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The Altitude hypothesis

  1. Aug 22, 2010 #1
    Hypothesis
    A contained body of gas that is within a field of gravity will have differing temperature in differing locations within the body. These differing temperatures can be utilised to by a heat engine, to convert heat energy into other forms.

    Background
    Heat can be described as the disordered vibrations and movements of molecules. Even though it is differentiated from the other forms of energy, it is essentially an unordered form of kinetic energy.

    In a gaseous state, molecules are free to move with and against gravity. When they move with gravity they gain more velocity, increasing the contribution of energy that the particular molecule gives as heat energy in that particular location it enters. When they move against gravity they lose velocity, decreasing the contribution of energy that the particular molecule gives as heat energy in the particular location it enters.

    This is apparent in everyday live when you consider that it is generally colder in a tall mountain than at sea level as the gas molecules lose heat energy as they move to higher altitudes.

    The very important distinction must be made that moving an perfectly insulated contained body of gas to a higher altitude will not cool the gas, as the gas has not been transported to the location by its heat energy, but by mechanical energy applied to the container.

    Thought Experiment 1
    This hypothesis is best understood when depicted in a thought experiment.

    Imagine a very tall structure ascends from a hot desert into the sky, to a point where it is so cold that a bottle of water would freeze at the top. This structure supports an elevator style mechanism that is of the highest efficiency, which lifts a device and drops a device that is exactly the same simultaneously. The result is that if one device is lifted to the top of the structure, the other rests at the bottom in the hot desert.

    These devices are large bodies of water that are perfectly insulated, with the addition of reversible heat engine, that when activated will connect the insulated body of water and the outside world.

    The device at the top of the structure is at the same temperature as its surroundings and the one at the bottom is at the same temperature as the hot desert. The elevator is activated and the devices swap position. As both bodies of water are insulated they are not the same temperature as their surroundings anymore. The heat engines are activated allowing the heat of the desert to enter the cold body of water and the heat of the other body of water to disperse into high altitude. During this process the heat engines extract the maximum amount of energy from the heat gradients until both bodies are at equilibrium with their surroundings. This process can then be re conducted.

    Issue
    I assume that the moving of the devices could approach almost 100% efficiency theoretically with the heat engines approaching Carnot efficiency. Based on this assumption, the energy extracted from the heat engines is greater than the loss caused by changing the positions of the sub-devices, this device could perpetuate.

    Replacing the atmosphere with a long insulated container of gas. The device would not be able to perpetuate as it would absorb the heat energy from the system reducing it to a point where the device could no longer perpetuate. In this instance however, the system has reduced entropy.

    Such an assumption would contradict the second law of thermodynamics.
     
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  3. Aug 22, 2010 #2

    rcgldr

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    There are somewhat similar devices used to harness some amount of energy from the ocean via very tall pipes, but I'm not sure how much the difference in salinity as well as temperature versus depth plays a role.
     
  4. Aug 22, 2010 #3

    alxm

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    Wrong.

    Wrong. The energy gets continually re-distributed in the intermolecular collisions. That's how diffusion works. And the potential energy difference is ridiculously tiny compared to a gas molecule's kinetic energy. By that kind of reasoning, we should all suffocate since the heavier CO2 in the atmosphere should collect at ground level.

    No, that's not why it's colder at altitude. It's colder at altitude because you're farther away from a warm body, namely the earth.
     
  5. Aug 22, 2010 #4
    It not perpetual motion machine in any sense, the 'extra' energy you see comes from the desert being heated by the sun.
     
  6. Aug 22, 2010 #5
    i get what you are saying alxm, heat does diffuse throughout the the body and that the difference in heat on earth is partially due to the the source of heat. However when you consider mountains, they are close to the warm body, as the high altitude surroundings are absorbing the em radiation given off by the sun.

    You stated that gravity would affect the temperature of particular locations with in a given body, just not significantly. If I changed the location of the thought experiment from earth to a more massive planet I would consider that this effect would become more significant, would you not also?

    rcgldr, interesting device. do you have a link to some info on it?

    Sakha, I would defiantly agree with the heat source reasoning, if one can highlight that in no way does gravity induce a heat difference within a body of gas.

    Now I am wondering that if hypothetically a long piece of copper wire was placed against the structure in the thought experiment, with the entire piece covered in a perfectly heat insulating material except for a small length at the end on to of the structure. If one left this for a significant amount of time and then cut the wire at the bottom, exposing some copper, so that one could measure the temperature of the copper. Would the copper at the bottom, be as cold as the top?
     
  7. Aug 23, 2010 #6

    alxm

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    Why are you even trying to debate this point? It's a simple fact that gravity has nothing to do with why it's cold farther up in the atmosphere. And mountains are colder because a 'mountain' is by definition a protrusion of the earth's surface up into higher, colder, altitudes, where the layers of air are - on average - much farther from the earth.

    No, I did not say that.
     
  8. Aug 23, 2010 #7

    rcgldr

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    Wiki article about solar updraft tower:

    http://en.wikipedia.org/wiki/Solar_updraft_tower

    Ocean thermal energy conversion:

    http://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion

    Salt fingering: (I'm not sure if this caused the small fountain effect I saw in an old television show, related to perpetual salt fountain):

    http://en.wikipedia.org/wiki/Salt-fingers

    Not sure if perpetual salt fountains ever were useful, since wave powered tall vertical tubes in the ocean with one way valves would probably be more efficient.

    http://gcaptain.com/maritime/blog/tubes-in-the-ocean-→-bizarre-marine-technology
     
    Last edited: Aug 23, 2010
  9. Aug 23, 2010 #8
    Can anyone explain why a closed body of gas will have no variance in temperature in detail if subjected to gravity?

    thank you for the links, rcgldr
     
  10. Aug 23, 2010 #9
  11. Aug 23, 2010 #10

    alxm

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    Oh look! Someone else made the same erroneous claim on the internet! It must be true! (ooh and he's a BSEE.. That says a lot, given we all know how much atmospheric thermodynamics is in the EE curriculum these days!)

    Air temperature goes down with elevation due to increased distance from the earth. The atmosphere is heated by the Earth, not vice-versa. This holds up to the tropopause, after which, in the stratosphere, the temperature then increases with height again, due to conduction downwards from the ozone layer, which is heated by solar UV.

    Need I go on, or is this enough to convince you your 'hypothesis' has no basis in reality, and doesn't even come close to describing how the temperature changes with altitude?
     
  12. Aug 24, 2010 #11

    cjl

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    There is actually some truth to that claim. It isn't the basis for the earth's temperature gradient, but it is true that as a parcel of warm air rises, it will expand and cool, and this causes a natural maximum temperature gradient that the atmosphere can have (as if the temperature gradient becomes steeper than this, then convection will dominate the heat transfer into the upper atmosphere, which flattens the temperature gradient back down to this level).

    For more info, look up "Adiabatic lapse rate". The lower atmosphere of Venus has a temperature gradient driven primarily by this, as do gas giants.
     
  13. Aug 25, 2010 #12
    Im aware that temperature does not just simply drop with altitude, due to uv absorbtion. What i said is not the absolute reason as to why there is a difference in temperature within the atmosphere, but it does play a part. So how does one rule out the issue in the first post?

    Alxm can you find something that backs up your points?
     
  14. Aug 25, 2010 #13
    Without an external source of energy, every closed system will equalize in temperature as it approaches equilibrium. Can you give any reason why this would be different when gravity is involved? Any reason at all to think such an effect exists? (And as has already been pointed out, planetary atmospheres are not such a reason.)
     
  15. Aug 25, 2010 #14
    why is gravity factored into lapse rate?
     
  16. Aug 30, 2010 #15

    D H

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    No, you are wrong.

    Yes and no. It's cooler at altitude because air is in general a poor conductor of heat, a poor absorber of heat and because pressure decreases with altitude. That air does conduct heat to some extent and that the atmosphere does absorb some of the incoming sunlight mitigates the effects of altitude. The environmental lapse rate is considerably less than the dry adiabatic lapse rate.

    Wrong again. At least you are consistent.
     
  17. Aug 30, 2010 #16
    Exactly.
    Air pressure varies with altitude due to gravity. Temperature varies with altitude due to air pressure difference and adiabatic expansion (adiabatic lapse rate 9.8 degrees C per kilometer). See

    http://farside.ph.utexas.edu/teaching/sm1/lectures/node56.html

    In Death Valley National Monument (California), it is possible to stand on Telescope Peak (elev. +3366 meters) on the west side and directly look down at Badwater (elev -85 meters) where the air temperature is ~ 30 degrees C higher. As the air blows up the east side of Death Valley to Dante's View (elev ~ +1700 meters), it cools again, due to the adiabatic lapse rate of ~ 9.8 degrees C per kilometer.

    Bob S
     
    Last edited: Aug 30, 2010
  18. Aug 30, 2010 #17

    D H

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    As has already been pointed out, the pressure gradient in the Earth's lower atmosphere is the primary reason why temperature decreases with increasing altitude. As BobS already pointed out, the dry adiabatic lapse rate is 9.8 C per kilometer. This is explained solely by assuming that (a) air does not absorb or lose energy from sunlight or from the surrounding air (that's why this is called the adiabatic lapse rate), and (b) the atmosphere is in hydrostatic equilibrium.

    The true lapse rate is typically less than the adiabatic lapse because assumption (a) is not always true. Extremely humid air releases heat as water vapor condenses to form water droplets. Humid air is not transparent in the infrared, so it also absorbs energy from sunlight. Another example: Ozone absorbs energy from sunlight, which is why the lapse rate is positive in the stratosphere.

    Above the stratosphere the assumption of hydrostatic equilibrium fails. This thread however is not about the upper atmosphere.
     
  19. Aug 30, 2010 #18
    If I break the hypothesis into two parts:
    (a) A contained body of gas that is within a field of gravity will have differing temperature differing locations within the body.
    (b)These differing temperatures can be utilised to by heat engine, to convert heat energy into other forms.

    Part A appears to be confirmed by the more senior users who have posted.

    So two questions remain:
    (1) Is part B valid?
    (2) Is the hypothesis in violation of the second law of thermodynamics?
     
  20. Aug 30, 2010 #19

    D H

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    Part A is correct, but only on a very, very large scale. On a small scale (house or building size is small) the temperature can and does rise with increased height. Remedying this is why people install ceiling fans in their houses.

    Part B, I don't think so. Suppose you make a container that is very, very tall and very well insulated, heated only from the bottom. Fill it with dry air and let it come to equilibrium. The resulting temperature gradient that results will be the minimum energy configuration of the column. Just because there is a temperature gradient does not necessarily mean that usable energy can be extracted from the column.
     
  21. Aug 30, 2010 #20
    So considering thought experiment one, where do you think its shortcomings are?

    also would the temperature gradient differ for different gases?

    Would a temperature gradient exist for solids and liquids?
     
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