A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and volume = 14 L (0.014 m3) at T = 295 K. How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.1 L/min?

901.52 minutes

Step-by-step explanation:

To do this, we need to assume that the temperature is constant in all the process here. If this is true, then we can also assume that this is a case of an isothermal expansion, therefore, the expression to use is the following:

P1V1 = P2V2

Let P2 the atmospherical pressure, and V2 would be the remaining volume of the oxygen. The atmospherical pressure reported is 1 atm or 101.3 kPa

Solving for V2 in this expression we have the following:

13,800 * 14 / 101.3 = 1907.21 L

As this is a low pressure gas, part of it's volume will remain in the cylinder, so, we have to substract these 14 L to V2 to get the real volume of the remaining gas:

1907.21 - 14 = 1893.21 L

And we have now the flux which is 2.1 L/min, so:

t = V/F

t = 1893.21 / 2.1

t = 901.52 min.