Gas cylinder-volume of air, how long it will last

[NDbogan]

A gas cylinder contains 2 cubic metres of air at a pressure of 700 atmospheres at room temperature.

Calculate the volume of air in the cylinder at one atmospheric pressure at room temperature.

If the air is drawn from the cylinder at the rate of 15 litres/minute, how lonf will the cylinder last?


I have no idea how to work this out. A friend and I thought it may have to do with mass density D=m/V but then we just got more confused.

If you would be able to help, that would be great. If you could show calculations and explanation (or just calculations if it's too much ) much appreciated.

 

[Furby]

I'm pretty sure you would use the ideal gas law.

PV=nRT

 

[mgb_phys]

The question is a little imprecisely worded.
Does it mean 2m^3 at 700bar or 2m^3 at 1bar compressed to 700bar?
(I'm guessing #2 because 2m^3 is approx the volume of room pressure air that would fit into a scuba tank)

If it is #2 then you simply need to know how many litres are in 1cubic metre.

 

[NDbogan]

i ended up doing it using boyle's law
P1 x V1/T1=P2 x V2/T2
because temp is a constant
P1 x V1=P2 x V2
where
P1= 700 atm = 10290psi
V1=2m^3= .002L
P2=14.7 psi
V2=? because this is want we were to find
so
V2=(10290 x .002)/14.7
= 1.4L

probably isn't correct but i did try with some other figures and this just sounded more correct

 

[mgb_phys]

That's the correct technique, there is no need to convert to PSI, as long as your units of pressure and volume are the same on both sides of the equation.

The second part you don't need to worry about the pressure. Assuming you started with 2m^3 at atmospheric P and the 15litres are at atmospheric P then it's just a question of converting litres to m^3

 

[Furby]

V1=2m^3= .002L

Isn't 1m³=1000L?

Correct me if I'm wrong, because there appears to be some dissonance, but I'm pretty assured I'm reading the problem as:

A gas has a volume of 2m³ and a pressure of 700atm.
What is the volume of the same gas at a new pressure of 1 atm?
Temperature is constant.

Thus V₂=/=1.4L?

 

[mgb_phys]

If that's how you read the question then 2m^3 at 700bar (that's an expensive bit of engineering - but not really a cylinder) = 1400m^3 at room pressure or 1,400,000 litres.
Then at 15l/min that's just 1,400,000/15 mins.

Alternatively if you read it has 2m^3 compressed to 700bar then that's just 2000litres an so a rate of 2000/15 mins.

In engineering you normally quote the volume of compressed gas cylinders by specifying the volume at room pressure.
So a Scuba tank is called "80cubic ft" - meaning that 80 cu ft of air is compressed to 200bar into a tank with an actual internal volume of 80/200 = 0.4cu ft.