The volume of air in a kitchen is 100 m^3. The stove in the kitchen has been lef
ID: 1073221 • Letter: T
Question
The volume of air in a kitchen is 100 m^3. The stove in the kitchen has been left on, and is emitting CH_4 at a rate of 5 L/min. (1000 L= 1 m^3) This has been going on for some time, and the mole fraction of CH_4 in the kitchen has reached 4% by volume. Coming into the kitchen, we smell the gas and run to open two windows to let in fresh air. Fresh air comes into the room at a rate of 5000 L/min through one window, and out the other window at the same rate (5000 L/min). We run out of the house, without turning off the gas. How much time is needed until the concentration (volume fraction) of methane in the kitchen air drops down to 0.5%?Explanation / Answer
otal air volume in kitchen is 100 m3.
when windows has been opened the fresh air is coming at 5000L/min = 5m3/min
Also going out from other window as same rate i.e.5m3/min
CH4 emission rate is 5L/min = 0.005m3/min
CH4 in the kitchen air is 4% i.e.4m3
Air changes for kitchen is = 5/100 =0.05m3/min
CH4 emission rate is 5/1000=0.005m3/min
Time required to reach CH4 volume from 4m3 to 0.5m3 is = (4-0.5)/0.05 =70 min
additional amount of emission during this time is = 0.005*70=0.35m3 =0.35/0.05=7min
so total time required is 70+7 = 77mins
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