Plot P r versus r for the Peng-Robinson equation with T r = [0.7,0.9,1.0], showing both vapor

Plot P_r versus ρr for the Peng-Robinson equation with T_r = [0.7,0.9,1.0], showing both vapor and liquid roots in the two-phase region. Assume ω = 0.040 as for N₂. Include the entire curve for each isotherm, as illustrated in Fig. 7.1. Also show the horizontal line that connects the vapor and liquid densities at the saturation pressure. Use lines without points for the theoretical curves. Estimate T_r^sat by log(P_r^sat) = 2.333(1 + ω) (1 - 1/T_r^sat).

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8 00 7 6 LO 5 P (MPa) A 3 2 1 0 1.3 T₁ = 1.1 0.01 1.0 0.9 1 0.02 . I I 0.8 0.03 6 5 01 4 P (MPa) W 2 1 0 0 1.3/ / T, = 1.1 1.0 0.9 0.8 + 0.002 0.004 0.006 0.008 p(mol/cm³) p(mol/cm³) Figure 7.1 Comparison of the PpT behavior of methane (left) and pentane (right) demonstrating the qualitative similarity which led to corresponding states' treatment of fluids. The lines are calculated with the Peng-Robinson equation to be discussed later. The phase envelope is an approximation sketched through the points available in the plots. The smoothed experimental data are from Brown, GG, Sounders Jr., M., and Smith, R.L., 1932. Ind. Eng. Chem., 24:513. Although not shown, the Peng-Robinson equation is not particularly accurate for modeling liquid densities.