Problem $3.$ A distillation column is separating ethanol $(E)$ from water $(W)$ at a pressure of $1k\frac{g}{c}{m}^2.$ The column has one feed stream, one side stream, a total condenser, and a partial reboiler. The external reflux ratio, $\frac{L_0}{D}=3\mathrm{.}5$ for this separation. The two$-$phase feed is $40wt\%$ ethanol at $90C$ and is fed at a rate of $100k\frac{g}{m}in.$ The liquid side stream is $64wt\%$ ethanol and leaves at a rate of $12k\frac{g}{m}in.$ The bottoms product is $98wt\%$ water and the distillate product is $93wt\%$ ethanol. The distillate and reflux are both saturated liquid. Use Figure $2-4$ for enthalpy data.

a$.$ Find the flow rates $D$ and $B$ in $k\frac{g}{m}in.$

b$.$ Given the information above, calculate $Q_c$ and $Q_R$ in kca$\frac{l}{m}in.$ Show the enthalpy values of all streams in kca$\frac{l}{k}g$ and the vapor flow rate $V_1$ in $k\frac{g}{m}in.$