Sharing thoughtful approaches to teaching physics with the wider world.
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8 November 2016 at 21:53 #45324
(Warning: This is a bit of a ramble and probably won’t be helpful in the classroom, but I have had an interesting time thinking about it so thought I’d share)
I’m about to teach a fairly bright key stage 3 class about convection currents. I don’t much like convection currents. It’s one of those topics where kids have to learn a fairly detailed hand-wavy explanation for a very specific type of question, which they are unlikely to be able to build into a greatly improved mental model of How Things Work. Worse than that, I don’t think the model we use really makes sense.
The way I (and I guess most people) teach convection currents is basically like this: http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/heatingandcooling/heatingrev4.shtml
Gas heats up; particles move faster; spread out; gas becomes less dense; less dense gas rises. Fine.
This works perfectly well if the hot gas is in some kind of container (e.g. a balloon). Then you can say that the pressure x area on the bottom > pressure x area on top by more than the weight of the gas in the balloon and so the balloon rises.
But gases in general are not in any kind of container. In fact by ideal gas assumptions they do not affect each other at all except via collisions. It makes very little sense to ask students to consider gases in terms of individual particles moving more quickly in random, independent directions, and simultaneously consider the same group of molecules to be in a neat little parcel that moves as one. Any sensible model of convection ought to consider molecules as moving independently.
It took me a while to come up with a model that made sense for why hot air would rise as opposed to just spread out in all directions without invoking the above kind of reasoning. Along the way I discovered that air particles move at a few hundred m/s and collide every 70 nm or so. This meant that the effect of gravity on particles is incredibly miniscule compared to the effect of collisions. But it is significant.
Convection currents by particle
- Most of the force acting on particles comes from collisions with other particles
- At increasing altitude pressure/density gradually drop.
- This means that particles are hit slightly less often by particles above them than particles below, resulting in a small average force difference.
- This small force difference is exactly balanced by the force of gravity on the particle so the average force upwards and downwards are equal -> Equilibrium
- Heated gas particles move faster.
- This means they collide more often (with particles both above and below) and with greater force
- This means that the average force difference from collisions (net is upwards) has increased, while the force of gravity has not changed.
- The average force difference from collisions is now bigger than the force of gravity, so the “hot” (faster moving) particles rise.
Disappointingly, I don’t think I can teach this to my KS3 class.
If anyone else finds this interesting though, I would be interested in thoughts on any of the following:
- Is my reasoning sound/Does this individual particle based explanation make sense?
- If so, can anyone explain it in a better/clearer/more accessible way?
- Is my criticism of the usual model we teach fair, or is it better than I have given it credit for?
9 November 2016 at 19:12 #45334
I don’t believe that focusing on how an individual particle behaves is helpful. If you were to follow an individual particle you would observe that its speed and direction vary wildly and erratically. You would not be able to predict where a given”hot” particle will end up, in particular if it ends up above or below its initial starting point.
My recollection from gliding is that thermals form as bubbles that are initially attached to the ground, as the bubble grows it eventually reaches a point where it detaches and rises upwards. There ought to be a video of a lava lamp somewhere on the internet which would give a clearer picture of this part of the process. Once detached the bubble has a tendency to roll with a fast central core developing surrounded by a downward moving ring. The whole floats upwards looking something like a doughnut or like one of those water snakes that are difficult to hold.
10 November 2016 at 10:14 #45338
This video https://www.youtube.com/watch?v=pnbJEg9r1o8 gives some visualisation at a human speed of what the rising air is doing. You have to imagine the surface of the water as a vertical slice through the rising air. A later video https://www.youtube.com/watch?v=72LWr7BU8Ao using food dye underwater shows that the vortex is a single connected structure.
There is a a toy called a Airzooka which allows you to generate smoke rings in class. https://www.youtube.com/watch?v=Jsjm0gop-H4 Reminds me that I need to buy one or make one for myself.
I can’t comment on the safety of using smoke in a class 🙁
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I’m reasonably confident about the motion of the “bubble” of warm air once it is no longer in contact with the ground. I’m a lot less sure if the initial warming produces a bubble that is attached and later separates even though that was the explanation given to me when flying hang-gliders.
10 November 2016 at 09:22 #45336
Thanks for sharing your thoughts. This is a really interesting discussion and it is really useful to initiate this sort of reasoning among teachers. I have embedded a nugget from SPT that talks about conduction and convection. The treatment there seems to be that of ‘floating’ and ‘sinking’ of volumes of fluid in gases and liquids. A point is made that shifting energy by heating is more efficient in conduction “because it is easier for the random movements of the particles in one volume to affect the random movements of the particles in the next”.
I too am not sure about using individual particles to explain the phenomenon of convection, because if you take a bonfire for example, clearly many particles will begin to move much faster above the fire and in the areas surrounding it than anywhere else in the field. So, a large volume of air is affected by this shifted energy. I think we would all agree that a considerable volume of air above the fire is now less dense than the surrounding areas (even if there most probably is a gradient of density is reality, but there is only so much detail and complexity we can introduce at KS3 and GCSE before we disaffect students). So, I think considering this more or less defined volume of less dense air can be useful because the average kinetic energy associated with all the particles within this volume is greater than the kinetic energy associated with particles further away from this volume. So, yes, there is a gradient and yes, each particle has their own velocity (which is quite random taken on its own), but overall, as a body of air particles they exert a certain pressure against areas/volumes of air further away, hence, with less internal energy (again if we consider the rest of the environment as a volume of air with less average kinetic energy associated to the particles). This is why I believe it makes sense to see that whole volume rising as a satisfactory explanation. In fact, (apart from edge effects where particles transfer their energy in collisions with particles from cooler regions of air) the pressure from within this volume of air nearer the fire will be sufficient to keep that volume of air less dense for a longish period of time and that is why it rises a bit like a hot air balloon, or a bubble that Ian talked about. It will take some time and many collisions with particles outside this less dense volume of air to equalise the pressure again and decrease the density of air within it.
I hope this makes sense. At least it made sense to me when I was writing.
Thanks for your question Anrew, as I would not have thought about this much detail unless you had asked.
I always try to steer away from “hot/cold” particles, even if referred to with warnings that what we mean is particles with higher velocity, etc… Because what it translates to in exam answers is “hot particles rise and cold particles fall” which is (rightly) marked wrong.
10 November 2016 at 10:01 #45337
There is a a toy called a Airzooka which allows you to generate smoke rings in class. https://www.youtube.com/watch?v=Jsjm0gop-H4 Reminds me that I buy one or make one for myself.
I can’t comment on the safety of using smoke in a class 🙁
10 November 2016 at 10:57 #45343
The ‘smoke’ is from a non-toxic liquid which is used in theatres. It is generated using a smoke/fog machine, so should be OK in class.
10 November 2016 at 14:28 #45344
Thanks for your feedback everyone. I agree that the approach I’ve come up with is not particularly practical/useful for KS3-KS4, although I think it is valid (I’m thinking of the mean behaviour of particles; of course it is true that particles will not uniformly move in one direction). I think part of the problem I have with the normal model is that I always stress that pressure is something that exerts a force on a surface, and there is no real surface here. My model just shrinks the problem down to something with a tangible surface. I guess the more accurate macroscopic interpretation gets into gradients of pressure/temperature as Alessio suggests, which again is just going to get too difficult if you chase it any further.
Ian, I’m interested in the idea that air would form bubbles like a lava lamp. I thought they were caused by intermolecular attraction, which I didn’t think would be that significant in air. I will be looking out closely for them next time I do the smoke/convection demo!
10 November 2016 at 17:25 #45364
Bubbles was how they were described when gliding, I suspect bubbles is somewhat misleading as I don’t think there are any surface tension effects in pockets of air. I’ve experienced being unable to hook up with a thermal because I was too far below the other gliders. And also the strong central core and surrounding area of sinking air that would be expected from a rising torus. I don’t know the conditions required to get the torus shaped thermals to form, not all hot days produce good thermals.
10 November 2016 at 22:14 #45366
When I first started discussing the physics of meteorology with my wife (a forecaster) I was shocked by their treatment of bodies of air as discrete entities that flowed over and around each other with distinct boundaries – “a gas can’t behave that way” – but she was adamant that it did. These days I’m not so black and white, and the question is is it sensible to model a phenomenon in macroscopic or microscopic terms, and when to recognise that it is a mixture of both. For convection I use the term “parcels” of the fluid in question, by which I mean something between my wife’s air masses and Andrew’s individual particles, and I mean them as large enough for a macroscopic explanation to hold, but small enough for a bit of chaotic break up not to be a surprise. The kids are usually so distracted by my use of parcel in such an unusual context that they let the rest pass!
9 January 2017 at 20:05 #45891
Hello Andrew and all,
For my sins I studied meteorology at university (albeit at a basic level) and although I’ve forgotten most of what I learned, I do remember talking about ‘parcels’ of air quite a lot, but can’t ever remember discussing individual molecules so much in this context. So, if I remember correctly, I guess talking about ‘volumes’ of air to year 9 is not really dumbing down at all, in my opinion.
Its an interesting discussion though and I’m guessing (again) that once you start considering these parcels of air to begin to mix and consist of individual molecules, it must get very complicated?
10 January 2017 at 09:44 #45896
Thanks Steve and Christopher,
I like the idea of parcels of air. It seems simple enough to work with and reasonably accurate within the boundaries of a model, i.e. as far as the model goes. I think we need to remind our learners that models are just that – models. I.e. they are just a representation of the reality, which is much more complex. But weighing the benefits of models against their limitations is what makes some models better than others, or more appropriate to use in some situations, than others.
14 January 2017 at 19:44 #45967
Hi Andrew, Alessio and all,
Just going back to your ‘molecular reasoning’, Andrew. To the part where you say: ‘(when heated) the average force difference from collisions is now bigger than the force of gravity, so the “hot” (faster moving) particles rise.’
Perhaps this may just mean that a molecule is bumped up a bit, and it then in turn bumps up a molecule above it, and the result would be a stretched atmosphere (not convection). Once the atmosphere has stretched so far, it will reach equilibrium again. Interestingly, even though the atmosphere has increased in temperature (and stretched upwards or got thicker), the pressure at the surface will remain the same, because it is due to the weight of air above it, which hasn’t changed.
It’s an interesting question of yours and I would love to know more about it.
15 January 2017 at 00:23 #45968
Christopher – this has got me thinking more – try this train of thought and see if it makes sense:
Build a chimney that is sealed at the bottom and stretches up into space. Heat the air inside it. That air will “stretch” just as you describe. At the bottom the pressure will be unchanged, as you point out. As you get further up the air will be at higher pressure than the air outside the chimney as the atmosphere in the chimney is taller and there is more air still above (and less below).
Next drill a hole halfway up the chimney. Because of the pressure difference, air will flow out through the hole. This will cause the pressure at the bottom of the chimney to drop as there is now less air above it.
Now drill a second hole near the bottom of the chimney. Air will rush in to restore equilibrium. If that air is heated it will “stretch” as in the original set up – and so on. This sounds like a convection current.
15 January 2017 at 10:26 #45969
Andrew, I think you are making perfect sense and I agree that this does sound a lot like convection.
However, I’ve got a horrible feeling that technically it is not. I think you may have described the mechanism for a sea breeze. If the chimney stretches from Skegness to Blackpool, heated by the summer sun, then the cool air rushing into the hole at the bottom of the chimney is the sea breeze.
I’m not at all sure, but I think convection is more to do with thermals initiating things? But then again, maybe not! 🙂
16 January 2017 at 08:58 #45976
Yes that is how a sea breeze works, but it also how thermals work, the land is heated by the sun, the warmer air rises and cooler air is pulled in from surrounding areas. At the coast the cooler air comes off the sea, then later when the land cools the system is reversed and the airflow is back out to sea.
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