The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.
Problems with gas [chemistry warning]
joshofalltrades
Class TraitorSmoke-filled roomRegistered User regular
Class TraitorSmoke-filled roomRegistered User regular
No, not the ferting kind.
I'm trying to find a way to calculate, in real-world units, a theoretical simulation of gas effusion/diffusion involving several containers. I've taken the gram formula masses of the gases I'm interested in, calculated their molecular speeds and found their effusion rates.
Since this is for research I'm doing, I can't go into a great amount of depth regarding what gases I'm researching or the real-world applications for this research. So any information I give out on this has to be purely abstract and theoretical.
So say I have two gases in an enclosed box. One gas is obviously heavier and therefore effuses slower than the other. I have pinholes at the top and sides of the box, though the pinhole at the top covers more surface area than the pinholes at the sides. The gas molecules will be hitting each other, as well as the sides of the box. My question is this: is there a way to calculate the amount of each of the two gases that will escape through each of the pinholes involved over a specific amount of time, given temperature, pressure and the amount of each of the two gases present (either in moles or liters, makes no difference to me either way)?
I'm probably just being stupid and missing a really obvious formula. I've been poring over the Kinetic Theory of Gases for the last couple hours and can't find anything that would apply in this case. Even something in two dimensions would be helpful as a starting point.
I'm trying to find a way to calculate, in real-world units, a theoretical simulation of gas effusion/diffusion involving several containers. I've taken the gram formula masses of the gases I'm interested in, calculated their molecular speeds and found their effusion rates.
Since this is for research I'm doing, I can't go into a great amount of depth regarding what gases I'm researching or the real-world applications for this research. So any information I give out on this has to be purely abstract and theoretical.
So say I have two gases in an enclosed box. One gas is obviously heavier and therefore effuses slower than the other. I have pinholes at the top and sides of the box, though the pinhole at the top covers more surface area than the pinholes at the sides. The gas molecules will be hitting each other, as well as the sides of the box. My question is this: is there a way to calculate the amount of each of the two gases that will escape through each of the pinholes involved over a specific amount of time, given temperature, pressure and the amount of each of the two gases present (either in moles or liters, makes no difference to me either way)?
I'm probably just being stupid and missing a really obvious formula. I've been poring over the Kinetic Theory of Gases for the last couple hours and can't find anything that would apply in this case. Even something in two dimensions would be helpful as a starting point.
joshofalltrades on
0
Posts
This is why I can't simply use effusion rates. The actual amount of gas effusing out of each container will be different when used in real-world numbers, and when compared to one another.
If you know the general reaction, you can derive rate of appearance of a product from their respective constants, but it looks like you just want to measure rate of escape. We typically measure this empirically and do not model it theoretically as the way you want to set it up would require some heavy duty math (as you aren't fixing temperature or pressure or molar fractions). There is also a thermal equilibrium between your bouncing gas and the sides of the box that you may or may not have to worry about. I'm not entirely sure you can model what you are saying as written.
a much more eloquent version of what I was trying to convey via PM. Fuzzy with the save again
Say I've got a 2-dimensional box, and assume for the moment that all three pinholes in the box are of equal size. This means that the effusion rate for the two gases will apply equally to all three holes, correct? There is an equal chance that a gas molecule will hit one of the pinholes in the box over any other.
So T and P in the ideal gas law would be fixed, for that box. An equal distribution of gas would be effused from the initial box into the three adjacent boxes, correct? So would it also make sense to say that, for any given box from which gas is effusing, you can take the total amount effused and distribute the gas effused through each pinhole based on the percentage of how large the pinholes are?
So say there's a 5 cm hole in the top of the box, a 2.5 cm hole in one side and a 2.5 cm hole in a third. If 10L of gas escapes over a given period of time, 5 L would have effused through the top, and 2.5 L from each side.
So if I am able to computationally start with a gas in one box, I should be able to calculate how much effuses into connected boxes. From there, the P and T can change, but it's okay because I'm starting from a different point in time and just recalculating the amount effused based on the new Volume.
Is that right?
not really?
the problem is that that only works in a vacuum and gets exponentially more difficult from there. for instance, lets say (since you said this is an environmental problem) the wind is blowing from the side with the 5cm hole, you're looking at all of the gas escaping through the smaller holes. Even without the wind involved you're looking at it coming out of 1-2 holes less frequently for the air that replaces the gas. Add in the pressure of the air it compounds it more.
Assume no wind. This does not take place in an open-air environment.
Also assume these pinholes are 1-way.
Sorry, but I can't get any more detailed than that.
Then yes, i think all you'd have to calculate was temp, pressure, and rate of change in volume
I did find this from Wikipedia:
First off, I'm not even sure this is the equation I need to be using to find out the volume of gas escaping over unit time. And if it is, I can't tell how I'm supposed to use it.
This is really the heart of my problem right here. PV=nRT can tell you how much Volume you have at a specific point in time, but it doesn't tell you how fast gas escapes under those conditions.
EDIT: Fixed equation transparency.
In any case, ideal is good enough for now, I don't need to get super-realistic for the time being.
ooh right. Forgot that last post then
http://www.physicsforums.com/showthread.php?t=424720
You could assume a steady state approximation and then have a summation of each of those parameters for how many holes you had (A1, A2, A3, A4.......An).
The only other way I can think of is to use one of the Fick's equations for diffusion but you will have to use the del operator and make some assumptions about maxwell/boltzmann distributions.
Dude. This is awesome. Thanks!
If your simulation is over any extended period of time (which it presumably is given that you mentioned draining several liters of gas through pinholes) the single-hole solution is probably not going to be accurate when extended to multiple holes in widely separated parts of the box.
When the box is at equilibrium, holes in the container will let gas particles escape at the normal effusion rate regardless of position like you assumed. As gas escapes, however, the pressure in the regions near the holes will drop, making the box no longer at equilibrium. In a single-hole case this isn't an issue since gas will fill in rapidly, making a sort of unstable equilibrium where gas escapes the box at the same rate that gas from the more distant, higher-pressure regions of the box moves into the energetically favorable lower-pressure region near the mouth of the box.
If your holes are equidistant and all the same size then, in a situation ignoring gravity, the same solution would probably hold since you'd have a symmetric system. With an asymmetric system (including any system where one hole is higher in the container than another) certain regions of the box will be more energetically favorable than others. The rate of effusion is proportional to the area of the hole, so if one hole is twice the size of another, twice as much gas will escape in time T, making the pressure in the region around the hole twice as low as around a hole half its size. Effusion is based on random motion, but gas particles will be more likely to have vectors that head toward the lower pressure region of the box than otherwise, so you'll see gas filling in the low pressure zone near the big hole more quickly than the other low pressure zone, making it more likely that gas will escape from that hole than would be the case with purely random motion.
If the holes are the same size but one is higher up the box than the other, the additional gravitational potential of particles near the higher-up hole will have a similar (if less dramatic, depending on the mass of your gas and size/distance of holes) effect. Particles under gravity are more likely to be headed downward than upward.
For a momentary effusion rate these aren't terribly important. A gas at equilibrium has roughly randomized vectors for its constituent particles, even in a gravitational field, and fluid dynamics from changing pressure zones won't come in since it's a momentary calculation. But if you want accuracy over time those are things that would become important. Especially as your container starts to empty. If you have a heavy enough gas in a box with a big hole on top and a couple of small holes near the bottom, my intuitive guess is that you'll end up losing more gas through the small holes than the big hole. There'd be an initial rush of gas out of the top, then a continuous stream through the sides as the gravitational potential dominates over time.
I hate you so much (what I was trying to explain up a few posts)
Will a steady source of gas flooding in from the bottom of the box affect the initial box in any meaningful way? What about the other boxes attached to the initial box, where gas is steadily effusing into them via that constant source? I understand how pressure will invariably cause differences in the holes effusion rates, but I guess basically what I'm asking is if there is a constant source of gas streaming into the initial box, will that change anything?
yes, and yes. especially since, if the source stream potentials faster than the combined effusion of all holes, it mitigates the above problem, and if it's lower it alters the amount of change due to pressure
Oh yes.
If you had no holes in the box at all then the source would increase the pressure and, if you seep it in slowly enough, maintain a roughly equilibrium state. If the source is fast then you're going to get pressure waves inside the box as fronts of high-velocity particles move away from the input, slam into the far end of the box, and bounce back. It might be chaotic or it might form a stable standing wave; depends on the geometry.
Now you add holes. Not only are you going to have unstable behavior due to gas being sucked in different directions as the pressure around the holes changes, you also have a constant high-pressure zone at the bottom of the box for gas to run away from. If your geometry actually forms an unstable equilibrium without the input, where the various factors (hole size, position, gravity, gas temperature and mass) balance out such that it ends up escaping at a rate that's a simple function of N, adding a gas source would throw it off. You might be able to adjust a chaotic system to make it quasi-stable by pumping gas in at the same rate that it's effusing, but I would much rather just fiddle with a valve and some pressure gauges to do that than attempt to model it.
You mentioned that the gas is going to leak out of the box into another box. Presumably the other box has a gas in it? If they're not inert then you're going to have pressure changes do to the energy change as the gases interact. If the external box doesn't have holes in it then the pressure outside of the inner box will change, which is going to impact the effusion rate even if the holes are one-way.
I don't know what kind of research this is, but I'd recommend one of two things:
1) do a simple, back of the envelope sketch of the problem using an extension of the one-hole formula. Maybe account for gravity and try to figure out the effective effusion rate for the different holes under a potential before summing them if you're feeling frisky and your gas is heavy. If it looks okay, try a small-scale test.
2) get someone who knows how to do fluid dynamics simulations. These aren't new problems and there are software solutions that would probably let you get an answer. I don't know what they are as I stayed the hell away from fluid dynamics in grad school, but I know they exist.
If it wouldn't cost much to mock up a test apparatus and you just need to show your work, do 1. If this is a serious investment to even test, do 2. The software and getting someone to write a simulation for you plus computer power to run it isn't going to be cheap (probably; there may be an OSS solution for fluids like GEANT for mid-/high-energy) but may be cheaper than building your gas rig.
Be careful if you go this route, you absolutely need to have a concrete set of boundary conditions that describe the problem. You can get answers, but as to how correct they are is another matter entirely.
I assumed that he had a fairly solid idea of the experimental apparatus and procedure, but yeah. These aren't the kinds of simulations where you can guess the parameters.
*I am not a fluid dynamics expert
*I'm a graduate student studying turbulence using CFD.