Chemistry Versus Physics: Why does “Heat Rise”? (Part 2 of 2)

Part 1 presented a basic conundrum: particles that are hotter (or lighter) than their peers tend to rise; for example steam will rise off boiling water to condense on a glass lid. The “explanation” given in physics textbooks makes no sense because the hotter (or lighter) particles are not bound together in a separate volume. One cannot treat hot steam rising in the same way as one treats the gas in a hot air balloon. The steam particles can freely intermix with their cooler peers and there is no surface for the cooler air to push up against to buoy the steam upwards.

Thus, the rising of hot (or light) particles appears to directly contradict basic principles students learn in chemistry and physics courses. They are taught the Kinetic Molecular Theory, which claims the behavior of a gas is determined by chaotic, random collisions among its particles. They are also taught that the downward acceleration of gravity for each particle is the same. So how can some particles be favored to move upward if gravity treats them all the same and the chaotic motion is random?
Here is the 3-sentence answer:

The collisions between particles are random but on average they tend to work against gravity. Lighter particles are affected more by collisions than heavier particles, and faster particles undergo more collisions than slower particles. Thus, lighter and faster particles gain more upward momentum than their (heavier or slower) peers.

Two notes regarding the above explanation bear discussion. The first is simple. Lighter particles are almost always moving faster than their heavier peers because temperature is a measure of kinetic energy, which depends on both mass and speed. Thus, if a gas is a mixture of two or more kinds of particles (in thermodynamic equilibrium) the lighter particle must be moving faster on average to make up for having less mass. Thus, lighter particles are often buoyed by both principles.

The second note is more involved. In my books I emphasize contradictions taught by science textbooks. For example, a chemistry textbook will state that temperature is a measure of the average kinetic energy possessed by the microscopic particles of a substance. The same book will later claim that particles in a gas move much faster than particles in a liquid. But how can these statements both be true if water and steam can exist at the same temperature and pressure? If they have the same temperature, their particles have the same average kinetic energy, and if their particles have the same average kinetic energy (and the same mass), how can the particles of steam be moving much faster than those of water?

Hence, when I give the 3-sentence answer above, I immediately hope a student will ask, “But how can collisions work to push particles upward if all collisions conserve momentum? In any given collision, whatever upward momentum one particle gains is lost by the other particle.”

It would be great if students were taught to have such skeptical, discriminating minds. Unfortunately, most students are conditioned to accept whatever is told to them, in science class no less!

Regarding this hypothetical student’s question, the first thing that must be noted is that if collisions produced no net lift, all the particles would be lying on one another on the floor, and we would not be having this conversation because there would be no oxygen to breathe. The second point is that not all collisions conserve momenta among the particles. Consider a single particle striking the floor and rebounding. It gains upward momentum and is the only particle of interest involved.

These two points go together, of course. Consider a particle that has a mass of 1. If the negative acceleration of gravity is g, then gravity is reducing this particle’s momentum by 1*g every second. Assuming this particle is at equilibrium and is not changing its height much over time, the particle must be gaining 1*g momentum from some other source. The indirect source is the floor, which presses up on some particles, but the direct source is the individual collisions, which on average supply the particle with 1*g upward momentum.

These observations give us some confidence in the explanation, but one might still be puzzled as to how collisions have an average positive effect if only collisions between particles and the floor can have a net upward change in momentum, and most particles never hit the floor. The answer lies in a mathematical subtlety: the collisions undergone by each individual particle can (on average) increase momentum even if all the individual collisions between particles conserve momentum.

As an example, let’s say we looked at the collisions in a certain window of time and found:

  • Particle A rebounded off the floor, which increased its (upward) momentum by 5.
  • Then particle A, now moving upward, hit particle B, losing 4 units of momentum (which particle B gained).
  • This sent particle B moving upward, where it hit particle C, losing 3 units of momentum, which particle C gained.
  • Similarly, particle C hits particle D, transferring 2 units of momentum, and particle D hits particle E, transferring 1 unit of momentum. Particle E is at the top of the “cloud” of particles, so it does not hit another particle until it begins falling back down.

In this example, each individual collision conserved momentum, yet every particle enjoyed a net gain of (upward) momentum because it gained slightly more momentum in one collision than it lost in the other. This was, of course, a toy example, but it is easy to see that it must be this way because the interaction of the particles must counteract the force of gravity.


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  1. Dan Huisjen

    Not to be annoying, but I try to make a more important point, beyond the difference between hot particles rising and cold particles sinking: Heat does not rise; Warm air rises.

    The reason this is important is that most people don’t understand that heat moves by conduction, convection, and radiation, though I wish they did. Depending on circumstances, any of these can dominate, so that the net flow of heat is not necessarily upward. Warm air rising is a subset of convection, which is a subset of the total energy movement. Think big picture, people.

  2. Rudel

    Thanks, Dan, for posting.

    You are correct, a point I tried to clarify in Part I of this post, where I described that “heat” itself is not what is rising because heat refers to the _transfer_ of energy rather than the “hotness” of something.

  3. Matthew Bonnell

    invisible wrapper around hot air and consider it as a “parcel.”….

    well it is at the initial stage, there will be a wall made from cooler air particles (dense air) around the air that has taken the heat energy from the candle or whatever. The cool air takes time to react through diffusion.

    The wall of cooler air around the heat source will start to take some of the kinetic energy from higher K.E. particles but as this process takes place the particles closest to the heat source will create an area of less dense air, and higher pressure. They are forced in by the cool air whose particles start to absorb the K.E.(all mass, even air takes time to absorb energy).

    Now we have an area of low density gas sitting in a more densely packed pocket of cooler air. The rules of buoyancy apply, even though there are no walls the cooler air acts as a wall in the same way as a plastic wall would in a buoy. Particles hitting the walls of the boy bouncing back, and particles hitting the cool air, some bouncing back, some not. Kind of a semi-permeable wall.

    1. Rudel

      Hi Matthew, thanks for the comment.

      I don’t think this view really helps the situation much. There is not really a sheath of cooler air around the hot air in this case. There is hot air in the center, cooler air surrounding it, and cooler air surrounding that. There is just a gradient (albeit relatively steep at first) of temperature. More importantly, the cooler air has no structural linkage, so you cannot really apply principle of buoyancy because there is no definite boundary or volume. The imaginary boundary of cooler air is just as semi-permeable along one axis as another, so there is no favored plane to be picked out. Put another way, the hot air is not really “displacing” the cooler air because a molecule in the cooler air can move into the warmer region just as easily as it could move in any other direction. We don’t have one volume displacing another (required for buoyancy) we just have a region of hot air and molecules zooming around chaotically wherever they like.

      To put a finer point on this, I would say that this type of explanation could not explain why individual helium molecules (for example) rise. If you have individual helium molecules just floating around, dispersed evenly in a sea of other, heavier molecules, one cannot speak of any “less dense regions” at all…you just have a bunch of separate helium molecules scattered without any connection to one another. Yet they still rise, and by the same principle as the hot air off a candle.

  4. Matthew

    ok… so the packet i have described (i know you don’t like the idea of a packet of different density) will exist until the heat has diffused to neighbouring particles. During this time the packet (area of lower density) will have less mass and therefore less force downwards due to gravity than neighbouring packets of atoms of higher density.

    you say cooler air has no structural linkage, but you can feel wind blowing on your face when you run so dense air can create a reaction force to an increase of pressure.

    As we get closer to the surface of earth density increases due to gravity, therefore pressure also increases, and the amount of collisions on the bottom of the packet are higher compared to the top of the packet. Less collisions at the top will allow the particles to (generally and on average) travel further up before hitting the particles above (less dense due to gravity).

    Imagine 10 tennis players on one side of a court (this is the higher density air near the Earth’s surface) hitting many tennis balls (balls are less dense air) over to 2 players (the lower density air further from the Earth’s surface). Of course the players sometimes miss hitting the balls back and so some get through to the next line of players behind them, but on average the side with less players allows more of the balls through, creating convection.

    Looking at one atom of helium for instance… are you sure helium atoms rise after they are dispersed? Oxygen for another example once dispersed hangs around carbon dioxide, nitrogen and all the other gases on our atmosphere. If you put air in a jar and left it would it separate into different gases?

    1. Rudel

      You cannot speak of the force of gravity on the entire packet because there is no structural linkage. Gravity may be pulling down on each individual particle, but those particles are not connected, so the force felt by one particle is not transferred to others. The particles strike each other, of course, but they strike each other at random directions and during those collisions the no gravitational force is transferred.

      You cannot treat the group as an ensemble because they do not exchange force as an ensemble and their membership in one group or the other makes no difference with regard to how they interact with one another. If particle A strikes particle B, the outcome does not depend on whether particle A was deemed a “high density” particle and particle B a “low density” particle (by which I refer to the region, not the actual density of the particles themselves).

      When you feel wind blowing on your face, it is not because there is a difference in density. It is because you are striking the air particles, and you would feel the reactive force from those collisions regardless of whether there is a difference in density or not.

      To answer your question regarding Helium, etc., yes, helium continues to rise even when it is diffuse. This is why our atmosphere continually “bleeds” helium and so little is left today. The effect is much, much smaller for oxygen versus nitrogen, but the same principle applies. If you took a large volume of air, walled it off so there was no influx or outflux, then you would soon find a concentration gradient, where the air toward the bottom are more oxygen-rich and the air at the top are more nitrogen-rich.

      That is linked to another good example, perhaps the most universal one, showing that the buoyancy argument is not a good one. Imagine you did what I describe in the last paragraph: you took a big container of air and initially mixed it all up so that you had a nice distribution of individual particle velocities and individual concentrations. Not only would the oxygen tend to sink and the nitrogen tend to rise, but the air at the top would be lightly hotter than the air at the bottom, even though there were no “pockets” of hot air to begin with. The reason would simply be what I describe in my answer: at any given time, a molecule moving faster will undergo more collisions and the net effect will be to push such molecules upwards.

  5. Matthew

    Yes the net effect will push upwards, because there are more collisions happening underneath rather then from ontop… due to higher pressure on lower down. If all particles on the bottom bouncing off Earth exerted collided with lighter particles then the lighter particles will take some momentum and bounce up. As there are less particles above then it will gain more distance (on average) before it bounces down. This up, down, left right movement with less particles to collide with up will move it up.

    helium leaves our atmosphere because it has enough KE (on average) to escape the gravity well of Earth, much higher velocity than that of other gases…

    1. Rudel

      The escaping of helium particles is not due to their having greater K.E. Helium particles in the atmosphere, at thermodynamic equilibrium with other molecules, have the same KE on average as those particles, by definition of temperature. If two samples are at the same temperature, their individual particles have the same average KE. This means that a batch of helium particles at room temperature has the same kinetic energy (on average) as a batch of, say, nitrogen molecules at room temperature.

      With respect to the idea that particles rise because there are more collisions above them than below them, that explanation works okay for large objects but doesn’t work for microscopic particles. Yes, one can make the case that a molecule moving upward is likely to go farther before having a collision than a particle moving downward (because the pressure is changing a bit as it moves), but this effect is mitigated by the opposite effect that that upward-moving particle will then likely move farther downward after that collision because it is in a slightly less-dense region than the other particle who moved downward into a more dense region.

      More importantly, the above discussion of molecules moving upward or downward applies to heavier molecules as well, so on its own it cannot explain why lighter molecules rise compared to their heavier peers.

      That is why I laid out the answer as I did: collisions provide net upward momentum on ALL particles (without any regard to pressure or buoyancy, which does not apply where there is no definite boundary or structural forces to transfer force within a condensed phase) and the reason faster and lighter molecules rise more is because faster-moving particles encounter more collisions and lighter-moving particles are affected more by each one. Thus, of the upward force supplied by the collection of all collisions, faster-moving and lighter particles get a greater share of that upward momentum.

      If the net upward momentum received by a particle is greater than the loss of upward momentum caused by gravity, the molecule rises. If it is less, it will fall. When the net upward momentum a particle receives from its various collisions equals the net momentum it loses over the same period of time to gravity, the particle is at equilibrium.

      Note that this last point exposes why a buoyancy argument is flat-out wrong. A buoyancy argument suggests that the collisions (i.e. pressure) is what pushes some fluid down and pushes some fluid up. In other words, it says that the effect of the collisions is to provide a negative momentum to the particle. But this is quite wrong because if that were so the particles would be falling FASTER than in freefall, which almost never happens.

      Rather, even if the pressure above a molecule is higher than the pressure below it, the net effect of the collisions that particle undergoes are almost always positive, just not positive enough to overcome gravity.

  6. Joly

    Are we to assume that the number of particles per cubic inch are thereby constant the farther from the earths surface we go? if the particles per inch decreases the “higher” or farther we go from the earths surface then wouldn’t it make sense that the faster particles would naturally be moved to the more readily available space? Is this then why we are told that the transfer of thermal energy is often referred to as going from hot to cold because the kinetic energy is being transferred to slower moving particles and then parhaps to the earths surface itself thereby creating a layer of equilibrium at the surface?

    1. Rudel

      It does make sense that faster particles would more easily diffuse to the lower-populated area, but the difference in population density is so gradual that I don’t think it can account for the actual rates. Also, lighter gases like helium or hydrogen would naturally rise even if there were no difference in the concentration of particles (i.e., a cylindrical container in a constant gravitational field).

      Your remark actually leads to another reason why I think the explanation I gave is best. One might ask “Why are lighter particles faster?” The answer is the linked to the explanation in the blog post: lighter particles are faster because they are affected more by individual collisions. This is the qualitative reason behind the mathematics of thermodynamic equilibrium: if a population of particles are all “at the same temperature,” they have to be in thermodynamic equilibrium, and for lighter particles to be in thermodynamic equilibrium with heavier ones, they must be moving faster as a natural consequence of their being affected more by collisions.

      It is this same feature of lighter particles: that they are affected more by collisions, that explains why they tend to rise: the collisions provide a net positive pressure to particles in the population (countering the gravitational pressure pulling the particles down), and lighter particle receive a disproportionally large share of this positive pressure because they encounter more collisions and are affected more greatly by each one.

  7. Chad Warren

    Dr. Rudel
    I have a house with a basement. The upstairs is cooler than the upstairs in the summer time. Will opening the basement doors allow for the overall tempeture in the house to be cooler or will there always be this separation.

    1. Rudel

      Thanks for dropping by, Chad. Quick question: could you clarify your post. I’m assuming you meant to say that the basement is cooler than the upstairs in summer time, is that true?

      If so, then sadly opening the basement door will not (by itself) necessarily make much difference.
      However, if you can set up some circulation (with a fan or through some other means) to push the air from the basement into the ground floor, that should cool things down some. However, even this might not be a good idea if you use air conditioning in your main house and the basement is not well sealed.

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