Given: A restaurant kitchen has the dimesions 6m x 6m x 2m. Carbon monoxide (CO)

Question

Given: A restaurant kitchen has the dimesions 6m x 6m x 2m. Carbon monoxide (CO) is emitted from the cooking stoves at a rate of 1 mg min-1. Clean air (i.e. negligible CO concentration) enters the room, the room is well mixed, and the air exiting the room from the ventilation system leaves at the same flow rate as the clean air entering the room. Find: (a) What is the minimum flowrate (in m3 hr-1) needed to maintain a maximum CO concentration of 1 ppm in the room at steady-state? (b) What is the residence time of air in the room?

Explanation / Answer

The room has a volume of 1000 cu ft. Let x be the amount of CO in the air, 60 cu ft initially. Every minute, 0.1 cu ft more of CO enters and 1/100 of x leaves (10 cu ft / 1000).Set up the DE: dx/dt = 0.1 - x/100 = (10 - x)/100 dx/(10 - x) = dt/100-ln (10 -x) = t/100 + Cln(10 - x) = -t/100 + C10 - x = Ce-t/100x = 10 - Ce-t/100 ; and when t = 0, x = 60 so C = -50x = 10 + 50e-t/100Solve for x = 30: 30 = 10 + 50e-t/1000.4 = e-t/100-t/100 = ln(0.4) = -0.916291t = 91.63 sec

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