Why the Atmosphere is Thermally Asymmetric.

One concept which exists in Physics is, that if a surface has a greater coefficient of absorption, to one specific electromagnetic wavelength, then the degree with which this surface will emit EM radiation, at the same wavelength, due to incandescence, will also increase in a linear fashion. This is also known as Kirchhoff’s Law.

This fact seems to contradict what has been observed in the Earth’s Atmosphere, regarding how an increase in CO{2} levels has led to warming of the planet. It would be tempting just to assume casually, ‘The Earth’s Radiation of heat into space is low-temperature incandescence, Why does it not increase in-step with thermal absorption?’ And while there are several answers to this question, all of which require a more-complex analysis of what happens in the atmosphere, or of how the Sun is different from the Earth, this posting of mine will focus on one of the answers, which may also be the easiest to understand.

The temperature of the atmosphere at sea-level, may be around 20⁰C wherever it’s Summer. But at an altitude of 15km, the atmospheric temperature is close to -70⁰C. What this means is that, along with actual surfaces of the planet, the CO{2} in the lower layers of the atmosphere may be radiating electromagnetic radiation – i.e., deep infrared light – towards space. But because at an altitude of 15km the atmosphere also contains a matching level of CO{2}, those molecules in the upper atmosphere will mainly just catch this radiation again, and transform it back into stored heat. ( :1 )

So what happens among other things, is that an atmosphere differs from a surface of matter, and from the basic principle mentioned above, in being asymmetric. And what makes it asymmetric, is Gravity. It’s much more difficult for heat to escape, than it is for heat to be absorbed. Now, if there was some way to make the temperatures in the upper atmosphere not-different from those at lower altitudes, then the effect of global warming might not even take place. But the atmosphere’s CO{2} ‘which space sees’, is in the upper atmosphere, which is constantly very cold, while the atmosphere’s CO{2} ‘that humans see’, is at sea-level, which has the (increasing) temperatures we witness in everyday life.

Now, I have never been asked to provide this information. But seeing as there seems to be a question in Physics, which nobody else provides an answer for, and which nobody else seems to recognize as existing, I felt I should spontaneously provide an answer here.

(Updated 04/22/2018 : )

(As of 04/19/2018 : )

There exists a related question, of whether two bodies that coexist in some state of equilibrium, are actually emissive at the same wavelengths. I.e., the Sun, which provides all the Earth’s heat and light, is mainly incandescent at wavelengths close to visible wavelengths. This is also why Humans have evolved to be able to see the wavelengths which we see. But, because the Earth has a lower temperature overall, from the surface-temperature of our Sun, it will be emissive at much longer wavelengths. And so the thought is also plausible, that the Earth’s absorption coefficients could have increased, at wavelengths which the Sun emits, thus absorbing those wavelengths more. But, the Earth’s absorption coefficients at wavelengths it will actually emit, could hypothetically not have changed much… And the result would again be, that the changes in the Earth’s atmosphere will favor its warming, more than its self-cooling. However,

CO{2} is a gas already known to be active at certain deep-infra-red wavelengths, which have also made it useful in the design of CO{2} lasers. Those wavelengths correspond to the Earth’s emission wavelengths, more closely than they do to the Sun’s emission wavelengths. And so what CO{2} can only do, is slow down the rate, at which the Earth re-radiates heat, not change the degree, to which the Earth absorbs the Sun’s heat.

(Edit : )

As usual, there’s an issue with the WiKiPedia article about Kirchhoff’s Law: The article states that it only applies, to bodies in thermal equilibrium. The WiKi does not explain, how the properties of a quantity of matter should change, depending on the net flow of heat to and from a body.

In my Universe, the properties of a quantity of matter do change, as a function of temperature eventually. In other words, a surface of a particular chemical composition may have one color at room temperature, but at 300⁰C it could take a different color. These sorts of changes don’t usually happen within the tropospheric temperature-range, unless complex chemistry is also involved. But the net (im)balance of heat flowing to versus from a voxel of matter, should go no further than eventually to change its temperature. And of course, a phase-change of water to gaseous / liquid / solid phase, can also change its properties.


 

I get the impression that both Kirchhoff and Planck used the hypothetical concept of blackbodies in thermal equilibrium, in order to prove certain assertions.

But I infer, that their theories were meant to help people understand matter, not to help us understand the actual state of equilibrium. Further, I infer that their theories were not meant to help people understand literal blackbodies, because those were already understood not to exist in the days of Planck and Kirchhoff.


 

(Edit 04/20/2018 : )

It should also be noted, that the reason for which air is progressively colder at upper altitudes, has nothing to do with that part of our atmosphere being closer to space. It has to do with the adiabatic expansion and compression of any air, that changes altitude.

When air rises in altitude, the pressure on it ‘from air above’ decreases, which allows it to expand, and which instantly causes its temperature to decrease.

Conversely, when air sinks in altitude, the pressure on it ‘from air above’ increases, which compresses the air which has changed in altitude, and which instantly causes its temperature to increase. This phenomenon is exactly the same one, which causes the air to heat up during the compression-stroke of a diesel engine, to a temperature high enough to ignite injected diesel fuel, except that in the atmosphere, the pressure-changes are not as drastic.

This type of expansion and compression contrasts with diabatic compression, in which heat gets transferred. In the design of some practical compressors, the compressed air is first compressed adiabatically, and is next cooled, so that a gas volume results, the temperature of which matches the surrounding temperature again. And the net effect is diabatic compression.

Well as air changes altitudes, the only body with which it can transfer heat – mostly – is more air. So air that reaches high altitude mainly contacts air at high altitude, and its expansion remains adiabatic, and the same is true for air that reaches lower altitudes, which mainly comes into contact with more air, at lower altitudes, in addition to coming into contact with the actual surface of the Earth.

Thus, the way in which air heats up and cools off, due to gravity, is symmetrically consistent with altitudes, so that for this additional reason, very little diabatic transfer of heat takes place, due to changes in altitude.

(Update 04/20/2018, 18h40 : )

A possible misconception has come to my attention, about how incandescence works. It can be observed commonly, that surfaces start to give off visible wavelengths of light, near a specific temperature. This fact has been confused to mean, that surfaces start to radiate energy at that temperature, and independently of their composition.

The problem with this form of observation is related to how Max Planck needed to create the concept of a thermodynamic equilibrium, between quantities of radiated light. The Sun is not only known to radiate more power than the Earth, but also to radiate more of that power, at shorter wavelengths, than the wavelengths at which the Earth does.

By itself, this does not mean that the amount of ‘light’ which the Sun radiates in the deep infra-red, is actually less than how intensely the Earth does so. What it means is that some excuse needs to be found, to normalize the spectral curves of both the Sun and the Earth, and in the Computer Age, we might find a more-convenient excuse to do so, than simply to insist that these bodies need to be in equilibrium. In that case, the amount of ‘light’ which the Sun emits in the deep infra-red, is actually weaker than what the Earth does.

(Corrected 04/21/2018 : )

I suppose that there is a related fact which I should admit. Modern analysis of the temperature-equivalence of EM radiation, only goes so far as to relate the photon-energy to a temperature. What this means is that the wavelengths of light which result, are a direct function of temperature, as is Planck’s Curve. But the resulting intensities of radiation at each wavelength, are what I have stated Human vision as being weak to distinguish, and result when Planck’s Curve is modulated by the emissive constant for a given substance, at the given wavelength.

Similarly, there is no magical reason why a surface of matter starts to radiate heat at one specific temperature. It’s just that at significantly lower temperatures, the peak of the radiated energy is not in the visible part of the spectrum. And, because Human vision is more accurate about the hue of visible light, than it is about the intensity, we recognize the hue that gets given off by substances, as they start to glow red. Human perception actually prevents us from recognizing, what the total light intensity is. But, a surface of steel at 800⁰C will have less intensity of radiated light, than a surface of coal, again at 800⁰C.

In short, the Human body also radiates energy. It just fails to do so at visible wavelengths. And, the fact that in addition to its absorptive and emissive constants, which exist as a function of wavelengths as well as of the chemical composition of the Human skin, real bodies such as the Human body, also reflect light, can confuse some people on this subject. Because, we see the visible, reflected light, not the body’s own emitted light. But, using Thermal Imaging Cameras, Humans can use Technology actually in order to see Humans as a product of Humans’ Thermal Radiation.

What we do know, is that to try to image surfaces Thermally, starts to become infeasible to us, if the temperature of the surfaces drops to -70⁰C. OTOH, If we assume that the Humans have their full range of technology available to them, Human Technology can also image phenomena that take place in distant space, at the lower temperatures. One example how, lies in radio-telescopes being able to recognize radio-waves, the equivalent temperature of which would be 2 Kelvin, and which are also known as ‘The 2 Degree Kelvin noise’.


 

Contrarily to how the article words it, which I linked to above, I’d say that at a temperature of “800⁰C”, the radiated energy of a surface of matter hasn’t just reached the infra-red spectrum, but has completely filled it, and started to contribute to the visible part of the EM spectrum.

Near 525⁰C, surfaces will start to radiate visible light, but just barely so, that Human vision can recognize the fact. Around 800⁰C, a surface should be glowing bright-red.

Another fact which the article fails to point out, which I linked to above, is that the infra-red and the ultra-violet parts of the spectrum are subdivided.

There exist certain infra-red video cameras, which need a light source, and which will not function at the thermal wavelengths, which bodies emit just above room-temperature. Those types of cameras will often have specific LEDs, designed to emit considerable amounts of infra-red light. The way those cameras work, the IR-LEDs just act as if they formed a ‘lamp’, by which those cameras can see. They operate in the near-infra-red part of the spectrum, and do not require complex, internal refrigeration. And this near-infra-red part of the spectrum, is also the part, which surfaces will fill with energy, around 500⁰C.

But the deep-infra-red part of the spectrum, is closer to microwave wavelengths, and is the part in which Human bodies give off energy, because Human bodies are just slightly warmer at their surface than the surrounding temperatures. Cameras which sense the deep-infra-red, mainly require that their sensor-chip be cooled to about -80⁰C, just so that the sensor’s own heat does not blind it from the heat radiated by what it is imaging. And then, this temperature will define how low a temperature such a camera can sense, together with the gap-energy of the semiconductor used – belonging to silicon. This gap-energy needs to be exceeded by the photon-energy of the EM radiation, in order for a photon to be able to strike up an electron – electron-hole pair in the silicon. And this also sets a lower limit, to the photon-energy / i.e. temperature, which those cameras can sense.

This gap energy is also a main reason why silicon itself is usually not used to build LEDs, because silicon LEDs would mainly emit light, in the deep-infra-red part of the spectrum, which may not be useful. Practical LEDs will use semiconductors with higher gap-energies, than silicon has.


This thought-exercise can be taken further, into the subject of how the properties of certain substances will change, as a function of temperature, even if their chemical composition does not change.

The question could be asked: ‘Since the absorption / emission coefficients of the surface of the Sun are presently close to 1.0, where the Sun’s photosphere has a temperature of 5500K, would those gasses already have such a high coefficient, if their temperature corresponded to room temperature?’

And the short answer is ‘No.’ The composition of those gasses is still strongly dominated by hydrogen and helium, even though there are traces of carbon in them. And at room temperature, those gasses would also have a much lower coefficient. The reason for which the coefficient changes is complex, and has something to do with how individual particles are excited by their thermal agitation, and by the collisions between particles which result.

What tends to happen at higher temperatures is, that these coefficients, which are nominally stated as a function of wavelength, start to become more uniform, and less dependent on wavelength. And the short explanation of why is, the fact that thermal agitation eventually overcomes the structure of matter, so that we’re eventually only left with a chaotic quantity of (excited) particles.

Now, many people possess electric stoves, with those (traditional) spiral heating elements that we tend to recognize in Canada and the USA. If your spirals are deep-black, then this is probably due to a film of organic matter on them. If the reader simply turns one of those spirals on-high, first the organic film evaporates, and perhaps causes some smoking effect. After that, the ability of the spiral to keep its composition, is a function of how high the tensile-strength of the steel is (and on the hardness of the refractory substances inside). And when the surface is pure, this steel tends to have a gray coloration. Well this shade of gray is lighter, than the natural colors which coal would have. And for this reason, the intensities of visible light which are given off by this steel, will be lower, than the intensities which actual coals would give off.

But what practically nobody does, is to find a lump of coal, and to place it on the spiral, before the spiral heats up, and then to see whether that lump of coal contrasts with the steel spiral, once both are red-hot. What we should see, is that the hues of radiated color match, but that the intensities do not. What we’d more-probably see, is that it will be difficult to get the real temperature of the lump of coal, actually to match that of the spiral. And the reasons I’d suggest, would be poor thermal contact between the two solids, along with the fact that the lump of coal will be acting as a radiative heat-sink. So the lump of coal should really end up staying a deeper shade of red, than that of the spiral.

A homologous question arises about the tungsten filament, in the classical incandescent light-bulbs, which are presently being replaced by energy-efficient light-bulbs. Tungsten has high tensile-strength, as well as having the highest melting-point of all the elements. But in a light-bulb designed after the middle of the 20th century, Engineers have nevertheless chosen to place the temperature of the filament, close to the temperatures at which it starts to sublimate, i.e. close to temperatures at which the bonds between the tungsten atoms break.

The result should therefore be, that the emissive constant of such a filament is closer to 1.0, when that kind of light-bulb is switched on, than the mid-gray luster it has, when turned off.


 

Now, I’m going to take this thought-exercise even further, and look for a quick answer to the question, of whether the emissive constant may be finely-tuned. I can take the statement which I made above, that changes in color taking place due to temperatures changing, but within the tropospheric range, may only happen due to complex Chemistry, and I can add the observation that photosynthesis taking place on the surface of Earth is a complex form of Chemistry, which can produce finely-tuned changes in visible wavelengths – let’s say, between ‘clearly green foliage’ and ‘brown, dead foliage’. And based on that observation, I could ask, whether the fine, spectral differentiation in emissive constants can in turn affect thermal equilibria strongly.

My own answer to this made-up question would be ‘No’, because Planck’s Curve does not allow the photosynthetic substances to be differentially emissive over the thermal wavelengths. Again, because the thermal wavelengths would be in the deep-infra-red, and the resulting visible coloration-changes at visible wavelengths, it seems that the thermal processes do not deviate from simpler behavior, even though they can change coloration at visible wavelengths. OTOH, If we were to heat the foliage to temperatures at which visible wavelengths are also the thermal wavelengths, then we destroy whatever complexity made it green…

And as it happens, I can’t think of an example off the top of my head, where the emissive constant is so finely-tuned, that being so affects thermal equilibria strongly, because Planck’s Curve is also at a peak, near the finely-differentiated wavelengths. What I can imagine is that the stove spirals are more emissive at infra-red wavelengths, than they are at visible wavelengths, based solely on the strong bodily perception of their radiating heat, more-obviously than they radiate visible light. But this would not represent a finely-tuned differentiation, since the infra-red and the visible wavelengths involved are also at least an octave apart. ( :3 )

In other words, even though the emissive / absorptive constant is some function of wavelength, it is usually not as finely-tuned as complex coloration is, by the time temperature is high enough, for thermal radiation to be centered on visible wavelengths. Experiments which I carried out as a young teenager were such, that I wanted molten borax-droplets not only to become visibly incandescent, but to become so in a multicolored way. And what I got to my disappointment, was the borax droplets always losing their visual color, just before they started to glow. ( :2 )

In the 1970s there were published magazine-articles, which explained to many readers, that if they painted surfaces in ‘green paint’, those surfaces would become maximally-hotter due to solar heating, than if we painted those surfaces in other colors. But a question which I even had as a young teenager, was whether this effect was due to the paint differentiating between ‘red’ and ‘green’ wavelengths – which would have been spectacular – or due to the exact paint available in the 1970s, merely reflecting ‘green, visible’ wavelengths, but absorbing certain ‘near-infra-red’ wavelengths particularly well, which the customers could not see, but as an accidental side-effect of what one paint-chemistry might have been doing. The latter case would fail to exemplify fine wavelength-differentiation, affecting the equilibrium strongly. I think this question deserves modern attention, if only to answer some questions which remain unanswered to my mind. The mentioned paint may have scored additionally, just by having a low constant, in the deep-infra-red part of the spectrum, at which ambient temperatures would be emissive.

1: )

The question which I started this posting about, which was, ‘the nature of the relationship between Kirchhoff’s Law and Global Warming’, has a pattern which resembles the easily-observable effect, by which some clear nights are often colder on the surface of the Earth, than cloudy mights. Actually, whether the weather is actually colder on those mights, also depends strongly, on the temperature of any air-masses which might move in to a location, and which might be warmer or colder to start with.

But there is an aspect to the weather-pattern, which I initially left out of my description of global warming, which is reflection. Kirchoff’s Law does not mention reflection. Yet, if there is a cloud-layer on a given night, then heat which the lower altitudes radiate skywards, is actually reflected back to lower altitudes, and this phenomenon exists separately from the combined phenomenon of absorption and emission. This effect can act as a blanket, which will slow down the rate at which the lowest altitudes cool off.

There is a corresponding factor which I did not mention, that does relate directly to global warming, which is the fraction of sunlight which gets reflected by the upper atmosphere, back into space, and which therefore never reaches the lower layers of the Earth’s atmosphere. Again, this is a variable not really connected to atmospheric absorption and re-radiation. But it has increased slightly over the decades, due to pollutant particles in the upper atmosphere.

It should be remembered, that just as the phenomenon of reflection is really unrelated to absorption and re-radiation, one does not act as a substitute for, or as a solution to the problems caused by, the other. It’s perfectly possible to have slightly less sunlight enter our atmosphere, but for the atmosphere nevertheless to hold on to and capture energy ‘better’, once that energy was absorbed, and for Humanity to cook nevertheless.

And who’s to say, that the pollutants in the upper atmosphere, which increase reflection of sunlight coming in, won’t also reflect radiation headed out, back in?

 

2: )

As a child I owned a Chemistry set, with which I carried out experiments, and which – unlike Chemistry sets today – contained actual chemicals! :-D

One of the suggested experiments was, to melt a droplet of borax at the end of a high-temperature rod made out of magnesium oxide, and to allow some mineral salt to dissolve in this hot droplet. The droplet would take on several striking colors, which could in turn be used to identify the mineral in question.

What I had observed was that if I heated this droplet to temperatures much higher than suggested, it would eventually become visibly incandescent, and therefore, ‘to glow’. I made numerous trials to achieve the goal, that the droplet should glow in a color I had given it, instead of always in the red or orange colors, in which we were used to substances becoming visibly incandescent. And in spite of persistent efforts, I did not succeed once. Each time, the droplet would lose its visible coloration at some temperature, before its incandescence became visible.

(Update 04/22/2018 : )

3: )

I can add an observation, about the naked stove spirals seemingly giving off infra-red light, more strongly than they give off visible light.

Firstly, it’s to be understood, that to keep the spirals turned on high, when there are no pots on them, is a really bad idea, because doing so can easily burn them out. Their temperatures can get so high, that their materials just fail. Something which I do from time to time however, is just to turn them on temporarily, in order to boil off any grease that may be on them, to keep a close eye on them while they’re turned on, and then immediately to turn each spiral off again.

Each stove spiral is surrounded by other forms of sheet-metal, that also heat up, but not to the point where these other surfaces become incandescent visibly. Well those additional surfaces are also radiating heat. The apparently-higher emissive constant, when doing this exercise, at the infra-red wavelengths, from the constant in the visible part of the spectrum, may simply be due, to these additional, hot surfaces.

Dirk

 

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