In the paragraph immediately before Example 3-1, the following sentence occurs: " \(\mathrm{Q}_{\mathrm{c}}\) is proportional to \((1+\mathrm{L} / \mathrm{D}) \mathrm{F}\), and \(\mathrm{Q}_{\mathrm{R}}\) is proportional to \(\mathrm{F}\) and linearly dependent on \((1+\mathrm{L} / \mathrm{D})\). ." What is the practical difference between proportional and linearly dependent?

Example 3-1

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A steady-state, countercurrent, staged distillation column is to be used to separate ethanol from water. The feed is a 30 wt % ethanol, 70 wt % water mixture at 40C. Flow rate of feed is 10,000 kg/h. The column operates at a pressure of 1 kg/cm. The reflux is returned as a saturated liquid. A reflux ratio of Lo/D 3.0 is being used. We desire a bottoms composition of XB = 0.05 (weight fraction ethanol) and a distillate composition of xD = 0.80 (weight fraction ethanol). The system has a total condenser and a partial reboiler. Find D, B, Qc, and QR- =