# Is air less dense than chimney exhaust?

So there is this question in my text book that says us to arrange these following items by increasing density:

Air, exhaust from chimneys, honey, water, chalk, cotton and iron.

Everything is straightforward except for air and chimney exhaust.

My answer was that air is denser than chimney exhaust since the exhaust would be hot, so there would be more spacing between the particles, making it less dense. This can also explain why exhaust goes up through the chimney due to the buoyant force of the air.

But every single online source and my teacher says chimney exhaust is denser than air and their reasoning being it contains carbon particles which make it heavier as seen below:

Who is in the correct? And if my teacher and literally every other online source is correct (basically the matrix) is correct, how are they correct and so how does the exhaust exit the chimney?

• @ChetMiller No, you should NOT be comparing the densities at conditions that are inconsistent with those stated. Exhaust from chimneys is hot. Commented May 1 at 17:12
• @Whit3rd Agreed. If the question-setters wanted the comparison performed at the same temperature (as their answer implies) this should have been explicitly mentioned in the question, especially if one of the items is "naturally" at a different temperature. Commented May 2 at 6:20
• @gerrit Nope. The exhaust from condensing boilers may be less hot than the exhaust from older models, but it is still hot. This isn't hart to check if you have one (I have). Commented May 2 at 10:44
• @gerrit Then we also have to get into terminology. If it's not being used to exhaust hot gasses, is it even a chimney, or just a vent? Also terms like "chimney effect" which explicitly work because of the lower density of the hot exhaust gasses.
– JMac
Commented May 2 at 13:08
• How does your teacher explain how a chimney functions if the exhaust it is trying to draw is more dense than the surrounding air? (i.e. I agree with you and most of the answers and would love to hear your teacher talk themselves out of this one) Commented May 2 at 14:44

The question that you are quoting is a very poor question, since the answer depends on what is being burnt to produce the exhaust from the chimney and how far away from the chimney we measure the density.

It is true that smoke from low-quality coal or wood fuel will contain carbon particles. Although it is initially less dense than the surrounding air when hot (otherwise the chimney would not draw), it will cool quickly after it leaves the chimney and may quickly become more dense than the surrounding air.

However, chimney exhaust from smokeless fuel has fewer carbon particles and is hotter, so it will be less dense than the surrounding air for much longer. This is why smokeless fuel was widely adopted to improve air quality in the UK from the mid-1950s onwards. And the chimney exhaust from a properly designed gas fire contains no carbon particles at all.

• Exhaust from oil or gas fire also contains a lot of water vapour, which is less dense than air (even of the same temperature) - although some of this would generally condense to droplets quickly, forming white steam. Commented May 1 at 22:12
• NB: Another reason this is a poor question: modern boilers do not have a hot exhaust and a hot exhaust is a serious waste of energy. Therefore, the assumption that chimney exhaust is hot is probably invalid for real boilers and the question is unanswerable if this is not stated. Commented May 2 at 7:02
• would the (I assume) higher CO2 content of "chimney exhaust" compared to regular air make a difference here? AFAIK CO2 is denser than the standard air mix... obviously not enough so that it would offset the higher temperature (otherwise chimneys would not work). Commented May 2 at 9:30
• I think you mean that the question the OP is asking about is poor, not that the OP's question is poor, correct? Commented May 2 at 16:51
• @JimmyJames Correct. I have changed the first sentence of my answer to clarify this. Commented May 2 at 17:07

### Particulate matter

The density of airborne particulate matter (PM10 and PM2.5) in smoke is rather low, less than a few grams per cubic meter at most. (The linked paper contains direct ground-level measurements of the particulate density of wildfire smoke which turned out to be less than 50 milligrams per cubic meter.) The majority of these particles are less than a micron in diameter which makes smoke a colloid. Therefore it is rather unlikely that its mass is of significance compared to the change in density with temperature.

### Density and composition

Flue gas (exhaust gas emitted from chimneys in fireplaces, furnaces, power plants, etc) usually comprises nitrogen, carbon dioxide and water vapor. It is at several hundred degrees Celsius immediately after combustion so its density is less than half the density of air.

However, if you were to compare them at the same temperature, the exhaust has similar density as air according to this table which uses a sample composition. Without more information on the chemical composition of the exhaust, it is not possible to make a definitive conclusion because carbon dioxide is denser than air by about the same amount as water vapor is less dense than air.

### Conclusion

The exhaust cools as it rises. So the question, as stated, is ambiguous as it does not specify the temperature which is (together with chemical composition) the largest determinant of density here. The given reason (particulate matter increasing the density) is technically correct though, just not by any significant amount.

Chimney exhaust is pumped by the density of the cool ambient air being greater than that of the heated gasses coming from a fire.

Density times column height of the chimney puts less pressure at the bottom of the chimney, thus cool air pushes in at the bottom and hot vapors come out at the top

The pump which we call a chimney wouldn't work otherwise. As for 'air', there's no conditions stated, so we'd assume standard temperature and pressure. STP is the usual nomenclature in a chem lab with loose definition

• I very much agree with the idea that "chimney exhaust" should be interpreted to mean "the stuff coming out of a chimney" - if it's passively rising out of a chimney, it must be less dense than air. It would seem silly to think the question could be referring to a layer of soot or ash on the ground, simply because it came out of a chimney at some point. How would one even define the density of chimney exhaust once it's left the chimney and has dissipated and cooled in the atmosphere? Gas density is a bulk property not really related to the density of individual molecules. Commented May 1 at 18:02

This actually has an interesting connection to volcanism.

Volcanic plumes (similar to chimney exhaust) are far more dense than the air around them, but they rise, sometimes as high as 20 kilometers. How? By entraining and heating air.

The contents of the volcanic plume are really friggin' hot (usually in the 800 F range) and dense (most of it is volcanic ash, i.e., rock). The plume really only has enough upward momentum to carry it a few hundred meters up. Not all that far. It tries to fall, but in so doing, creates little vortices that suck cool air into the plume. That air gets heated to super high temperatures, which then makes the combination of plume material and air less dense than the cool ambient air, then letting the plume continue its rise. In cases where the plume can't suck in enough air, the plume stays dense and you get a pyroclastic density current.

Your answer is correct, simply because the high temperature of the chimney exhaust overcomes any difference in density between atmospheric air and flu gas because of chemical composition. The flu gas contains mainly nitrogen, carbon dioxide and water vapor. Particulates are not part of the fluid and thus are not relevant to the "chimney effect." If you do the calculation using the proper temperatures, you will see that the flu gas density is smaller.

BTW, that's why the flu gases go upward through the chimney and carry any particulates with them. The net pressure force acting on all the flu gas in the chimney is equal to the height of the chimney times the density difference between the flu gas and the outside air. (The mass of the particulates is very small compared with the mass of the flu gases.)

• Minor comment: a "flue" is a valve for opening and closing a chimney, while a "flu" is a respiratory disease caused by an influenza virus.
– rob
Commented May 5 at 14:51
• Exactly, I like how millions of people, maybe even a billion people and an entire council of educators which makes official textbooks for my country got it wrong. But something doesn't make sense, how could they all get it wrong? The textbook probably wants us to go with the assumption that more stuff or more varieties of stuff = more dense Commented May 7 at 5:17