Use a process simulator to determine the flow rate of saturated vapor benzene at \(176.2^{\circ} \mathrm{F}\) and \(1 \mathrm{~atm}\) to be mixed with \(100 \mathrm{lbmol} / \mathrm{hr}\) of liquid benzene to raise its temperature from 25 to \(50^{\circ} \mathrm{F}\). Prepare a good initial estimate. (Note: \(\lambda_{\mathrm{NBP}}=13,200 \mathrm{Btu} / \mathrm{lbmol}\), \(c_{p}=0.42 \mathrm{Btu} / \mathrm{b}^{\circ} \mathrm{F}\).)