Science of gasses in Earth atmosphere.

[sethoflagos]

7 minutes ago, exchemist said:

On the face of it, though, this seems ridiculous to me, though I do acknowledge that at very high artificial g forces, in a gas centrifuge, you can see a bit of partial separation due to this. This scenario will be where @sethoflagos's thermodynamic analysis  has a practical application.    

While posting, I had uranium enrichment by centrifuging UF₆ in mind.

While I have the opportunity, I need to clarify that I've quoted Gibbs' Free Energy rather too freely in my post. In context I'm referencing more of a total free energy so dH should be understood to include gravitational potential energy which is indeed the the active quantity. It's the -ve change in this that enables a +ve entropy change. Analogous to an exothermic reaction without actually being one!

[Ken Fabian]

12 hours ago, studiot said:

So why does do the lighter gases I mentioned not diffuse downwards to form a homogenous gas body inside a large commercial building (tin sheds I call them) ?

I see that you have both avoided this question.

It does diffuse downwards. Diffusion works in every direction. It is a case of lag time in mixing, with sources adding it faster than it mixes, not stratification. Any lighter gases accumulating in a roof space, (like CO2 does in low places), are not yet well mixed when they rise (or sink). They may not appear to be concentrated "streams" but there will be enough gas seepage - faster than diffusion can disperse it - to make volumes of lower density air, that flow and rise. Enough in otherwise still air for convection to carry it.

Edited November 22, 2022 by Ken Fabian

[TheVat]

This thread has massaged loose a recollection of enjoying Sam Kean's book, Caesar's Last Breath, which touches on many aspects of gas diffusion, entropy, and atmospheric chemistry... as the title whimsically suggests.  I thank Studiot, Ken, Seth, and Exchem for illuminating some of the tricky aspects of concentration gradients and a possible fresh excuse for avoiding retrievals of boxes stored in the attic (not well ventilated, and a perilous trip via ladder is required).  I hope I am correct in understanding that the troposphere tends towards homogeneity, where longterm gases are concerned, while the stratosphere is a bit different with a higher ozone concentration. 

[sethoflagos]

2 hours ago, TheVat said:

I hope I am correct in understanding that the troposphere tends towards homogeneity, where longterm gases are concerned, while the stratosphere is a bit different with a higher ozone concentration. 

'Weather' tends to keep the troposphere very well mixed as you suggest.

Ozone is a rather strange fish on several counts. The long and short of it is that it has a short half life at normal sea level temperatures so it's natural distribution is generally limited to the frigid upper atmosphere where it's created. 

[studiot]

8 hours ago, sethoflagos said:

'Weather' tends to keep the troposphere very well mixed as you suggest.

Ozone is a rather strange fish on several counts. The long and short of it is that it has a short half life at normal sea level temperatures so it's natural distribution is generally limited to the frigid upper atmosphere where it's created. 

 

"'Weather' tends to keep the troposphere very well mixed as you suggest."

Great statement. +1

Diffusion is a very slow and weak process. Weather is a very fast and strong process.

In most cases there are no 'streams' of carbon dioxide or methane (or other unwanted gases), just intermittent trickles.
So the words 'accumulation' or 'collection' appear again and again in most treatments.

Of course, accumulation is the opposite of diffusion.

 

 

Here is a simple experiment for your consideration.

12 hours ago, Ken Fabian said:

It does diffuse downwards. Diffusion works in every direction.

You have a bucket of hydrogen with a removable lid, suspended 100 feet up in the air.

What happens when you remove the lid ?

Ken seems to think that the hydrogen diffuses downwards towards the ground, as well as upwards and sideways.

So what would be the distribution of this diffused hydrogen above, below and to the sides of this bucket if you measured it ?

 

https://www.hse.gov.uk/pubns/gasdetector.pdf

 

Quote

https://www.weatherall-uk.com/articles/toxic-and-flammable-gas-level-monitoring-in-industrial-boiler-rooms/

Natural gas ( Mainly Methane ) expands rapidly and is lighter than air it therefore rises to the roof space in a boiler room.

Many gases such as natural gas, methane are flammable within a range of concentration known as the explosive or flammable range.

Quote

https://www.health.ny.gov/environmental/outdoors/air/landfill_gas.htm

Health Effects Associated with Methane and Carbon Dioxide

Methane and carbon dioxide are colorless, odorless gases that can displace oxygen in enclosed spaces. Health effects associated with both methane and carbon dioxide result from the lack of oxygen rather than direct exposure to these gases. Health effects caused by a reduced oxygen level include a faster heartbeat and having to take deeper breaths, similar to the effects felt after vigorous exercise. A greatly reduced oxygen level (that is, when the oxygen level is well below its usual level of 21% of the total air volume) can cause reduced coordination, fatigue, nausea, vomiting, and unconsciousness. These effects have rarely been reported from landfills.

Controlling Landfill Gas Migration at Landfills

When landfills have reached the maximum amount of waste they can hold, several feet of cover material are placed over the landfill mass. Gas collection wells are then installed throughout the capped landfill. These wells are made of perforated pipes which give the gas an easy path to move vertically to the surface rather than laterally (outward) toward off-site locations (e.g., buildings). As the gases enter these wells they are either vented into the outdoor air, passed through a flame and broken down by burning, passed through a filter, or used in an energy recovery program. Landfill gas vents need to be kept drained and clear of obstructions such as snow and debris. Older landfills and smaller dumps may not have gas control measures.

Reducing Landfill Gas in Homes

Homeowners should contact their Regional New York State Department of Environmental Conservation office if they suspect landfill gases are entering their home. A link for contact information is provided in the "For Additional Information: On a specific landfill" section of this factsheet. Measures a homeowner or developer can take to help prevent landfill gas from entering a building include minimizing entry points and making sure there is adequate ventilation. Entry points for landfill gas can be minimized by eliminating cracks and gaps in the basement by caulking and sealing. These measures will help to reduce the potential for landfill gases to build-up in indoor air. In some cases, additional measures may be needed to reduce landfill gas migration from soil into buildings. For example, installing a sub-slab depressurization system will direct soil vapor away from the building. A sub-slab depressurization system is often included in new construction on or adjacent to landfills.

 

https://www.designingbuildings.co.uk/wiki/Ground_gas

https://www.claire.co.uk/home/news/1149-british-standard-8485-code-of-practice-for-the-design-of-protective-measures-for-methane-and-carbon-dioxide-ground-gases-for-new-buildings-amended-and-updated

https://www.gov.scot/publications/research-project-investigate-prevalence-co2-disused-mineral-mines-implications-residential-buildings/pages/15/

 

There you go from New York to Scotland to British Standards to................

Ther is just loads of supporting data all to be be had for the googling and reading.

Edited November 23, 2022 by studiot

[exchemist]

14 minutes ago, studiot said:

 

"'Weather' tends to keep the troposphere very well mixed as you suggest."

Great statement. +1

Diffusion is a very slow and weak process. Weather is a very fast and strong process.

In most cases there are no 'streams' of carbon dioxide or methane (or other unwanted gases), just intermittent trickles.
So the words 'accumulation' or 'collection' appear again and again in most treatments.

Of course, accumulation is the opposite of diffusion.

 

 

Here is a simple experiment for your consideration.

You have a bucket of hydrogen with a removable lid, suspended 100 feet up in the air.

What happens when you remove the lid ?

Ken seems to think that the hydrogen diffuses downwards towards the ground, as well as upwards and sideways.

So what would be the distribution of this diffused hydrogen above, below and to the sides of this bucket if you measured it ?

 

https://www.hse.gov.uk/pubns/gasdetector.pdf

 

 

https://www.designingbuildings.co.uk/wiki/Ground_gas

https://www.claire.co.uk/home/news/1149-british-standard-8485-code-of-practice-for-the-design-of-protective-measures-for-methane-and-carbon-dioxide-ground-gases-for-new-buildings-amended-and-updated

https://www.gov.scot/publications/research-project-investigate-prevalence-co2-disused-mineral-mines-implications-residential-buildings/pages/15/

 

There you go from New York to Scotland to British Standards to................

Ther is just loads of supporting data all to be be had for the googling and reading.

Thanks. I've had a look at these but none of them seem to me to assert anything about gases concentrating themselves from a mixed state.

 

 

[studiot]

41 minutes ago, exchemist said:

Thanks. I've had a look at these but none of them seem to me to assert anything about gases concentrating themselves from a mixed state.

 

 

Have you considered that is because they are not mixed ?

[sethoflagos]

55 minutes ago, studiot said:

Here is a simple experiment for your consideration.

You have a bucket of hydrogen with a removable lid, suspended 100 feet up in the air.

What happens when you remove the lid ?

Ken seems to think that the hydrogen diffuses downwards towards the ground, as well as upwards and sideways.

So what would be the distribution of this diffused hydrogen above, below and to the sides of this bucket if you measured it ?

@Ken Fabian seems to be effectively stating that the maximum random-direction particle velocity due to thermal agitation exceeds the local bulk velocity of the ascending/expanding plume. Therefore at any point in the plume, some of the hydrogen content must be travelling downwards.

Is there a flaw in this logic?

It does appear consistent with the Briggs equations and Gaussian dispersion equation used in dispersion studies of flue and flare stacks that I've had some (albeit limited) exposure to. 

 

 

[studiot]

1 hour ago, sethoflagos said:

Is there a flaw in this logic?

Of course there isn't. But the operative word is 'some'.

This is a very very small fraction and is not accounted for by the dispersion equation.
It is also the reason that concentration boundaries are blurred and gradual, even with only the entropic dispersion acting.
It is accounted for by the kinetic theory.
Clearly some of the hydrogen molecules in their upwards path will collide with molecules many times their mass and bounce back downwards.
But in their downwards travel they will encounter a (very slightly) higher density of heavier molecules so will be even more likely to strike one and bounce back upwards again.
 

It should be noted that this mechanism is not always availble in the dispersion equation.
When the dispersion equation appears at 'the 'heat equation' the heat always flows in the direction from higher temperature to lower temperature.
Thermodynamics laws forbid the sort of dynamic equilibrium that is established for momentum transport.

But I'm sure you are well aware of all this.

BTW plume was a very good term to use.

 

Finally my commiserations to Ken for his team's loss in the World Cup.
The Aussie soccer team doesn't seem to be of the calibre of their rugger teams.

Edited November 23, 2022 by studiot

[sethoflagos]

4 hours ago, studiot said:

When the dispersion equation appears at 'the 'heat equation' the heat always flows in the direction from higher temperature to lower temperature.
Thermodynamics laws forbid the sort of dynamic equilibrium that is established for momentum transport.

But I'm sure you are well aware of all this.

Now you've sparked my interest! 

The Reynolds and Chilton-Colburn analogies describe strong correlations between the flows of heat, mass and momentum which apply irrespective of whether the transport mechanism is via molecular diffusion or eddy diffusion. 

Essentially, the direction of transport of each is so as to flatten the gradient driving it. 

For instance, one thing I am well aware of is that the further your hydrogen plume moves away from the source, the more dilute the hydrogen becomes due to convective admixture of air, and correspondingly, the higher the concentration of hydrogen in the surrounding atmosphere. The trend is uniformly toward equalisation of concentration. The gradient tends toward zero.

I don't see the thermodynamic exception you're referring to, and am curious since it suggests a significant and unappreciated asymmetry in what I understood to be a very consistent picture.

 

[studiot]

3 hours ago, sethoflagos said:

Now you've sparked my interest! 

The Reynolds and Chilton-Colburn analogies describe strong correlations between the flows of heat, mass and momentum which apply irrespective of whether the transport mechanism is via molecular diffusion or eddy diffusion. 

Essentially, the direction of transport of each is so as to flatten the gradient driving it. 

For instance, one thing I am well aware of is that the further your hydrogen plume moves away from the source, the more dilute the hydrogen becomes due to convective admixture of air, and correspondingly, the higher the concentration of hydrogen in the surrounding atmosphere. The trend is uniformly toward equalisation of concentration. The gradient tends toward zero.

I don't see the thermodynamic exception you're referring to, and am curious since it suggests a significant and unappreciated asymmetry in what I understood to be a very consistent picture.

 

Yes I agree that a rising plume expands horizontally.

But the ascent is much more rapid than the widthwise expansion.

I agree that diffusion, without an additional forcing function tends to flatten the gradient.

We have all agree these matters many times now.

 

But consider a thermally conductive bar, which is being cooled at one end (the cold end) and heated with the extracted heat at the other end (the hot end) via a heat pump.

Which way does the heat flow through the bar ?

Here is a reference for the benefit of exchemist.

Quote

http://physics.bu.edu/~duffy/py105/notes/Thermodynamics.html

The second law of thermodynamics

The second law of thermodynamics comes in more than one form, but let's state in a way that makes it obviously true, based on what you've observed from simply being alive.

The second law states that heat flows naturally from regions of higher temperature to regions of lower temperature, but that it will not flow naturally the other way.

 

I keep saying this but can't seem to get anybody to pick it up.

Diffusion is acting, but it is not only the not the only active process it is not the principal process in the cases under consideration.

Edited November 23, 2022 by studiot

[Ken Fabian]

11 hours ago, studiot said:

You have a bucket of hydrogen with a removable lid, suspended 100 feet up in the air.

What happens when you remove the lid ?

Initially most of the hydrogen would rise due to convection and accumulate in a partially mixed state at the top of an enclosed space - partially mixed because of turbulent mixing as it rises and to a lesser extent from diffusion as it goes. The diffusion would be happening from the moment you lift the lid and it will be in all directions, including sideways and down and around. I would expect the convection to effectively stop when it settles in the top of the closed space and so long at there are no temperature differences, will subsequently be dispersing  primarily due to diffusion downwards - because diffusion in other directions will be blocked by ceiling and walls.

Give it time and it will mix all the way through by diffusion - with the caveat that there is a very small difference due to gravity, just not enough to be significant, just as dispersal is time dependent and arguably approaches but doesn't ever quite reach absolute homogeneity. Also there are going to be differences in dispersal rate due to the bucket making less room going down from above - effusion?

Note that I'm basing this on my admittedly quite basic understandings. I can quote a diffusion coefficient of 0.61×10-4 m2 .s -1  for hydrogen gas (it has no term in it for gravity or direction) but struggle to do the calculations for how fast the accumulation at the top would take to diffuse through the whole volume. The reason I see for gravity to be effectively insignificant is that Hydrogen molecules move at around 2,000m/s at zero C and what gravity adds or subtracts is going to be relatively small. CO2 will diffuse lot slower because it is a heavier molecule - I haven't looked in the right places to a number to it - but it will still diffuse.

That heat flows to where it is colder and does not flow to hotter is very like the way concentrations of one gas in a mixture will disperse to lower concentrations but not to higher. Without a source or extreme conditions it all goes one way, towards homogeneity.

 

Edited November 23, 2022 by Ken Fabian

[exchemist]

21 hours ago, studiot said:

Have you considered that is because they are not mixed ?

Well of course. That's what several of us have been saying:  when gases accumulate in hollows or high points, they do so because they are not mixed, i.e. before they have a chance to diffuse away into the general body of the atmosphere.

The point we are taking issue with is your apparent contention, earlier in this thread,  that mixtures of gases can spontaneously separate, or stratify, at least partially, under the influence of gravity. 

It is this that I am saying is not supported by your references.

  

 

Edited November 24, 2022 by exchemist

[studiot]

23 minutes ago, exchemist said:

Well of course. That's what several of us have been saying:  when gases accumulate in hollows or high points, they do so because they are not mixed, i.e. before they have a chance to diffuse away into the general body of the atmosphere.

The point we are taking issue with is your apparent contention, earlier in this thread,  that mixtures of gases can spontaneously separate, or stratify, at least partially, under the influence of gravity. 

It is this that I am saying is not supported by your references.

  

 

 

I have repeatedly said they do not separate.

But I have also repeatedly said they were not mixed in the first place.

 

10 hours ago, Ken Fabian said:

Initially most of the hydrogen would rise due to convection and accumulate in a partially mixed state at the top of an enclosed space - partially mixed because of turbulent mixing as it rises and to a lesser extent from diffusion as it goes. The diffusion would be happening from the moment you lift the lid and it will be in all directions, including sideways and down and around. I would expect the convection to effectively stop when it settles in the top of the closed space and so long at there are no temperature differences, will subsequently be dispersing  primarily due to diffusion downwards - because diffusion in other directions will be blocked by ceiling and walls.

Give it time and it will mix all the way through by diffusion - with the caveat that there is a very small difference due to gravity, just not enough to be significant, just as dispersal is time dependent and arguably approaches but doesn't ever quite reach absolute homogeneity. Also there are going to be differences in dispersal rate due to the bucket making less room going down from above - effusion?

Note that I'm basing this on my admittedly quite basic understandings. I can quote a diffusion coefficient of 0.61×10-4 m2 .s -1  for hydrogen gas (it has no term in it for gravity or direction) but struggle to do the calculations for how fast the accumulation at the top would take to diffuse through the whole volume. The reason I see for gravity to be effectively insignificant is that Hydrogen molecules move at around 2,000m/s at zero C and what gravity adds or subtracts is going to be relatively small. CO2 will diffuse lot slower because it is a heavier molecule - I haven't looked in the right places to a number to it - but it will still diffuse.

That heat flows to where it is colder and does not flow to hotter is very like the way concentrations of one gas in a mixture will disperse to lower concentrations but not to higher. Without a source or extreme conditions it all goes one way, towards homogeneity.

 

 

Convection requires a source of heat.

I did not say anything about heatng the bucket or having the bucket at 0^oC.

You seem hung up on diffusion, yet you ar starting to admit that other mechanisms and processes are acting.
That is good.

Now let us take the experiment a little bit further, remembering that my bucket was freely suspended in the open air, clear of walls, rooves and so forth.

How quickly would the bucket of hydrogen empty compared to a bucket of plain air, noting that other air would diffuse into the bucket in both cases ?

In the experience of every engineer I know said bucket of hydrogen would empty immediately and pretty well all the hydrogen would go straight up, the plume widening with ascent as Seth says.

Whereas the bucket of plain air would take a long time to homogenize with the plain surrounding air.

This is always provided that both the hydrogen and the original plain air in the bucket were originally at the same temperature and pressure as the surrounding air.

 

[sethoflagos]

13 hours ago, studiot said:

How quickly would the bucket of hydrogen empty compared to a bucket of plain air, noting that other air would diffuse into the bucket in both cases ?

An interesting point that got me puzzling over the differences in Stokes drag between the macroscopic and molecular.

We know from school chemistry that one mole of say, hydrogen at stp can occupy a sphere of radius 0.175 metres and present a surface area of 0.096 m². Not much to resist the quarter of a Newton or so of buoyancy forces propelling it upwards.

But what happens when the hydrogen is diluted? It's still the same 2 grammes of hydrogen experiencing the same 0.26 N force, but now each molecule is an isolated 'sphere' of radius 4.46 nm in an ocean of heavier particles. And the total area presented for drag to act upon is a little over 150 km². 

I'm sure I've probably taken a few liberties in extrapolating viscous behaviour below the sub-micron scale. However, nine orders of magnitude is a pretty comfortable safety margin to conclude that buoyancy probably has considerably less impact at the molecular level than our everyday macroscopic experience might lead us to expect.

 

[Ken Fabian]

15 hours ago, studiot said:

I have repeatedly said they do not separate.

But I have also repeatedly said they were not mixed in the first place.

Which makes me wonder what we are arguing about - since that is what I have repeatedly been saying.

15 hours ago, studiot said:

Convection requires a source of heat.

I think this is incorrect - convection requires a difference in density (and gravity... or an acceleration like a centrifuge provides); different density due to temperature difference is just the most common, but having a different mix of gases with a different density will do it. Hydrogen, being lower density, will make convection.

15 hours ago, studiot said:

 

I did not say anything about heatng the bucket or having the bucket at 0^oC.

My citing the velocity of hydrogen molecules at 0 C was what I found and was intended as illustrative of the high velocity of gas molecules, far exceeding what gravity will do. I should add that doesn't mean I think hydrogen molecules will be bouncing off the walls and floor in a fraction of a second - they will run into other molecules along the way and how fast it disperses depends on (iirc) mean free path.

15 hours ago, studiot said:

You seem hung up on diffusion, yet you ar starting to admit that other mechanisms and processes are acting.
That is good.

Read my posts and you will find I spoke of other mechanisms all along. It looks more like you being hung up on diffusion, as if it were inconsequential. It isn't.

 

15 hours ago, studiot said:

How quickly would the bucket of hydrogen empty compared to a bucket of plain air, noting that other air would diffuse into the bucket in both cases ?

I don't see how that reveals anything different than what I have been saying. Sure, the hydrogen in the bucket will be displaced faster by bulk gas movement (convection) than it could by diffusion.

Not sure I am reading it correctly but a table of properties of Hydrogen (here) has convection (bouyant velocity) at 1.2 - 9 m/s - a lot faster than diffusion velocity of under 2 cm/s, but 2 cm/s is still significant in this hypothetical - the convection won't persist for long but diffusion will - from ceiling to floor of a 3m high space in a few minutes. Which won't be to homogeneity - I am assuming for the first molecules arriving? Sethoflagos or someone else likely knows better than me.

Most of it will settle temporarily at the top but diffusion will happen from the moment the lid is removed. Do it in zero gravity without convection and the hydrogen will disperse faster than plain air - because hydrogen molecules move faster and that makes them disperse faster. The specific air molecules of plain air will disperse (and be exchanged by Brownian Motion), without changing concentrations.

 

Edited November 25, 2022 by Ken Fabian

[sethoflagos]

I think I owe @Ken Fabianand @exchemistan apology here.

I took a closer look at the overall changes in gravitational potential energy due to isothermal nett downward diffusion of CO₂ in the atmospheric column and obtained a result I didn't expect. 

For sure, descent of CO₂, and the corresponding ascent of an equimolar flow of the lighter gases does result in a small local reduction in GPE, However, It also results in a small local reduction in pressure due to the reduced mass of the air above, and this results in expansion. The figure is tiny, but it is not local - it raises the entire air column above it with a corresponding increase in GPE. As far as I can tell, the two effects cancel out exactly at least when subject to a uniform gravitational field.

So wiith zero contribution from GPE and enthalpy, the only drivers for Total Free Energy are the entropy terms which favour a constant mole ratio. 

I'm sure variation of gravity with height must have some small second order effect. Because centrifuges again, where such gradients are many orders of magnitude greater.