Sunday, January 10, 2010

Radiative Symmetry

In our previous posts (Absorption, Not Reflection and Glass Houses) we showed that heat enters the atmosphere by convection and absorption of radiation, and leaves by emission of radiation.

Let us examine this process of absorption and emission in more detail. Suppose a planet were surrounded by a transparent atmosphere. An atmosphere consisting entirely of oxygen and nitrogen would meet our requirements. Both gases are transparent to visible and infrared light, so they would absorb no radiation from the sun or from the planet. Heat would enter a transparent atmosphere only by convection from the planet's surface.

If heat is to leave this transparent atmosphere, it must do so by radiation. But can a transparent gas radiate heat? Imagine that we put a cubic meter of our transparent gas in a room with reflecting walls (we could use surface-coated mirrors). The cubic meter of gas is contained in a transparent balloon. Also in the room is a large, black box. We suck all the air out of the room with a vacuum pump. At the beginning of our experiment, the gas and the black box are at the same temperature. The black box radiates heat. This radiation passes through the vacuum and the transparent gas, reflects off the walls, and is re-absorbed by the black box.

Now, let us assume that our transparent gas radiates heat. If so, this radiation will be absorbed by the black box. The black box will warm up because is is absorbing the heat it radiates itself as well as the heat radiated by the gas. The gas, meanwhile, must cool down, because it is radiating heat but absorbing none at all, on account of its being transparent. The gas continues to cool down and the black box continues to heat up. Heat is passing, of itself, from one body to a hotter body.

The second law of thermodynamics states that heat cannot, of itself, pass from one body to a hotter body. A transparent gas that radiates heat violates this law. All gases, and indeed all objects, must absorb and emit radiation with the same ease. Any difference between a gas's ability to absorb radiation of a particular wavelength and its ability to emit radiation of the same wavelength amounts to a violation of the second law of thermodynamics.

The second law dictates that a transparent gas cannot radiate heat. The transparent atmosphere around our imaginary planet does not radiate heat. It retains all the heat it acquires by convection from the planet's surface. It continues to absorb heat by convection until the entire transparent atmosphere is at the same temperature as the planet surface, and at that point convection stops and the atmosphere is in thermal equilibrium with the planet surface.

If the atmosphere of the earth were made up only of nitrogen and oxygen, the entire atmosphere, from the troposphere to the exosphere, would be warm.

But the earth's atmosphere is not warm. The surface of the earth has an average temperature of 14°C. The atmosphere at altitude 10,000 m is at around −40°C. The earth's atmosphere is not warm because it radiates heat. It radiates heat because it is not transparent. It is not transparent because it contains carbon dioxide and water, both of which are good absorbers of infrared light, and therefore good emitters of infrared light also.


  1. Hi Kevan,
    With my nitpicking hat on, I would be inclined to suggest that heat enters the atmosphere by means of conduction, radiation and evaporation rather than by convection. Once the heat is in the atmosphere convection and advection come into play shifting it around. I'm not sure where your argument is leading but...

  2. Hugh,

    You are, of course, correct, if you are looking at the manner in which heat passes across the boundary between the earth and the atmosphere. But I'm considering the main body of the atmosphere. Once heat crosses the boundary, it seems to me that it moves around almost entirely by convection and mixing.

    If you consider the first one meter of the atmosphere, it seems to me that convection dominates the heat transfer through the top of of this one-meter layer.

    As to where I am going with the argument, I assure you that you will not be disappointed.

  3. Kevan,
    1. You write:
    "It continues to absorb heat by convection until the entire transparent atmosphere is at the same temperature as the planet surface, and at that point convection stops and the atmosphere is in thermal equilibrium with the planet surface."
    Would there not still be, when equilibrium was reached, a temperature gradient corresponding to the dry adiabatic lapse rate?
    2.You write: "If the atmosphere of the earth were made up only of nitrogen and oxygen, the entire atmosphere, from the troposphere to the exosphere, would be warm."
    With an O2-N2 atmosphere (and maybe a bit of Argon) what would you expect the earth's surface temperature to be?
    Interesting experiment!

  4. Hugh,

    1. The dry adiabatic lapse rate is, I believe, the cooling of a gas as it is allowed to expand without heat exchange at the edges, as in a well-insulated piston being drawn out. In the atmosphere, it seems to me that such expansion must be accompanied by the displacement of air above, which must move down and be compressed, leading to heating. Over time, the heat will distribute itself due to repeated convection and even conduction (if we give it a million years).

    2. Yes, that would be an interesting experiment, but I can't figure out how to do it yet. I do have a vacuum chamber, however, and I'm willing to use it.

  5. Kevan,
    My term 'interesting' was intended to apply to the experiment you have already done. But yes, there are further interesting possibilities.
    Are you familiar with the brief description by Wood(1909)of his experiment comparing solar warming rate in an insulated black box with a glass lid with that under a rock salt lid?
    He didn't take it far and gives few figures on times and dimensions. I find it hard to believe no-one has taken it further during the intervening 100 years. But maybe no-one has.
    One of the things Wood encountered was that he needed a glass plate above both lids to ensure that the box was getting the same amount of incoming solar energy. Without the glass plate the glass lid on its own slowed the warming as it intercepted the incoming solar infrared while the salt lid let it through.
    I would be interested to compare heating rates in such a box, possibly heated from below (e.g. by a hot plate) with and without CO2 (also with and without H2O) in the contained atmosphere. Your vacuum set-up might be useful there, to help exclude the GHGs or add them in multiples of the present atmospheric concentration. The purpose would be to compare heating due to conduction (from the heat source/sides of the box into the air) with that due to radiation. It might be that to achieve a realistic scale one would need a taller box.

  6. Dear Hugh,

    I'm glad you find the experiments interesting. I had a most enjoyable week in the lab figuring out how to isolate radiation. Yes, I am familiar with Wood's work from 1909. Peter Newnam pointed it out to me. I had the idea of using rock salt after reading his results. I was unable to find rock salt panes at Fisher Scientific, so I used a big crystal I had on my shelf.

    I have a hot plate and I can get CO2 as dry ice. But I'm still trying to figure out the details of getting my sensor wires in and out, and shining heat into the chamber in a reliable way, and also isolating the system from the base of the enclosure, which will radiate. If you have a detailed plan, I'll be glad to consider performing the experiment.

    Yours, Kevan

  7. Kevan,
    I still think it is better to distinguish conduction from convection, although within the troposphere they accompany each other.
    This leads on to the possible experiment which I have been thinking about. Note that I have no background or experience in experimental physics, or in radiation physics. I am a geologist.
    I would like to estimate the relative contributions of conduction and radiation from the surface into the overlying air.
    This would require initially entirely excluding GHGs including H2O from a container of air; in subsequent runs adding CO2 in known amounts, correspding to pre-industrial, present and possible future concentrations.
    I don't see how one can proceed far without the GHG-free step. The GHG-free air should be as near as possible of the composition of real air, so 79% N2, 20% O2 and 1%Ar or whatever. If the 'air' differs too much from those proportions one will spend too much time arguing with critics as to whether it matters.
    If there are no GHGs present, and no water or plants present that can evaporate or transpire, then the only way that energy can get from the 'ground' into the air is by conduction.
    Having solved the problem of getting a suitable sensor into the container, one could track the change in T with time and final equilib T.
    Then repeat the experiment with the only change being to add a standard or measurable amount of CO2, again tracking the T. The difference between the two results will be the GHG contribution for that CO2 concentration and that height of container.
    It will make a difference how tall the container is. For CO2 at present levels I would expect a significant amount of radiation to be intercepted within about 3 metres or so. Enlarging the experiment up to that scale might be tricky though. One could start small and work up.

  8. I take your point about convection and conduction. Of course the actual transfer of heat into the lower layer of air is by conduction, and the transfer within the air is by convection. I might go through and edit my posts to make your point more clear.

    My vacuum chamber is only 30 cm high. As you say, to perform your experiment with 400 ppm CO2, we would need a chamber several meters high, or perhaps higher: I still don't have an absorption spectrum for CO2 with the absorption length marked in clear units. I was hoping to avoid these more difficult experiments by appealing to the Second Law of Thermodynamics, as I have done in my most recent post.

  9. The suggested experiment would not be easy, but still possible. Someone ought to do it. Theory should be tested. Even a 30cm high chamber might show some results. If not, perhaps add more CO2 until it makes a difference.