Could you solve this maths problem for me?
in a car with capacity 3000 litres. (there is already air in the car)
Gas cylinder is 9% nitrogen and 91% helium.
The gas cylinder size is 7.57m3 or 7570 litres.
The gas flow is 100 litres per minute.
how long would it take to achieve a 1% concentration of nitrogen in the car?
- Ian HLv 76 months ago
It would never happen. With many gas cylinders the nitrogen percentage would approach the cylinder ratios of 9% nitrogen and 91% helium, so would need further quantities of gases other than nitrogen to get down towards 1%.
Clearly the oxygen removal would be life threatening so do not do this.
But suppose you asked how long would it take to achieve a 10% concentration of nitrogen in the car?
The changes would be continuous of course; but to get some sort of rough
and ready estimate consider step changes of 1 minute.
Start: 2400 of nitrogen and 600 oxygen
Add: 9 of nitrogen and 91 of helium
Result; 2409 nitrogen + 600 oxygen + 91 helium = 3100
But we must assume that the car is not like a balloon expanding with the added gas. To maintain constant volume let us assume that 100 litres leaks away, as fast as you like leaving 30/31 of those contents calculated
Result: 2331.29 nitrogen + 580.645 oxygen + 88.065 helium
Nitrogen: At each step add 9 and multiply by 30/31
You could try lots of steps like that, (computer program?), but cheating a bit more we could make the somewhat unjustified assumption that each step reduces by 2331.29/2400
So we ask what is n for 2400*(0.97137)^n = 300 ?
That gives 71.5 minutes.
The gas cylinder runs for about 75 minutes. The approximate volume of nitrogen based on these (dubious) calculations would be
2400*(0.97137)^75 ~ 272 litres wich is about 9% nitrogen.
Then you might have to open the car to start on another cylinder !
Note: Smaller steps in time would give better estimates. Perhaps someone would like to introduce calculus, to represent concentration changes dC for infinitesimal time advances dt.
- Steve4PhysicsLv 76 months ago
EDIT in reply to your comment/correction:
I’m assuming the question is:
How long would it take to achieve a 1% concentration of argon in the car if:
car’s capacity = 3000 litres;
gas cylinder’s capacity = 7570litres;
gas cylinder supplies 9% argon and 91% helium by volume;
gas flowrate is 100 litres per minute.
Since flow rate is 100 litres/minute and argon is 9%, argon enters car at 9 litres/minute.
1% of 3000litres = 30litres. So we want to know how long ii takes to supply 30 litres or argon at 9 litres/minute. This gives the 1% argon in the car.
Time = volume / flow rate = 30/9 = 3.3minutes (=3mins 20s)
Note. 30litres of argon (9%) have been transferred, so the total volume of gas transferred = 30 x 100/9 = 3000/9 = 333.3 litres which is less than the tank's capacity (7570litres); so the tank has (more than) sufficient gas to do the job.
But this is a very silly/unrealistic question!
Trick (or maybe incorrect) question.
The air in the car is already 80% nitrogen (atmospheric composition).
The gas from the cylinder is 9% nitrogen.
So, however much gas is added, the nitrogen level is *always above 9%*. It can never be 1%.
- Anonymous6 months ago
about 3 min.........