Calculating gradual chamber filling (CO2 displacing air)

[Mahdivets]

Homework Statement

Hi guys. I need to calculate the gradual filling up of a chamber with CO2 gas for biological test according to international guidelines. So I need is to know what is the speed of CO2 piling up in the chamber. In short, the chamber has 5653.5 cm^3 volume filled up with normal air.
The CO2 tube is being inserted into the chamber, and the CO2 valve gets open and 100% co2 gas with the speed of 3L/min rushes into the chamber. Now, the question is what is the graph, replacing air with Co2 looks like? how should we change it in order to adjust the filling speed.

Relevant Equations

It is critical for us to calculate the exact ratio of filling up the chamber with right speed of Co2. while the percentage of co2 concentration rises up according to our needs. So, we should reach the concentration of about 20% in 50 second, and 30% in 100 second, and 50% in 200 second (see the attached). the numbers are not exact so some degree of flexibility is ok.

 

[berkeman]

Welcome to PF.

The CO2 tube is being inserted into the chamber
View attachment 317847

How is the tube attached to the chamber? How does the air in the chamber leave as it is displaced by the CO2? How will the distribution of the CO2 in the chamber as it fills affect the experiment?

 

[Mahdivets]

Welcome to PF.How is the tube attached to the chamber? How does the air in the chamber leave as it is displaced by the CO2? How will the distribution of the CO2 in the chamber as it fills affect the experiment?

Thank you Berkeman.

The lid on the chamber has a hole size of the CO2 tube( 4mm) which the tube is inserted in. In addition there is an air filter placed with multiple holes in it. All together these small holes makeup of approximately (1*1 cm) (see the attached). The gas distribution pattern is not relevant for our need, and any distribution pattern is fine.

 

[Steve4Physics]

Hi @Mahdivets. A few thoughts...

Missing information includes:
- if the required graph is % by volume or % by mass (weight);
- the system’s temperature and pressure;
- the mixing requirements (as already hinted at by @berkeman) – see below.

It sounds like there are 2 extreme mixing possibilities, each leading to a different graph:

Extreme Mixing Case A:
The CO₂ sinks (due to its density) to the bottom of container, displacing the air upwards with no mixing. So you get a growing layer of pure CO₂ at the bottom and a shrinking layer of air above it.

Extreme Mixing Case B:
Perfect mixing of air and CO₂ continually occurs. So the gas in the container is always a uniform mixture of CO₂ and air.

The reality will, of course, be somewhere between these 2 extremes. But It is very hard to say ‘where’ between the extremes. Because of this, ideally, the result would be obtained by experimental measurement of CO₂ concentration and not by calculation.

Also, it would be useful to know the purpose of this equipment – so that individuals considering answering are aware of any ethical issues.

If you haven’t yet read the forum rules, they are here:
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[berkeman]

The gas distribution pattern is not relevant for our need, and any distribution pattern is fine.

You tagged this thread with a "Biology" label, which implies that you are conducting biology experiments with this chamber. And as @Steve4Physics mentions, this brings ethical issues into play. You need to share with us what the purpose of this setup is, so we can 1) give you the best technical advice we can, and 2) judge whether your experiments are taking into account current ethical standards.

 

[Chestermiller]

That 3L/min: Is that before the CO2 enters the valve of after it exits? What is the pressure before and after the valve?