A New Correlation for the Critical Amplitude of the Coefficient of Isothermal Compressibility

Correlation dependence Γ ₀ = Γ ₀(γ ,ω ,Zc) is established between critical amplitude Γ ₀ of coefficient isothermal compressibility KT , acentric factor ω, critical compressibility factor Zc , and critical index γ . A description of critical amplitude Γ ₀^(e) of 24 substances is used as an example to show that the correlations of Gerasimov (2003); Perkins et al. (2013); and Abbaci (2024) in the form Γ ₀ = Γ ₀(ω ) , and of Ivanov (2008) in the form Γ ₀ = Γ ₀(γ ) , are vastly inferior to the proposed correlation Γ ₀ = Γ ₀(γ ,ω ,Zc) in their accuracy of calculation. Three intervals of the critical index γ are considered: γ ∈ [1,1.242] (interval I), γ ∈ [1.1,1.242] (interval II), and γ ∈ [1.239,1.242] (interval III). In intervals II and III, the dependence of Γ ₀^(e) on γ is close to linear, so it is described by others that are linear in respect to ω, Zc , and γ . The dependence of Γ ₀^(e) on γ is nonlinear in interval I. The correlation for Γ ₀ has the form Γ ₀* = C₀ + C₁ω + C₂Zc^ - n + C₃γ ^ - g , where $$g = 9.1$$ and $$n = 2$$ . It is established that in all three considered intervals of γ , the accuracy of nonlinear correlation Γ ₀* is superior to the others studied in this work for Γ ₀ . Deviations of Γ ₀ from Γ ₀^(e) in, e.g., interval I for correlations of Gerasimov, Ivanov, Perkins et al., and Abbaci, and for linear correlations and correlation Γ ₀* proposed in this work, are estimated using absolute average deviations 22.1, 8.5, 16.5, 21.6, 6.6, 5.5, and 2.7%, respectively.