Hello every one, can any one answer me about this question: A room has a volume of 800 cubic feet. The air in the room contains chlorine 0.1 gms. per cubic feet.Fresh air enters at the rate of 8 cubic feet per minute. The air is well mixed and flows out of the room at the same rate.
(i)Compute the chlorine concentration in the room as function of time?
(ii)Suppose the flow rate of the air is adjustable, find the flow rate required reducing the chlorine concentration to 0.001 grm. per cubic feet in 20 minutes?
Since the assumption is that air is well-mixed, you should use the complete mixing model.
Volume of room (V) = 800 ft3
Air flow (F) = 8 ft3/min
Time constant (tau) = V/F = 100 min
Initial concentration C0 = 0.1 g/ft3
Cl2 concentration at room outlet can be calculated from the following equation:
C(t) = C0 * exp(- t / tau).
The model can be set up using an Excel spreadsheet. To reduce the Cl2 concentration from 0.1 g/ft3 to 0.001 g/ft3, use the Data / What-if Analysis / Goal-seek function such that C(20 min) = 0.001 by varying F. You obtain F = 184.21 ft3/min (minimum air flow).
See attached graph.
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