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

[td21]

Homework Statement

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)

Homework Equations

rate = volume/time

statistical mechanics
fluid dynamics

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)?

 

[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...

 

[td21]

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...

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 into 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"?

 

[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.

 

[HalfLostAndSearching]

Your attempt at a solution is a good start, but as you mentioned, it is not that simple. The answer would indeed be more complicated due to the old gases remaining inside and the rate of diffusion. To accurately calculate the minimum rate at which gases should be pumped into the box, you would need to consider statistical mechanics and fluid dynamics.

Statistical mechanics deals with the behavior of individual gas molecules and how they interact with each other. This would be important in determining how quickly the old gases would mix with the new gases being pumped in.

Fluid dynamics, on the other hand, deals with the movement of fluids (in this case, gases) and how they flow through a system. This would be important in determining the rate of diffusion and how quickly the new gases would spread throughout the entire box.

In order to accurately calculate the minimum rate at which gases should be pumped into the box, you would need to use equations and principles from both of these fields of study. This would likely involve using equations such as the ideal gas law and the diffusion equation, as well as considering factors such as temperature, pressure, and the size and shape of the box.

Overall, it is not a simple calculation, but it is an interesting challenge question that highlights the complexities of gas behavior and the importance of understanding different scientific disciplines in order to solve real-world problems.