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Does the atmosphere cool with altitude due to gravity?

  1. Jun 21, 2015 #1
    I read an article a day or so ago titled Hydrostatic Lapse, which makes the case for a phenomenon that I thought was well and truly confirmed; that gravity is responsible for the cooling of air with altitude. However I discover in the sequel article The Gemini Cycle that this phenomenon is supposedly in conflict with the second law of thermodynamics.

    After a bit of research, I find that Vanquish Opprobrium (author of those articles) isn't the only one who thinks the two are incompatible. Robert G brown from Duke University also makes the case for incompatibility in Refutation of Stable Thermal Equilibrium Lapse rate.

    Although both agree that they are incompatible and assert that in very similar ways. Robert G Brown comes to the conclusion that a hydrostatic gas is isothermal in nature, where as Vanquish Opprobrium comes to the conclusion that the second law is likely false.

    Vanquish Opprobrium is probably a crackpot, hence the nom de guerre. Yet hydrostatic lapse seems so intuitive. If an atmosphere's gas particles didn't slow at higher elevations, they would escape earth's gravity field and we would be left with no atmosphere.

    Surely they are both wrong?
  2. jcsd
  3. Jun 21, 2015 #2
    They are.
  4. Jun 21, 2015 #3


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    hi kyle
    welcome to PF :smile:

    atmospheric temperature profile is very well known and if it had anything to do with gravity, a profile like this wouldn't be possible.....
    note the dramatic positive and negative temperature swings with altitude !!


    source ....
    http://www.srh.noaa.gov/jetstream/atmos/atmprofile.htm [Broken]

    Last edited by a moderator: May 7, 2017
  5. Jun 22, 2015 #4

    Does that diagram hold true at night?
  6. Jun 22, 2015 #5
    Night/Day makes little difference to avarage atmosphere temperature.
    It does have noticable effect, but nothing very dramatic.
  7. Jun 22, 2015 #6
    As in both wrong?

    Neither of those bloggers makes the case for an isothermal or uniformly decreasing atmosphere. They are talking isolated hydrostatic gases.
  8. Jun 23, 2015 #7
    Well, I remember hearing that if Nazi Germany built the Volkshalle (gigantic dome structure) that it would of rained inside. Can that dome be classed as hydrostatic? Why would it rain inside?
  9. Jun 23, 2015 #8
    Does the atmosphere cool with altitude due to gravity?

    The atmosphere is cooler with altitude because gravity is less, and pressure is therefore less, it is colder because of the altitude, I don't think 'it cools'.
    The reason why it is colder is because there is less of it. This is because of the 'adiabatic process', the same amount of heat over a large area is a lower temperature. This the same amount of heat (I think) but in a large area.

    But if you got a sealed box of 30 Deg air and went to high altitude on a balloon that air would not get cooler because of the effect of gravity being less, even if you took it into outer space with no gravity, it would still be 30 Deg, but if you doubled the volume of the box (with the same amount of air) the temperature would be 1/4 of it's original.

    Well this is my take on this anyway, I could well be wrong (I guess that is a possibility!) :)
  10. Jun 23, 2015 #9
    It is a difficult thing to explain the temperature of the atmosphere at different altitudes due to immense number of factors that come into play. While explaining how the air of a massive hall might cool with elevation is simpler than dealing with the atmosphere as a whole, it is still a very complicated question. You have the breaths of people to contend with in addition to the thermal conductivity of the walls and dome.

    To get a clear cut answer requires a clear cut question. A similar "question" was asked 5 year ago in this thread
  11. Jun 23, 2015 #10


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    no it doesn't. and yes you are wrong

    did you not see my post and graphic above ?

  12. Jun 24, 2015 #11
    Has anyone reviewed that math proof in the hydrostatic lapse article?

    Instead of going through and checking the proof each step at a time, I just inserted a formula for the change in pressure with altitude in excel and then had the discreet adiabatic formula reference its result. This should determine the temperature of a parcel of air that has risen.

    In another cell I inserted the typical dry adiabatic lapse formula, that should also determine the temperature of the parcel of air.

    For those two formulas to produce the same result, I had to input the ALR as the hydrostatic atmosphere's lapse rate. So that proof might be right....or not
  13. Jun 25, 2015 #12
    Can you link the spreadsheet?
  14. Jun 26, 2015 #13
    Google Sheet linked
  15. Jun 26, 2015 #14
    What is the scientific consensus on a static gas in an insulated box?

    Will its temperature vary or be uniform throughout?
  16. Jun 27, 2015 #15
    I'm not sure if it would be hydrostatic, but it would be possible theoretically to rain inside if there was room enough for the water cycle to take place. Givin enough humidity and whatnot. I'm obviously not a genius in this field but from my own knowledge it should be able to maybe someone else could give an in depth answer
  17. Jun 28, 2015 #16
    I would expect the warm breaths of cold hearted Nazis to rise, given what I know about convection. As those breaths rise they will be moving from higher pressure low elevations to lower pressure high elevations, resulting in adiabatic cooling of the moisture laden breaths. If the dome is the right height, the breaths moisture will eventually condense due to cooling. Could be wrong on this, fell free to correct or elaborate.
  18. Jun 28, 2015 #17
    The standard climatological explanation for the tropospheric lapse rate is distance from the earth's surface. The troposphere receives some 74% of its thermal energy from the Earth's surface--mostly in the form of longwave thermal radiation. Hence, the farther you get from the surface, the cooler the air is. Above the troposphere, a number of other factors come into play, and the lapse rate changes in response.
  19. Jun 28, 2015 #18
    Seems too simple an explanation of a complicated topic. This logic works well when explaining why you should move away from a camp-fire when you want to cool down, but works less well when dealing with the earth. The inverse square law may not have much of an effect when you consider the curvature of the earth is so faint, that many in the past thought it was flat.

    The big ? for me is if a hydrostatic gas will cool altitude because of gravity. This should have an answer that doesn't require a book!
  20. Jun 28, 2015 #19

    Simple or not, this is the explanation proposed in nearly all textbooks on the atmospheric sciences. Moreover, it is supported by the weight of scientific evidence. Yes, it does get more complicated in advanced studies, but the basic premise remains valid.

    The inverse square law doesn’t really enter into it, since virtually all surface radiation is absorbed by the lower 100 meters of the atmosphere. It is more a matter of absorption and radiation, absorption and radiation, with each layer radiating more to the layer above it than to the layer below it. Eventually, the outgoing global terrestrial radiation is equal to the incoming global absorption of insolation and the Earth’s “heat budget” is maintained.

    * * * * *

    Your question on gravitational cooling of the atmosphere gets a qualified “sometimes” answer from kinetic gas theory and statistical thermodynamics. When a mass of air is at rest (no winds or currents), the number of molecules with an upward component of translational motion is equal to the number with a downward component (about 1.21 X 1025 per cubic meter each way at 25°C and 105 Pascals).

    The speeds of all upward molecular movements are decelerated by gravity; and the speeds of all downward molecular movements are accelerated by gravity. These changes in molecular speeds are reflected in the mean kinetic energies of translation and hence in the temperatures. In still air, these ongoing temperature changes cancel one another out.

    When there is net upward or downward air movement, the proportions change—with more molecules moving in the flow direction than in the opposite direction. If the net air mass movement is upward, more molecules will be cooled than warmed. If the net air mass movement is downward, more molecules will be warmed than cooled. This explains the adiabatic cooling and heating of rising and sinking air masses.

    You might think that these convectional flows would average out and that there would be no net heating or cooling because of them. This is true except for water. Atmospheric water rises as a gas (water vapor), but sinks as a solid or liquid (rain, snow, hail, etc.). Hence there is slightly more adiabatic cooling of the atmosphere then there is adiabatic warming. How much more is a good question.

    * * * * *

    I am a bit uncomfortable with your reference to the atmosphere as a “hydrostatic gas”. The hydrostatic equation requires a number of conditions to be valid—conditions that are not met by the free atmosphere. Most importantly, however, it requires that a condition of equilibrium exist in order to be valid. The global atmosphere is never in a condition of equilibrium or even close to it. Hence, the hydrostatic equation does not really apply to it.
  21. Jun 28, 2015 #20
    Ok, so a massive insulated box full of still air will be isothermal?
  22. Jun 28, 2015 #21
    I thought that atmospheric lapse was mainly a result of adiabatic heating and cooling resulting from convection. My bad

    So a Hydrostatic Gas is Isothermal. Thanks for answering the question.

    Could you please also explain why https://medium.com/criminal-clouds/the-isothermal-elevator-part-3-of-3-7d828edb3c1a [Broken] wouldn't work?

    I never said the atmosphere is hydrostatic.

    Robert G Brown and Vanquish Opprobrium focus on hydrostatic gases. To answer Kyle's second question you need to deal in terms hydrostatic gases.
    Last edited by a moderator: May 7, 2017
  23. Jun 30, 2015 #22
    I'm thinking that the Isothermal explanation has to be the right one. Everyone thinks that hydrostatic lapse is in conflict with the second law, except it seem the simple wiki for the second law which states:

    "over time, differences in temperature, pressure, and density tend to even out in a horizontal plane, but not in a vertical plane due to the force of gravity. For example, density and pressure do not even out in a vertical plane, and nor does temperature because gravity acts on individual molecules, and this means molecular kinetic energy interchanges with gravitational potential energy in free path motion between collisions."

    Good reason to never trust Wikipedia maybe.

    The last week I've been daydreaming something that looks very similar to the below, trying to get my head around all this:


    I think its time to return to daydreaming about a Ducati I've been saving for, yet I don't think I will able to until this is all put to bed.

    For the sake of my sanity, can someone please why this isothermal elevator doesn't work!!! :confused:
    Last edited by a moderator: May 7, 2017
  24. Jun 30, 2015 #23


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    Please provide a reference for this claim. An obvious source, like wikipedia, says:

    Indeed, the "lapse rate" is often called the "adiabatic lapse rate".

    The wiki makes mention of the idea of radiation playing a role (only above the tropopause?), but the reference is a dead, self-published source that is plastered with warnings about it being an insufficient source.
  25. Jun 30, 2015 #24
    I think I would have to look closer, but at a glance it looks like they leave out a lot of work. You can fill up a tank with sea level air, and fly it in a plane to high altitude, and extract the energy from the pressure difference, but you use a lot of energy in raising the container.

    I would guess that including the process of pumping a vacuum in the cylinder would stop the process from being free. Same as it takes energy to fly that tank to a high altitude, you cannot get it very high without an energy expenditure.

    Further, you know how the atmosphere supports a column of mercury 760 mm high, or a column of water about 30 feet high? There is a limit to how high any particular mass can be lifted. Even if the mass was just the mass of the air and the tank was weightless, there is still a thing being lifted. And that air would not actually be lifted all the way to the top by a vacuum. The perfect vacuum would only lift a (weightless) tank of air at the lower mass of the upper altitude air, to the top. It would not lift a (weightless) tank of air at the lower pressure, because it weighs more.

    To me it looks like they are leaving out the fact that the tank will never get lifted that high by a vacuum, and that it takes energy to make that vacuum. I rather suspect that it is a huge waste of energy overall.

    If that is all completely wrong, feel free to tell me. I formed that opinion without a detailed reading.
    Last edited by a moderator: May 7, 2017
  26. Jun 30, 2015 #25
    Best to have a closer read votingmachine,

    The gas containing vessel is lifted by a pulley inside an elevator shaft. I'm guessing that the elevator shaft is a vacuum so buoyancy doesn't have to be factored in, not to actually conduct the work. Because of this, I'm actually quite confident on the vessel lifting calculations being correct. The calculations are just a combination of the ideal gas law and gravitational potential energy formulas. They are so straightforward I expect high-school students to be able to do the calculations.

    The isothermal expansion formulas are far more complex. I'm thinking that they must be out by a factor of 2. If the expansions only produced half the energy then there would be no net energy production. This is what I would expect from anything that has been idealised, so that friction and other inefficiencies are not factored in.
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