Key words: regular equation of state, scaling, crossover function, critical point, approximation of Р-ρ-Т data, helium, sulfur hexafluoride
A new joint equation of state (EOS) is proposed to describe the Р-ρ-Т data on 4Не and
SF6 in a wide range of densities -1 < Δρ < 1,
where Δρ = (ρ-ρc)/ρc, and reduced tempe
ratures -0,3 < τ < 0,3, where τ = (T - Tc)/Tc,
including the critical region. A dimensionless joint EOS is written in terms of explicit
functions of Δρ and τ, and includes a regular
part that approximates experimental data beyond a critical region, a nonparametric scaling
equation of state which adequately describes the P-&rho-T data near critical
points and a crossover function that smoothly combines these two equations of state. A crossover
function is proposed as a classical exponential function, which reduces the influence of
density and temperature fluctuations typical for a critical region and damping at
increasing distance from the critical point. Two various equations of state were taken
as a regular part of the joint EOS: 1) a new cubic EOS proposed in this work with five
system-dependent fitting constants, three of which are conjugated by conditions in a
critical point; 2) a physically valid Kaplun Meshalkin EOS with seven fitting constants
(three of which are also related to critical conditions) to describe the data within the
above limits, including liquid state. As a scaling part of EOS, a nonparametric scaling
equation of state (as an explicit function of reduced variables Dr and t with three
system-dependent constants) suggested by authors is used. In the joint EOS, like in
classical equations of state, the (∂P/∂v)T=0,
and (∂2P/∂v2)T=0
conditions are satisfied in a critical point and binodal and spinodal are present.
Approximation of the most accurate data for 4Не and SF6 by the new
joint EOS indicates that this equation correctly describes the Р-ρ-Т data
within error ranges of ±0,5% with respect to pressure.