Oxygen mixture problem - first-order differntial

[Nakita]

Hi, I'm just going through my study guide and this problem has stumped me. I believe I could work it if I just knew how to set it up.

Oxygen flows through one tube into a liter flask filled with air, and the mixture of oxygen and air (considered well stirred) escapes through another tube. Assuming that air contains 21% of oxygen, what percentage of oxygen will the flask contain after 5L have passed through the intake tube?

I'm guessing the initial condition is at t = 0, y = .21 , but I don't know how to go from there. Can anyone help?

 

[DrMike]

Hi, I'm just going through my study guide and this problem has stumped me. I believe I could work it if I just knew how to set it up.

Oxygen flows through one tube into a liter flask filled with air, and the mixture of oxygen and air (considered well stirred) escapes through another tube. Assuming that air contains 21% of oxygen, what percentage of oxygen will the flask contain after 5L have passed through the intake tube?

I'm guessing the initial condition is at t = 0, y = .21 , but I don't know how to go from there. Can anyone help?

The clue is here :

what bla bla bla after 5L have passed through

It may be best to set up the problem as 'proportion of oxygen' vs 'volume passed through', rather than vs 'time'.

If P(v) is the proportion of Oxygen when a volume v has passed through, then when v=0, P=.21, like you said.

Then, you need to set up the DE - at any time, if you pass an extra dv of oxygen into the tank, then an amount Pdv comes out. The change in the proportion is dP = dv - Pdv (since the tank is 1L), therefore, dP/dv = 1-P.

Now you have a DE, and an initial condition.