Correlation between a Critical Index and the Critical Amplitude of a Saturation Line

Abstract

Correlation dependence B₀ = B₀(β, ω) is determined as a function of β and acentric factor ω, based on an analysis of experimental information about critical amplitude B₀ and critical index β of the saturation line. The proposed correlation uses 20 substances for which there are experimental data on B₀ in ranges 3.15 ≤ β ≤ 3.85 and ω ≤ 0.365. It is established for all considered substances that the absolute values of the maximum relative deviations \(\delta {{B}_{{0,{\text{max}}}}}\) of the experimental values of critical amplitude \({{B}_{{0,{\text{exp}}}}}\) from ones calculated using correlation B₀(β, ω) are no greater than 6%. Some values of \({{B}_{{0,{\text{exp}}}}}\) for H₂O (|\(\delta {{B}_{{0,{\text{max}}}}}\)| = 6.64%), SF₆ (|\(\delta {{B}_{{0,{\text{max}}}}}\)| = 8.75%), and ⁴He (|\(\delta {{B}_{{0,{\text{max}}}}}\)| = 10.3%) are exceptions. In the course of this work, D.Yu. Ivanov’s hypothesis of (2007) of the universality of the critical amplitude B₀ (up to the critical index β) is considered. It is shown that his proposed correlation dependence B₀ = B₀(β) produces values of |\(\delta {{B}_{{0,{\text{max}}}}}\)| that reach 35%. It is also established that new correlation B₀ = B₀(β, ω) agrees with correlation dependence B₀ = B₀(ω) proposed by R. A. Perkins et al. (Int. J. Thermophys. 34, 191 (2013)) at β = 0.326. However, deviations δB₀ for all considered groups of substances are greater than 10% when B₀ = B₀(ω), even for β ≥ 0.34. The assertion that amplitude B₀ characterizes a substance is confirmed because it is affected by the nonsphericity of the molecules, which is characterized by ω. The possibility of using new correlation B₀ = B₀(β, ω) to determine the critical amplitude of the saturation line of ⁴He is discussed as well.