Spinodal and equation of state of liquids in the region of reduced stability

On the basis of the analysis of experimental data, the equations of a binodal $\omega=\pm B\theta^{0,323}+(B-1)\theta$ and a spinodal $\omega=\pm B \frac{2-l}{l}\theta^{0,323}+(B-1)\theta$ are obtained, where $\omega=\rho/\rho_k-1,\theta=1-T/T_k$; the plus sign refers to the liquid branch and the minus sign to the vapor branch. The value of l is universal and close to 1.20; B is an individual characteristic. New variables characterizing the remoteness of the state of the material at temperature T and density $\rho$ relative to the spinodal and the "rectilinear-diameter" line, $\omega = (B-1)\theta$, are introduced. In the new variables $\tau = \frac{l}{2-l}[\omega+(B-1)\tau], X=\tau+|Y|^{1/0,323}$ where $\tau=-\theta$, the spinodal converts to the axis Y, the "rectilineardiameter" line to the axis X; the binodal and critical isotherm are shown by symmetric curves. For the region adjacent to the spinodal, an equation of state is proposed: $\pi-\pi_c = \Pi YX^{1,26}$, where $\pi=\rho/\rho_k$; $\pi_c$ is the reduced pressure at the spinodal (for $\theta>0$) or the pressure at Y = 0 (for $\theta<0$). This equation describes the singularity of the compressibility at the spinodal and at the critical point, and ensures the calculation of the PVT relations in the metastable region, at the binodal, and in the adjacent regions of state.