Simplified Gas State Equations at Saturation and Isotherm

Abstract

This paper further simplifies the gas state equation (EOS) by introducing a thermodynamic constant, P_c^*, into the equation, a theoretical pressure that all gas converts into liquid. In the gas–liquid saturation system, linear regressions of ln P–ln x₂ from M.P. to T_c give P = P_c^*x₂. It verifies Henry’s law of gas solubility. Meanwhile, P_c^*s for most substances are found in the range of 15–16, i.e., 3.269–8.886 MPa. Hence, EOS deforms into $P=\frac{P_c^{*}RT}{{10}^{-3}{P}_c^{*}{V}_G+RT}$. Isotherm is a forced equilibrium system sustained by an outer force. Isothermal EOS is derived by differentiating heat over V_G. $P=\frac{(\beta +\gamma )P_c^{*}RT}{{10}^{-3}{P}_c^{*}{V}_G+(\beta +\gamma )RT}$, where $\gamma =-{\left[\frac{\partial \ln P}{\partial {\ln V}_G}\right]}_T$ or $\gamma =-{\left[\frac{\partial \ln x_2}{\partial {\ln V}_G}\right]}_T$. Empolying Ar as an example, EOS are demonstrated over the whole pressure range, 0–1000 MPa, including the supercritical state. Applausive results are obtained in the pressure range before the gas–liquid transition and high temperatures (1000–2000 K), respectively. The supercritical state of intermediate temperatures (160–800 K) is likely liquid-like. Hence, EOS is not fittable.