A particular bubble cap distillation column for methanol + water has 12 trays numbered from top to bottom. Each tray is composed of 4 kg of materials and holds 1 kg of liquid. The heat capacity of the tray materials is 6 J/g-K and the heat capacity of the liquid is 84 J/mol-K = 3.4 J/g-K. During start-up, the feed is turned off. Roughly 15 minutes after the reboiler is started, tray 12 has started to boil and the temperature on tray 11 begins to rise. The reboiler duty is 6 kW and the heat loss is negligible. Tray 11 starts at 25 °C and the temperature of the liquid and the tray materials is assumed the same during start-up. Assume the liquid inventory on Tray 11 is constant throughout start-up.
(a) Tabulate and plot the temperature versus time for tray 11 until it starts to boil at 70 °C. (b) Plot the vapor flow V12 as a function of time.
