Today Puzzle #550
Puzzle No. 550鈥� Wednesday 21 August
On 9 Aug there was a news story on the 大象传媒 website (/news/world-africa-49290641) saying that an odour had arisen and the speaker needed to evacuate the chamber. If the debating chamber is 10,000m3 and the ventilation rate is 10 m3/s, assuming the air is well mixed how long does it take for the concentration of pollutants to halve?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution
Click here for the answer
The answer isn’t as simple as the time to displace half the volume, which would be (5000m3) / (10m3/s) = 500s. The reason is that the fresh air coming in mixes with the air in the space, so that the air which leaves over is not leaving with the initial concentration except at the very beginning. Instead, the concentration c of pollutants at time t in a room of volume V, ventilated at a rate v, is given by the expression c=C exp(-vt/V) where C is the initial concentration. We seek the solution of c/C=0.5. This is given by ln(0.5) = -v x t / V, so t= 0.69 x 10000 / 10 = 693 seconds (i.e. 11.5 minutes).
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