Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

# Could you solve this maths problem for me?

Update:

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?

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• 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.

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!

END EDIT

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%.

• Steve4Physics
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