Overcome Entropy: Understanding Mixing & Separation of Gases

[lilrex]

I am trying to figure out a problem. When hydrogen and nitrogen are mixed, the entropy of the gas tends to mix them despite the large difference in mass while exposed to the acceleration of gravity. As I visualize it at a micro scale the gas molecules are translating at a velocity represented by its individual kinetic energy, these molecules collide with adjacent molecules of whatever type and find a new trajectory and kinetic energy from the properties of the collision. Due to the random nature of the collision the new trajectory can be in any direction this is the direct cause of the mixing of gasses, what I want to understand is: is my understanding of this effect correct? At what point does the effect of gravity or acceleration overcome the effect of entropy and cause the separation of the gasses? And at a micro scale how would that be represented?

as an intellectual analysis of the problem gives me, I believe that this is the mechanism that will separate the gasses: a molecule of nitrogen with a as a result of a collision velocity of x1,y0,z0 when exposed to acceleration x0,y1,z0 the new result of the collision as exposed to acceleration would be (if I used the right method) x1,y.5,z0 this would show that if the acceleration is high enough that there will be a point that the normal distribution of the vector would favor a separation despite the mixing tendency of the collision.

Now as I think about it in a macro scale I am not familiar enough with the units of measure as applied to thermodynamics to produce any methods to solve what I have described in the text above without much effort. But I am still thinking about it.

Any education, thoughts, advice, and ridicule will be appreciated.

Thank you.

 

[Dale]

Think about the gravitational potential energy difference between a molecule of hydrogen and nitrogen in a container. Now think about the kinetic energy of those same molecules. The kinetic energy is HUGE compared to the potential energy. That is the main reason that, on a macro scale, you don't see them unmix.

 

[lilrex]

ah so the point where they are the same is where one would begin to see a separation?

 

[lilrex]

I am trying to wrap my head around your statement and am having a hard time with the potential energy of the molecules. In order for you to have potential energy there must be a distance involved when it is stored in acceleration, how do you find a mark to start from? We already know that nitrogen is 7 times more massive then hydrogen and the kinetic energy of the molecules are keeping them mixed but how do you find the potential energy of the molecules?

hmm... it seems like I should know the answer to this...

 

[lilrex]

I feel dumb! Of course you simply normalize the comparison with a unit of time changing the energies into velocities per unit of time and comparing them that way. I guess there are many ways to skin a cat huh.

 

[Dale]

This kind of comparison becomes important in other situations as well. I work with MRI and the analogy I usually use is if you put a bunch of compasses on a table they will all line up, but if you start to add disorganized energy by shaking the table they will tend to be unaligned on average.

 

[lilrex]

I am still having problems with the specifics on this subject. I am also having problems with asking an intelligent question. I know that gasses tend to mix; I know that it is the entropy of the gasses that cause this effect. It makes sense that the energy is essentially shaking up the "jar", I know that acceleration will separate the gasses and that the potential energy must be high enough that it will overcome the entropy of the gas, but what I want to know is where the point that it will mix is at? Is it when the energy levels are equal?

If we have an active pool of disorganized gas the heavier molecules will impact with much ease the lighter molecules causing them to be much more mobile so if the difference of the energy is overcome, it will separate out according to the mass of the molecules.

So the comparison would be true: in a centrifuge it would be easier to separate UF6 into its isotopes then hydrogen from UF6.

So if I was going to separate hydrogen with 28.836 J mol K entropy from nitrogen with 29.124 J mol K entropy at 249K

The point that it would separate would be 71.712 J per mol of acceleration or 51.875 Gs to start its separation. (The method I used is: the difference in entropy of the two gasses are multiplied by the temperature and divided by the product of one mole of the gas mix and 1 G squared)


Am I thinking right on this?

Thanks, cheers!

 

[lilrex]

Am I on a rabbit trail with this? It gives me a number, so I guess I could try it and find out, if I set up a DeLavel nozzle and sent super sonic gas along a curve I could easily get the acceleration needed to test my conclusions. Of course I would then have to calculate the efficiency of the device. Hmm that would be a task.