Correlation of Zeno (Z = 1) line for supercritical fluids with vapor-liquid rectilinear diameters

摘要

For a wide range of substances, extending well beyond the regime of corresponding states behavior, the contour in the temperature-density plane along which the compressibility factor Z = P/(rho)kT is the same as for an ideal gas is nearly linear. This Z = 1 contour, termed the Zeno line, begins deep in the liquid region and ascends as the density decreases to the Boyle point of the supercritical fluid, specified by the temperature T(sub B) for which (dZ/d(rho))(sub T) = 0 as (rho) (r arrow) 0; equivalent, at T(sub B) the second virial coefficient vanishes. The slope of the Z = 1 line is (minus)B(sub 3)/(dB(sub 2)/dT), in terms of the third virial coefficient and the derivative of the second, evaluated at T(sub B). Previous work has examined the Zeno line as a means to extend corresponding states and to enhance other practical approximations. Here the authors call attention to another striking aspect, a strong correlation with the line of rectilinear diameters defined by the average of the subcritical vapor and liquid densities. This correlation is obeyed well by empirical data for many substances and computer simulations for a Lennard-jones potential; the ratios of the intercepts and slopes for the Zeno and rectilinear diameter liens are remarkably close to those predicted by the van der Waals equation, 8/9 and 16/9, respectively. Properties of the slightly imperfect fluid far above the critical point thus implicitly determine the diameter of the vapor-liquid coexistence curve below the critical point.