Carlos

Science Brain Bogglers (Round 1?)

77 posts in this topic

Have you ever observed the behavior of smoke from a fireplace when the flue is closed? It quickly fills up the room looking for a way to escape. When the flue is opened, voila! The smoke has somewhere to go. Now, imagine the ozone hole over the Antarctic as a giant flue. The warm air resulting from the thermal heating of the Earth's surface now has somewhere to go. Therefore lower temps at higher altitudes.

But seriously, would the answer have something to do with gravity and the ideal gas law? When one moves farther away from the center of the Earth, the force due to gravity decreases. Now begins my wild guess: When we have P=F/A, where P is the pressure, F is the force exerted and A is the area upon which the force is acting, substitute w=mg for F, where w is weight, m is the mass of an object and g is acceleration due to gravity. We can see that as g decreases (all else held constant), P will likewise decrease.

On to the ideal gas law. We have PV=nRT. For a given volume, V, as P decreases, T will follow proportionately (R is a constant and n, I think, can be held constant).

Is that it? What did I win?

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But seriously, would the answer have something to do with gravity and the ideal gas law? When one moves farther away from the center of the Earth, the force due to gravity decreases. Now begins my wild guess: When we have P=F/A, where P is the pressure, F is the force exerted and A is the area upon which the force is acting, substitute w=mg for F, where w is weight, m is the mass of an object and g is acceleration due to gravity. We can see that as g decreases (all else held constant), P will likewise decrease.

On to the ideal gas law. We have PV=nRT. For a given volume, V, as P decreases, T will follow proportionately (R is a constant and n, I think, can be held constant).

Is that it? What did I win?

The radius of the Earth is a little over 6000 kilometers. The troposphere--the lowest layer of the atmosphere, where we live and virtually all weather phenomenon as well as the majority of the mass of the atmosphere resides--is only about 20 kilometers thick. Whatever variation in g occurs over 20 kilometers of altitude will be so small as to be insignificant (do you feel any difference in your weight on an airplane?).

The ideal gas law has different forms depending on whether you are dealing with the number of moles or the number of molecules (n/N) enclosed within the volume V.

You are thinking about important things though, which is considering how the density/pressure/temperature change with altitude. The atmosphere becomes "thinner" with altitude, which is to say that both the density and the pressure of the air decrease with height off of the ground. This is very important in relation to why temperature decreases with altitude.

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How does the atmosphere actually cool on the nightside of the Earth? Outer space may be extremely cold, but it is close to vacuum, so there is nothing to conduct the heat away from the Earth.

You had mentioned earlier that rising warm air would encounter cold air, so the rising air would cool off and sink back down. But in doing so the cold air should be constantly gaining heat energy and warming up. Why doesn't the atmosphere eventually become isothermal?

This is how I think the atmosphere cools on the nightside of the Earth. You mentioned that "65F water feels really cold while 65F air only feels slightly cool; the much denser water is a much greater conductor of heat energy, and it can cool you off much more rapidly than air alone." The Earth is a greater conductor of heat energy than the air. When the sun is no longer heating up the surface, the Earth begins to loose the heat energy. As it is cooling off, it absorbs what heat energy is in the air around it, cooling it down as well. Basically the earth warms up and cools down quicker than the air and directly controls the temperature of the air around it.

So one side of the Earth is heating the air while the other side is cooling the air and the atmosphere cannot become isothermal.

But this leads to the problem that the lower you are the cooler it would be when it is night. This is not right, correct? I will have to give this problem some more time.

Sorry, this isn't the correct answer but your observations are on the right track. The Earth is a greater conductor of heat than air, and the Earth (through absorbing sunlight) is what primarily heats the air, but it cannot in general cool off more quickly than the air. The air is able to change in temperature with the greatest rapidity simply because there is very little mass in the air compared to all the enormous amount of mass that is in the ground beneath our feet and the bodies of water around us. This is especially obvious when there is very little water vapor in the air right around sunset, as you can feel over a span of 30 minutes the air rapidly dropping in temperature.

But there can actually be situations where (at the higher latitudes in North America) when the ground is covered in snow the ground can cool so rapidly so as to cause a temperature inversion in the atmosphere (near the Earth the temperature increases with height briefly, then reverses and decreases with height). This pile of cold air near the ground can then drain southwards in N. America. The physical mechanism behind this is rather interesting; although snow almost perfectly reflects optical light, it still can emit infrared light very well almost as if it were a perfect blackbody. Therefore during the day an enormous amount of sunlight is reflected back to space instead of being absorbed and heating the ground, and then at night the snow covered ground radiates copiously in the infrared, draining even more heat energy from the ground.

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Heat rises because it is less dense than cold air: in effect, it has more buoyancy. So it is a given that it will cool as it equilibrates with the surrounding air above it.

But why doesn't the colder air warm as the warmer air equilibrates, over time causing it all to become isothermal?

The warm air does warm the cooler air above it. It can only become isothermal if it is in a closed system. As I said before, without a roof covering the earth, heat his radiated to space. Thus, there is a long term tendency for the atmosphere to cool. But that doesn't mean that, locally, warm air can not be above cooler air due to air currents in the atmosphere, such as warm air over the ocean moving over land that has cooler air, or warm air over land moving over cooler air over the ocean.

But the Earth is constantly cooling by emitting radiation, as are all layers of the atmosphere. This alone can't explain why our atmosphere isn't isothermal.

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I'm not sure if I'm allowed to comment, since I deal with heat flow issues from time to time in connection with electronic equipment design and electronic devices that consume power and need to dissipate the heat somewhere. I learned a little about thermal conductivity in college and have learned more in my professional work since then, although my main specialty is the electronics rather than the thermal issues.

First, there is radiated energy. The sun radiates; the Earth absorbs. The Earth's atmosphere is largely transparent to the sun's radiated energy, but the ground absorbs the Sun's energy when facing the Sun, and can get rid of the energy when facing away from the Sun.

There are two ways for the Earth to get rid of energy that it receives from the Sun: radiate it back into space through a largely transparent atmosphere, and/or conduct it into the material of the atmosphere, which will then naturally be warmer closer to the ground and cooler farther away from the ground (closer to outer space). The difference in temperature between the ground level of the atmosphere and the highest "space" level is essential in order to cause heat conduction through the material of the atmosphere. The atmosphere, like all materials, has thermal "resistance," i.e., a relation between temperature differences and conducted heat flow. A temperature difference is needed to drive the flow of the heat (by conduction).

In the case of electronic devices, dissipating power in the device causes the "junction" temperature (inside the material of the device) to rise. The temperature keeps on rising as high as needed to cause sufficient conducted heat flow through the material of the device and out into the surrounding environment, so that the total heat energy conducted outward exactly matches the energy being driven into the device electrically. If the thermal resistance of the conduction path is too high, the temperature inside the device can easily rise to a high enough level to cause internal damage to the device. This is why device cooling is extremely important in electronic equipment design where significant electrical power levels are involved. The electrical power gets converted to heat, and the heat has to flow somewhere. If it is blocked, it builds up, in the form of rising temperature, until there is a high enough temperature difference to drive the heat outward at a rate sufficient to balance the electrical power being pumped in. If this doesn't happen before the device gets excessively hot, it may melt and stop working, like a fuse. Or it may simply deteriorate gradually over time and become increasingly degraded in its performance. (Hot devices can also cause discoloration of circuit boards and serious burns to human fingers, too, often at far lower temperatures than would be needed to damage the devices. I will never forget the experience of touching a 3 watt wire-wound resistor once that was dissipating about 2.5 watts of power. It was operating within its rated specification, but was easily hot enough to burn my finger in less time than the automatic human reflex of withdrawing my finger.)

So what I think we have with the Earth's atmosphere is a layer of material that acts like a partial heat insulator (for conducted heat). Radiated energy from the Sun passes through the atmosphere without doing much to the atmosphere itself, depending on how cloudy or smoky the air is, and the Sun's radiated energy is absorbed by the Earth. The ground is a good absorber. The Earth warms up. The Earth keeps warming up until there is a high enough temperature difference between the ground and the outermost level of the atmosphere to drive heat conduction through the material of the atmosphere out into space (in addition to any heat radiated directly into space instead of being conducted). The atmosphere won't be of constant temperature because it has thermal resistance, a heat source on one side, and a heat sink (outer space) on the other. It is not a perfect heat conductor.

Boiling water is another example. The bottom of the pot will be hotter than the surface of the boiling water, because that temperature difference is what drives the conducted heat flow updward, through the water and into the air above and around the pot. (The side of the pot bottom in contact with the flame or burner will also be hotter than the side of the pot bottom in contact with the water. That temperature difference, again, is what drives the heat conduction through the material of the pot, although pots with thin copper bottoms won't need as great a temperature difference as thicker iron or aluminum pots.)

To those who know the physics more fully than I do, am I on the right track here? (Or if I know too much, should I keep quiet?)

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As a quick reply, you are of course allowed to post your reasoned out answer. I just didn't want people to look up internet resources or to answer my question if they already knew the answer (because this would ruin the fun).

Thank you for your reply System Builder, I'll read it carefully later today when I have more time available!

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There are two ways for the Earth to get rid of energy that it receives from the Sun: radiate it back into space through a largely transparent atmosphere,
The atmosphere is almost perfectly transmitting for optical light, but it is nearly perfectly opaque for infrared light. The infrared light (also called longwave radiation) emitted by the Earth is largely absorbed by the atmosphere. The atmosphere then reradiates this energy, with half of it being radiated upwards to higher atmospheric layers, and the other half radiated back down on the Earth itself. (this is an incredibly crude and stripped down picture of the greenhouse effect).
and/or conduct it into the material of the atmosphere, which will then naturally be warmer closer to the ground and cooler farther away from the ground (closer to outer space). The difference in temperature between the ground level of the atmosphere and the highest "space" level is essential in order to cause heat conduction through the material of the atmosphere. The atmosphere, like all materials, has thermal "resistance," i.e., a relation between temperature differences and conducted heat flow. A temperature difference is needed to drive the flow of the heat (by conduction).
The Earth as a whole cannot cool by conduction of heat because there is nothing to conduct the heat to. Outer-space is close to vacuum, and cannot conduct any meaningful amount of heat away from the Earth, regardless of how cold it is. Our planet as a whole cools nearly entirely by emitting long-wave radiation.
So what I think we have with the Earth's atmosphere is a layer of material that acts like a partial heat insulator (for conducted heat). Radiated energy from the Sun passes through the atmosphere without doing much to the atmosphere itself, depending on how cloudy or smoky the air is, and the Sun's radiated energy is absorbed by the Earth. The ground is a good absorber. The Earth warms up. The Earth keeps warming up until there is a high enough temperature difference between the ground and the outermost level of the atmosphere to drive heat conduction through the material of the atmosphere out into space (in addition to any heat radiated directly into space instead of being conducted). The atmosphere won't be of constant temperature because it has thermal resistance, a heat source on one side, and a heat sink (outer space) on the other. It is not a perfect heat conductor.
Good try, but sorry the atmosphere of the Earth is much too thin to transport heat energy simply by conduction. How the atmosphere does help to transmit heat away from the surface of the Earth is by convection (the rising of warm parcels of air) and also by evaporation and condensation of water. Evaporating water from the surface of the Earth drains heat energy from the surroundings, and when the water vapor rises in the atmosphere and condenses to form clouds that energy is released as latent heat at a higher altitude, helping to "pump" heat from the surface of the Earth to higher altitudes in our atmosphere. (which is why extreme heat usually occurs in very dry areas.)
Boiling water is another example. The bottom of the pot will be hotter than the surface of the boiling water, because that temperature difference is what drives the conducted heat flow updward, through the water and into the air above and around the pot. (The side of the pot bottom in contact with the flame or burner will also be hotter than the side of the pot bottom in contact with the water. That temperature difference, again, is what drives the heat conduction through the material of the pot, although pots with thin copper bottoms won't need as great a temperature difference as thicker iron or aluminum pots.)
Boiling water in a pot though is a good example to consider and compare to our atmosphere being heated by the ground. The water in the pot is heated by the hot metal bottom, and convection causes the water to rise and turn over until the water is nearly isothermal throughout the pot. Why doesn't this ever happen with the Earth's atmosphere?

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The air cools as it rises because there is lower air pressure at higher altitudes. Pressure is proportional to temperature.

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The air cools as it rises because there is lower air pressure at higher altitudes. Pressure is proportional to temperature.

Ok, we are really getting on the right track, but this still isn't an explanation of the physical mechanism.

Yes, pressure is proportional to temperature in the ideal gas law PV=NkT but this doesn't answer the question. You can say that pressure decreases as the density of air molecules N/V decreases with altitude without having to consider temperature at all. Something else is needed for an explanation...

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Some additional questions and observations:

1. I was thinking further about the boiling water pot myself and realized that for a very vigorous, rolling boil, there is probably enough stirring of the liquid to keep it all at about the same temperature, particularly if it has reached the temperature at which the liquid starts changing into gas. As I recall, at the "phase change" temperature, the temperature remains constant as more and more material changes phase (e.g., from liquid to gas) as a result of the continuing heat being pumped in. At the same time, water vapor is being released into the air above the pot, which will eventually result in the pot boiling dry if there is no new water to replace the boiled off water vapor as the heating continues.

2. Could it be that we don't see that same effect for the earth as a whole because the "boiling" simply isn't vigorous enough to stir up the atmosphere to that degree? Wouldn't a pot that hasn't yet reached the phase-change temperature show a temperature difference between the liquid near the top and the liquid near the bottom? Isn't it also true that very little of the earth's atmosphere is ejected into space, unlike the water vapor bubbles in a rolling boil? (And whatever material is ejected is replaced by new emissions, mainly from natural sources such as volcanoes and decay of living matter?)

3. If heat pumped into the atmosphere (due to radiation from earth at a long wavelength, conduction from earth, and convection of heated air) is matched by heat radiated into space by the atmosphere, and heat radiated back toward earth by the atmosphere, then doesn't that explain why the temperature at higher altitudes is cooler (along with the pressure drop)? And doesn't it still reduce, in terms of the overall effect, to heat flowing away from the earth through the atmosphere because of the temperature difference between upper and lower altitudes? To get atmospheric heat that is radiated into space to balance the heat pumped into the atmoshpere from the warm earth, doesn't there have to be a temperature decrease as altitude increases (given the lack of the "rolling boil" and "boil off" effects)? I.e., it's still basically a heat source and heat sink, separated by material (atmosphere), even considering that the final heat flow from atmosphere into space is by radiation rather than conduction? And doesn't the process *have* to reduce to that as long as the atmosphere allows new heat energy to reach the earth from the sun without much blockage between the sun and earth's ground level?

4. As already noted in earlier discussion, there can be cases of "temperature inversion." Are these primarily due to water condensation effects? I also seem to recall that the Los Angeles basin in California is nearly always under an "inversion layer" that greatly aggravates LA's smog problems. Is that a temperature inversion?

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OK, here's my attempt:

(1) We feel cold when we send some of our heat away. We do that by radiation, but mostly by transpiration & by heating up the air layer next to our skin. When we transpire, we effectively heat up a very small quantity of water (we "charge" it with heat, if you wish), and then we send it away. Therefore we cool off. We also cool off by heating the layer of air closest to our skin and then sending it away, for example with a ventilator. If the air is cold to start with, then we shed even more heat to warm it off, and we get even cooler - hence, AC.

(2) In high altitude the low pressure leads to a faster evaporation. Therefore we shed away more heat via transpiration. We might also loose other warm gases from our skin. In addition, the layer closest to our skin is less dense, so on one hand there are fewer molecules to be heated up by direct contact, but on the other hand the layer is renewed much faster. Finally, we might (I'm not sure about that) be shedding heat faster via radiation (IR emission) because the less dense air is more permeable to our radiation than the dense, moisture & particulate rich air at sea level.

(As a side note, what would happen to a perfect sphere of say steel heated up to say 800 C? Would it cool off faster at high altitude than at ground level? I suspect it wouldn't. Looking forward to being enlightened on this.)

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We might also loose other warm gases from our skin.

Or via respiration. We would almost certainly loose some warm nitrogen which at sea level is dissolved in our blood. Barring a bad case of the bends, this warm gas would normally escape via respiration, if I'm not mistaken.

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The air cools as it rises because there is lower air pressure at higher altitudes. Pressure is proportional to temperature.

Ok, we are really getting on the right track, but this still isn't an explanation of the physical mechanism.

Yes, pressure is proportional to temperature in the ideal gas law PV=NkT but this doesn't answer the question. You can say that pressure decreases as the density of air molecules N/V decreases with altitude without having to consider temperature at all. Something else is needed for an explanation...

I believe the Second (or third?) Law of Thermodynamics holds that an expanding gas cools, hence we have air conditioners. So as the pressure drops at higher altitudes, it expands and cools.

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I believe the Second (or third?) Law of Thermodynamics holds that an expanding gas cools, hence we have air conditioners. So as the pressure drops at higher altitudes, it expands and cools.

This is very close, so here is the answer:

Pressure drops exponentially with altitude, and the primary source of heat energy for our atmosphere is through direct conduction from the ground (which is the dominant absorber of solar radiation). When a parcel of air near the ground warms sufficiently it will begin to rise upwards in our atmosphere. Since pressure decreases with altitude our warm parcel of air will expand, but in order to expand this warm parcel of air must push the surrounding air out of the way.

When the warm parcel of air expands and pushes back the surrounding air, it is doing work on that surrounding mass of air. Work requires energy, and that energy comes from the thermal energy of our rising warm parcel. Therefore, as the warm parcel expands it cools and lowers its temperature.

Due to the very low thermal conductivity of air, the amount of heat that gets transferred between the warmer rising parcel of air and the surrounding colder air is negligible; this means that the surrounding colder air doesn't get any warmer, and the heat of the rising parcel of air is converted mainly to the mechanical energy of pushing the surrounding air out of the way.

It is in this (very simplified) way that near the ground we remain relatively warm, but higher in the atmosphere the temperature drops significantly.

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As a note to everyone: thank you very much for participating, and sorry for my negligence of this thread during the last two weeks. My semester began on Aug 24th at a breakneck pace and I completely forgot about monitoring this thread.

I have several good ideas for further science brain bogglers, but I'm first going to consider whether I can set aside enough appropriate time and focus given what will be a very busy and stressful semester.

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As a note to everyone: thank you very much for participating, and sorry for my negligence of this thread during the last two weeks. My semester began on Aug 24th at a breakneck pace and I completely forgot about monitoring this thread.

I have several good ideas for further science brain bogglers, but I'm first going to consider whether I can set aside enough appropriate time and focus given what will be a very busy and stressful semester.

Thanks for the fun exercise, Carlos.

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This is very close, so here is the answer:

...

There is a much simpler explanation that everyone should routinely know and which does not required knowledge of thermodynamics: border collies herd the phlogisten to keep us warm and safe.

The principle of hot air rising is very different and is related to politicians.

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New Brain Boggler

This one is actually literally based on a personal experience:

You have before yourself a selection of metal coins (currency) from different countries. You also have a small, very powerful magnet. By moving the magnet around through the pile of metal coins you can very quickly verify that some of the coins are magnetic while others are not magnetic at all. (by magnetic, I mean that when the magnet is placed near the metal coin the coin becomes magnetized and is strongly attracted towards the magnet).

You take from the pile a coin that is not magnetic. You set it on a smooth wooden surface, and hold the magnet very near (but not touching) the coin. In a quick, sudden movement you jerk the magnet to the right and the coin briefly jerks to the right as well. You do the same, but this time to the left and the coin jumps to the left again. Perplexed, you hold magnet a distance horizontally away from the coin and very swiftly pass it over the coin just high enough so that it doesn't strike the coin; as the magnet passes over the coin the coin briefly tries to move and follow the magnet.

What's going on here? Remember, the coin is not magnetic at all.

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There is a much simpler explanation that everyone should routinely know and which does not required knowledge of thermodynamics: border collies herd the phlogisten to keep us warm and safe....

Are the border collies wearing fire-suits??

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There is a much simpler explanation that everyone should routinely know and which does not required knowledge of thermodynamics: border collies herd the phlogisten to keep us warm and safe....

Are the border collies wearing fire-suits??

They have double insulated fur coats. No border collie has ever been fired.

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Perplexed, you hold magnet a distance horizontally away from the coin and very swiftly pass it over the coin just high enough so that it doesn't strike the coin; as the magnet passes over the coin the coin briefly tries to move and follow the magnet.

What's going on here? Remember, the coin is not magnetic at all.

The explanation is that you were perplexed because you didn't know why the magnet moved the non-magnetic coin.

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New Brain Boggler

This one is actually literally based on a personal experience:

You have before yourself a selection of metal coins (currency) from different countries. You also have a small, very powerful magnet. By moving the magnet around through the pile of metal coins you can very quickly verify that some of the coins are magnetic while others are not magnetic at all. (by magnetic, I mean that when the magnet is placed near the metal coin the coin becomes magnetized and is strongly attracted towards the magnet).

You take from the pile a coin that is not magnetic. You set it on a smooth wooden surface, and hold the magnet very near (but not touching) the coin. In a quick, sudden movement you jerk the magnet to the right and the coin briefly jerks to the right as well. You do the same, but this time to the left and the coin jumps to the left again. Perplexed, you hold magnet a distance horizontally away from the coin and very swiftly pass it over the coin just high enough so that it doesn't strike the coin; as the magnet passes over the coin the coin briefly tries to move and follow the magnet.

What's going on here? Remember, the coin is not magnetic at all.

The changing magnetic field, from your movement, creates and electric field in the metallic coin. The electric field has a corresponding magnetic field which responds to the magnet in your hand.

Interesting example, but I have never tried to do that experiment.

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