Investigation of gas and liquid densities on the saturation line: some scaling models and numerical data on H2O example

Abstract

Some thermodynamic functions are discussed in the work. They have a form, F(τ,D,C), and are associated with one of thermodynamic properties, F, at the saturation line (the fluid density (ρ1), the gas density (ρg), the order parameter (fs), the middle diameter (fd), etc.) in a specified neighborhood of the critical temperature, Tc. F (τ,D,C) model follows to the scale theory of critical phenomena and includes critical characteristics, D = (α, β, Tc · ), a relative temperature, τ = (Tc – T )/Tc, indexes, α, β, and adjustable coefficients, C. A model of fd = (ρ1 + ρg) (2ρc)−1 − 1 is investigated; it contains scaling and linear components. Another model, fd (τ,D,C), is developed in the work. The model is referred to as a combined scaling model. Its structure contains a component with the index, 2β, a component with the index, (1 − α), and regular components. Similar combined models are developed including fs(τ,D,C), ρ1(τ,D,C) and ρg(τ,D,C). There is considered a nonlinear technique, which allows us to calculate D characteristics and adjustable coefficients of these models. Due to the technique, we have determined numerical values those are related to the combined scaling models and based on tabulated (ρ1, ρg,T) data of H2O in a wide temperature range including the critical region. We have calculated data on F = (ρ1,ρg, fs, fd) those are placed in a wide temperature range, 1 10−5 < τ < 0.1, including the extent of an extrapolation. It is made a comparison of these values with relevant data those are obtained with an usage of known literary equations.