# Given a box contain 50m3 of gases, how fast should I pump gases into?

1. Sep 3, 2014

### td21

1. The problem statement, all variables and given/known data

Given a house(with ventilation system) contains 50m3 of gases, what is minimum rate should I pump gases into the box so that the box contains completely new gas from outside in an hour? (Challenge question)

2. Relevant equations

rate = volume/time

statistical mechanics
fluid dynamics

3. The attempt at a solution

50m3/60min = 5/6 m3/min?
I do not believe the question being that simple I think some old gases will remain inside. Also, should the the answer be 10/6 m3/min (the double)?

2. Sep 3, 2014

### BvU

Yeah, could well be they try to trick you. Context decides here if it's really that simple or whether you should pump at infinite rate (and even then: some gas molecules might make it from the exhaust to the pump inlet ! -- this is not unrealistic: last week we had to evacuate our building because pentadiene was nicely sent outside by the exhaust system, but weather conditions made it return to the 'fesh air' inlet faster than anybody had ever foreseen!)

Taking the double isn't so smart: arbitrary. Either 5/6 or infinity (but then you get blown out too, probably, so maybe 5/6 is the better gamble) !

Not very physics, this exercise...

3. Sep 3, 2014

### td21

Thank you for the response. What if no gas molecules might make it from the exhaust to the pump inlet? This should be a pretty good assumption.

The reason for me to consider double is that the gas pumped in will repel the gas originally inside out of the house through the ventilation, but on the other hand the gas pumped in may get repelled by other gases pumped in as well. Therefore, the probability of the new gas pumped in to remain in house or be expelled from house is 1/2 (or not?) in the overall process. Therefore to fill the house with completely new gases, the rate should be double to do this in a certain amount of time (an hour). Is this a good "approximation"?

4. Sep 4, 2014

### BvU

I agree with you. Whatever one pumps in gets mixed with what's already inside. Type of mixing is then also part of the discussion. But I still think the simplest answer is what's intended here, or else they would have given some criterion by which to choose: double, e times, or 99% refreshed, or whatever.