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Thread: Temperature decrease with altitude

  1. #1
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    Temperature decrease with altitude

    I've got a question about why the atmosphere gets colder with altitude.

    Consider a perfectly insulated chimney stack many kilometres high on the surface of the Earth. It contains air, or any permanent gas.

    Apparently Maxwell stated that the temperature would be the same throughout the height of the air column. The reason air gets colder with altitude is due to convection and adiabatic cooling as parcels of air rise. This is the explanation I am aware of.

    However, now consider there is now a single gas molecule in the chimney stack. At the bottom it has kinetic energy and a velocity component in the direction up the stack, away from the surface of Earth. As it shoots up the stack it slows due to gravity. It is swapping kinetic energy for potential energy. At a certain height all of its kinetic energy (associated with the velocity component in the "up" direction) is converted to potential energy. At this point its kinetic energy is reduced, and in the case of a molecule with no transverse velocity it is basically at a temperature of zero Kelvin. Or at least zero-point energy.

    It will then start to fall back down to Earth, swapping potential energy for kinetic energy, until it regains its initial kinetic energy (and temperature) at the bottom of the stack. All this seems to mean there is indeed a temperature gradient in a column of gas caused simply by gravity, and not requiring any adiabatic expansion to explain it.

    Which is correct ?

  2. #2
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    All gross movement in the atmosphere is due to pressure . Heat transfer is mostly by molecule to molecule. In a chimney or in a bubble of gas, the molecules get heated mostly by the surface of the Earth. This reduces the density relative to colder gas. Gravity acts on both and thecolder column has higher pressure so the warmer air rises. In a chimney heat loss is limited so the lift is stronger.

    The energy as temperature is reduced by conduction to colder molecules. Or by radiation as the mean free increases.

    So the molecule does not use its ke to rise, it is pushed. Eventually it radiates ke away.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    All gross movement in the atmosphere is due to pressure . Heat transfer is mostly by molecule to molecule. In a chimney or in a bubble of gas, the molecules get heated mostly by the surface of the Earth. This reduces the density relative to colder gas. Gravity acts on both and thecolder column has higher pressure so the warmer air rises. In a chimney heat loss is limited so the lift is stronger.

    The energy as temperature is reduced by conduction to colder molecules. Or by radiation as the mean free increases.

    So the molecule does not use its ke to rise, it is pushed. Eventually it radiates ke away.
    I should also have said the base of the chimney stack is also perfectly insulated. The gas placed in the stack was initially at the same temperature as the stack walls and base. There is no heat source at the base of the stack. In this thought experiment there is no convection.

    The above reasoning (Post#1 para. 4) leads to a temperature gradient in the gas, caused only by gravity and the movement of gas molecules up and down. Some people think this is correct, others (such as Maxwell) say it can't be correct. I personally can't think what it is wrong with it, which is why I am asking.

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    The problem with Loschmidt's "gravithermal effect" is that it seems to have become some sort of weird supporting plank for the climate-change deniers, so sensible discussions tend to get drowned out in the search-engine results.
    The problem with your kinetic energy argument is that gases consist of more than one molecule, and while the kinetic energy of every molecule will decrease with height, the number of molecules also decreases with height, because slower molecules fall back before reaching the threshold height. This means that the average energy per molecule (=temperature) can stay the same with height. The classic paper on this is by Coombes and Laue (1985), unfortunately behind a paywall, but the first page gives you the gist of the argument, and I found a complete mathematical discussion and expansion of Coombes and Laue here.

    Grant Hutchison
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    Quote Originally Posted by grant hutchison View Post
    The problem with Loschmidt's "gravithermal effect" is that it seems to have become some sort of weird supporting plank for the climate-change deniers, so sensible discussions tend to get drowned out in the search-engine results.
    The problem with your kinetic energy argument is that gases consist of more than one molecule, and while the kinetic energy of every molecule will decrease with height, the number of molecules also decreases with height, because slower molecules fall back before reaching the threshold height. This means that the average energy per molecule (=temperature) can stay the same with height. The classic paper on this is by Coombes and Laue (1985), unfortunately behind a paywall, but the first page gives you the gist of the argument, and I found a complete mathematical discussion and expansion of Coombes and Laue here.

    Grant Hutchison
    I'm not getting it from that first page of the article that I can see.

    It seems to be saying that because the gas is less dense with altitude, that somehow compensates for the average kinetic energy of the molecules reducing with altitude. I don't see that at all, the temperature depends on the average kinetic energy and is nothing to do with the density of the gas?

    Oh hang on, is it a selection effect? The hot molecules travel further up and are therefore subtracted from the average of the cold molecules that don't travel as far up?

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    There's two reasons why is this happening. The first reason is gravity. Earth's gravity pulls air as close to the surface as possible.
    The second reason is density. As altitude increases, the amount of gas molecules in the air decreases—the air becomes less dense than air nearer to sea level. This is what meteorologists and mountaineers mean by "thin air." Thin air exerts less pressure than air at a lower altitude.
    High-altitude locations are usually much colder than areas closer to sea level. This is due to the low air pressure. Air expands as it rises, and the fewer gas molecules—including nitrogen, oxygen, and carbon dioxide—have fewer chances to bump into each other.

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    Yes, the problem with modelling the atmosphere from a single molecule is that it quickly yields an unphysical result. Because the molecule is moving more slowly at the top of the chimney than the bottom it will spend more time at the top. A collisionless population of molecules identical to this one would therefore yield an atmosphere that was colder and denser at the top--because at any given moment more of the molecules would be at the top rather than the bottom.

    But the real atmosphere contains molecules with a range of velocities, so the bottom of the chimney will contain some slow molecules that never get to the top, and some fast molecules that spend more of their time at the top than the bottom. To understand the real behaviour of the atmosphere you then need to understand how velocity is parcelled out among the various molecules, and to do that you need to invoke collisions between the molecules, like a real gas.

    In such a system, it's not individual molecules that are transferred from bottom to top, but kinetic energy. And the total kinetic energy at the top of the chimney is indeed lower than at the bottom, because of the potential energy gradient, as you say. But the total number of molecules at the top is also lower than at the bottom--less energy is parcelled out among fewer molecules, with the result that the average kinetic energy per molecule (=temperature) remains the same as you move from top to bottom in such a system. Molecules rising up the chimney lose kinetic energy, and then transfer that reduced kinetic energy by colliding with molecules higher up the chimney. But on average they collide with fewer molecules, so the average kinetic energy per molecule is conserved. (Imagine 10 molecules rising, losing energy, and then colliding with 9 molecules. One molecule must get hit twice, and therefore gains more energy, which it can then share collisionally with its 8 colleagues.)

    There's an obvious degree of handwaving above, but my two links put the conclusion on a mathematical footing.)

    Grant Hutchison
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  8. #8
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    As pressure decreases by altitude, the mean free path becomes a better way to understand why more energetic molecules can rise. Lower downthe rate of collision and ke sharing dominates.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by ChrisDecrow View Post
    There's two reasons why is this happening. The first reason is gravity. Earth's gravity pulls air as close to the surface as possible.
    The second reason is density. As altitude increases, the amount of gas molecules in the air decreases—the air becomes less dense than air nearer to sea level. This is what meteorologists and mountaineers mean by "thin air." Thin air exerts less pressure than air at a lower altitude.
    High-altitude locations are usually much colder than areas closer to sea level. This is due to the low air pressure. Air expands as it rises, and the fewer gas molecules—including nitrogen, oxygen, and carbon dioxide—have fewer chances to bump into each other.
    They have fewer chances - but if they were equal temperature, they would collide with the same energy when they do.
    Imagine a high and well insulated chimney.
    If the air in the chimney is sparse, the molecules readily fly from bottom to top and back without colliding, unless they fall back by gravity. If there is a small temperature difference, the molecules would rapidly mix and the difference be diminished by conduction.
    If the air is denser, the molecules collide before reaching the other end of chimney. The conductivity would be smaller - but the energy of molecules would still mix, and in absence of any heat flow, the stable result would still be no temperature difference after time.
    Now, if a small amount of heat is let into one end of chimney, it would slowly be conducted to the other end - irrespective of whether the heating is from below or from the top.
    However, if the heat flow from the bottom up gets big enough and the temperature gradient big enough, suddenly it becomes favourable for large amounts of air to rise and carry heat along. Convection only happens upwards.

    Air is colder at high altitudes when air is heated from below and somehow cooled from above. If air were heated from above, like by absorption of ultraviolet, and cooled from below, air would be warmer at high altitudes.

  10. #10
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    If the thought experiment is a tall vacuum chamber with a single molecule, or so few molecules they never collide, and so well insulated, we have a molecule bouncing about. If we also assume negligible loss by radiation, because the cylinder is also at constant temperature, a vertical moving molecule is gaining potential gravity energy and this must come from its KE, like a thrown ball. But this thought experiment is like space. It is so far removed from an atmosphere as to be negligible.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    But the important point is that in the limit of perfect insulation, like under a cloud deck opaque to all wavelength, if there is no heat flow then conduction will result in no temperature gradient, even if gravity still causes a density gradient. If heat flow is from above to below, like atmosphere which is heated by ultraviolet absorption above and cooled by infrared emission below, the temperature will fall downwards.

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    Quote Originally Posted by chornedsnorkack View Post
    But the important point is that in the limit of perfect insulation, like under a cloud deck opaque to all wavelength, if there is no heat flow then conduction will result in no temperature gradient, even if gravity still causes a density gradient. If heat flow is from above to below, like atmosphere which is heated by ultraviolet absorption above and cooled by infrared emission below, the temperature will fall downwards.
    In this scenario, the planet is colder than the 10/10 cloud. This must be temporary!
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    If the thought experiment is a tall vacuum chamber with a single molecule, or so few molecules they never collide, and so well insulated, we have a molecule bouncing about. If we also assume negligible loss by radiation, because the cylinder is also at constant temperature, a vertical moving molecule is gaining potential gravity energy and this must come from its KE, like a thrown ball. But this thought experiment is like space. It is so far removed from an atmosphere as to be negligible.
    I'm content to believe there is no temperature gradient caused only gravity. But that is because there are published articles by people who have much deeper understanding of thermodynamics than me, and I bow to their superior understanding. I don't get it myself.

    In the example you mention, a single molecule or sub-atomic particle can be assigned a "temperature". Simply a measure of kinetic energy per particle.

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    Quote Originally Posted by profloater View Post
    If the thought experiment is a tall vacuum chamber with a single molecule, or so few molecules they never collide, and so well insulated, we have a molecule bouncing about. If we also assume negligible loss by radiation, because the cylinder is also at constant temperature, a vertical moving molecule is gaining potential gravity energy and this must come from its KE, like a thrown ball. But this thought experiment is like space. It is so far removed from an atmosphere as to be negligible.
    I'm content to believe there is no temperature gradient caused only gravity. But that is because there are published articles by people who have much deeper understanding of thermodynamics than me, and I bow to their superior understanding. I don't get it myself.

    In the example you mention, a single molecule or sub-atomic particle can be assigned a "temperature". Simply a measure of kinetic energy per particle.

  15. #15
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    Quote Originally Posted by kzb View Post
    I'm content to believe there is no temperature gradient caused only gravity. But that is because there are published articles by people who have much deeper understanding of thermodynamics than me, and I bow to their superior understanding. I don't get it myself.

    In the example you mention, a single molecule or sub-atomic particle can be assigned a "temperature". Simply a measure of kinetic energy per particle.
    As has been said, temperature is an average of many particles. The energy of a single particle includes its velocity but also its state. Its velocity is a relative quantity. Its state includes its nuclear energy. This can be raised and lowered by photon transfer not related to gravity. In an atmosphere gravity causes pressure which we can manipulate as a separate parameter related to temperature by oldschool gas “laws”. But we know conduction and radiation have different explanations. This is partly why it was necessary to define the thermodynamic zeroth law to explain the temperature concept.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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