transition of FEoS to the virial equation; b) in a wide vicinity of the critical point, the transition of FEoS to the Berestov equation; c) taking into account asymmetry in the behavior of the isochoric heat capacity, isothermal compressibility coefficient and other thermodynamic functions relative to the critical isochore. To calculate the singular component of FEoS, the Pokrovsky transformations and the similarity relation connecting the parameters of a lattice gas and a real liquid are used. It has been shown that such an approach requires only knowledge of the density data on the saturation line and the values of the critical indices to calculate the singular component of FEoS. This allows us to exclude data on the isochoric heat capacity from the calculation scheme and recommend this method for constructing FEoS of substances little studied in the vicinity of the critical point. The method has been tested on the example of constructing carbon dioxide FEoS. The workspace of FEoS has been set: by temperature 216.592 ≤ T ≤ 1100 K and by pressure up to 200 MPa. The results obtained are discussed.