A distillation column separating ethanol from water is shown in the following figure. Pressure is \(1 \mathrm{~kg} / \mathrm{cm}_{2}\). Instead of having a condenser, a stream of pure, saturated liquid ethanol is added directly to the column to serve as the reflux. The feed to the column is \(40 \mathrm{wt} \%\) ethanol at \(-20^{\circ} \mathrm{C}\). Distillate concentration is \(80 \mathrm{wt} \%\) ethanol, and bottoms composition is 5 wt \(\%\) ethanol. A total reboiler is used, and the boilup is a saturated vapor. The reflux stream is input at \(\mathrm{C}=1000 \mathrm{~kg} / \mathrm{h}\). Find the external boilup rate, \(v\). Note: Set up the equations, solve in equation form for \(\mathrm{v}\), including explicit equations for all required terms, read off all required enthalpies from the enthalpy composition diagram (Figure 2-4), and then calculate a numerical answer.

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