Abstract
Correlation dependence \({{\Gamma }_{0}} = {{\Gamma }_{0}}(\gamma ,\omega ,{{Z}_{c}})\) is established between critical amplitude \({{\Gamma }_{0}}\) of coefficient isothermal compressibility \({{K}_{T}}\) , acentric factor ω, critical compressibility factor \({{Z}_{c}}\) , and critical index \(\gamma \) . A description of critical amplitude \(\Gamma _{0}^{{(e)}}\) 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 \({{\Gamma }_{0}} = {{\Gamma }_{0}}(\omega )\) , and of Ivanov (2008) in the form \({{\Gamma }_{0}} = {{\Gamma }_{0}}(\gamma )\) , are vastly inferior to the proposed correlation \({{\Gamma }_{0}} = {{\Gamma }_{0}}(\gamma ,\omega ,{{Z}_{c}})\) in their accuracy of calculation. Three intervals of the critical index \(\gamma \) are considered: \(\gamma \in [1,1.242]\) (interval I), \(\gamma \in [1.1,1.242]\) (interval II), and \(\gamma \in [1.239,1.242]\) (interval III). In intervals II and III, the dependence of \(\Gamma _{0}^{{(e)}}\) on \(\gamma \) is close to linear, so it is described by others that are linear in respect to ω, \({{Z}_{c}}\) , and \(\gamma \) . The dependence of \(\Gamma _{0}^{{(e)}}\) on \(\gamma \) is nonlinear in interval I. The correlation for \({{\Gamma }_{0}}\) has the form \(\Gamma _{0}^{*} = {{C}_{0}} + {{C}_{1}}\omega + \) \({{C}_{2}}Z_{c}^{{ - n}} + {{C}_{3}}{{\gamma }^{{ - g}}}\) , where \(g = 9.1\) and \(n = 2\) . It is established that in all three considered intervals of \(\gamma \) , the accuracy of nonlinear correlation \(\Gamma _{0}^{*}\) is superior to the others studied in this work for \({{\Gamma }_{0}}\) . Deviations of \({{\Gamma }_{0}}\) from \(\Gamma _{0}^{{(e)}}\) in, e.g., interval I for correlations of Gerasimov, Ivanov, Perkins et al., and Abbaci, and for linear correlations and correlation \(\Gamma _{0}^{*}\) 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.
