“The heat retention in the greenhouse Earth is caused by all gas components…mainly by nitrogen and oxygen. It is not permissible to exclusively assign the GH effect of 33° to water vapour, CO2, and the other trace gases.” – Ullmann and Bülow, 2024
Chemical physicists Helmut Ullmann and Martin Bülow have published a new paper detailing the lack of meaningful or noticeable “specialness” that trace greenhouse gases like carbon dioxide (CO2, 0.042% of the atmosphere) and methane (CH4, 0.00018%) possess in determining Earth’s greenhouse effect heating.
Image Source: Ullmann and Bülow, 2024
The imagined 33°C greenhouse effect thought experiment
The popularized greenhouse effect thought experiment requires imagining what temperature the Earth would be if there were no atmospheric greenhouse gases (water vapor, CO2, CH4). It is believed these trace (less than 0.1% of the atmospheric composition combined) heat-absorbing gaseous agents, combined with water vapor (up to 4% of the atmosphere in tropical areas), are the only gases capable of restricting heat loss to space. Thus, greenhouse gases are thought to ultimately keep the Earth’s land and ocean surface temperature 33°C warmer (288 K vs. 255 K) than it would otherwise be in their imagined absence.
It is simultaneously imagined that even though oxygen (O2, 21%), nitrogen (N2, 78%), and argon (Ar, 0.9%) together account for 999,000 ppm (99.9%) of the atmosphere’s gaseous composition, none of these gases absorb and re-emit heat, and thus they cannot slow cooling or count as contributors to the imagined 33°C warmer Earth atmosphere. Only the trace gases and water vapor – the so-called greenhouse gases – can slow cooling, or retain heat.
That’s what the thought experiment says, anyway. Physics say otherwise.
The O2 and N2 greenhouse effect
Ullmann and Bülow point out that the greenhouse effect is not only not exclusively determined by trace greenhouse gases like CO2 or CH4, but these trace gases play such an unimportant role that they’re not even noticeable. Only water vapor has the capacity to absorb heat to a degree that is detectable. The primary gaseous determinants of Earth’s greenhouse effect are not trace gases like CO2 and CH4, but, consistent with their atmospheric abundance, N2 and O2.
“The basic constituents of the atmosphere, nitrogen and oxygen, are the main contributors to heat storage in the Earth’s GH [greenhouse effect].”
“The heat retention in the greenhouse Earth is caused by all gas components…mainly by nitrogen and oxygen. It is not permissible to exclusively assign the GH effect of 33° to water vapour, CO2, and the other trace gases.”
Non-greenhouse gases absorb heat too
There is good reason to conclude O2 and N2 are the primary greenhouse effect determinants. Contrary to popular belief, real-world experiments show that N2, O2, and Ar actually do absorb heat, albeit about 20% less effectively than the so-called greenhouse gases do. A mere 20% dropoff is not significant when the abundance (99.9%) of these gases is considered relative to the abundance (less than 0.1%) of greenhouse gases.
“The heat capacities of polyatomic gases, H2O and the trace gases such as CO2, CH4, and SO2 are a further approx. 20% greater than those of O2 and N2 molecules. … Multiplied by the low concentration of trace gases, they cannot noticeably increase heat storage in the air. Only H2O…is able to store great amounts of heat.”
As mentioned, this phenomenon has been observed experimentally. For example, when air (99% O2 and N2), pure (100%) CO2, and pure (100%) Ar are warmed in experimental conditions, they all absorb heat to nearly the same degree.
Image Source: Allmendinger, 2016
Scientists agree: O2 and N2 are greenhouse gases
An earlier work published in Geophysical Research Letters (Hopfner et al., 2012) also clarifies that O2 and N2 should be considered “natural greenhouse gases in Earth’s atmosphere.” Although O2 and N2 absorb heat (infrared radiation) more weakly than CO2 and CH4, they do indeed absorb heat, and they do not have a negligible role in Earth’s greenhouse effect because of their relative abundance when compared to CO2 and CH4.
“This work challenges a common perception on the negligible role of O2 and N2 as natural greenhouse gases in Earth’s atmosphere…”
“It is in fact the large abundance of oxygen and nitrogen which compensates for their only weak interaction with infrared radiation…”
“Due to the atmospheric concentration of atmospheric N2 (O2) that is about 2000 (550) times higher than that of Co2 and about 4.4 x 10⁵ (1.2 x 10⁵) times more abundant than CH4, even the weak infrared absorption of N2 (O2) can become radiatively important.”
“Thus, we object to the view that the radiative forcing of N2 increase operates only indirectly by broadening the absorption lines of other gases.”
Image Source: Hopfner et al., 2012
CO2 is nothing special
Finally, Drs. Ullmann and Bülow emphasize just how non-special CO2 is as a greenhouse gas in Earth’s atmosphere. As noted above, they point out that CO2’s contribution to the greenhouse effect is not even noticeable. They also assert that the laws of physics require there is no so-called “hotspot” in Earth’s atmosphere due to the conglomeration of CO2 molecules. There is nothing CO2 does that is thermally “special” relative to other gases.
“According to the 2nd Law of Thermodynamics, heat is distributed from hot to cold molecules; there are no hotspots among molecules or types of molecules in the atmosphere. A special role of carbon dioxide cannot be confirmed.”
Who knew?
I have been saying for many years that O2 and N2 are the real greenhouse gases for one simple reason they absorb heat to the same temperature as CO2 etc both by radiation and kinetic means, but do not radiate in LWIR.
They therefore hold the heat longer than LWIR radiating gases.
Everything below is explained in detail and mathematically proven here:
https://www.patriotaction.us/showthread.php?tid=2711
A higher concentration of radiative polyatomics allows any given parcel of air to more readily emit. Thus the polyatomics radiative cool the upper atmosphere as fast or faster than they can convectively warm it. This sets the beginning of the lapse rate (the upper atmosphere) at a lower temperature, which translates down through the lapse rate to a cooler surface. We’re just working through the massive thermal capacity of the planet… give it time, it’ll catch up.
The low-DOF monoatomics (Ar) and homonuclear diatomics (N2, O2) dilute the higher-DOF radiative polyatomics, reducing the molar heat capacity of that parcel of air and the number of emitters per parcel of air and thus hindering that parcel from more efficiently emitting. That is why I state that the monoatomics and homonuclear diatomics are the true “greenhouse gases” (in the ‘actual greenhouse effect’ sense, not in the “greenhouse effect (due to backradiation)” sense of the climatologists)… they reduce the ability of air to convectively transit energy to the upper atmosphere and emit it to space.
Remember that ~76.2% of all surface energy is removed via convection, advection and evaporation… without the polyatomics, surface radiant exitance would have to pick up that energy transfer, which would necessitate a higher surface radiant exitance. And per the S-B equation, a higher surface radiant exitance implies a higher surface temperature.
In an atmosphere consisting solely of monoatomics and homonuclear diatomics, the ability of the atmosphere to radiatively cool itself would drastically decrease, thus the surface would have to warm due to the adiabatic lapse rate starting (in the upper atmosphere) at a higher temperature.
That energy can only be emitted upwelling due to the energy density gradient (except under temperature inversion conditions) because energy can only spontaneously flow down an energy density gradient, and that energy density gradient slopes downward from Earth to atmosphere to space.
The climatologists have conflated their “greenhouse effect (due to backradiation)” with the Kelvin-Helmholtz Gravitational Auto-Compression Effect (aka the adiabatic lapse rate). The lapse rate has nothing to do with any “backradiation”, nor with any “greenhouse effect (due to backradiation)”, nor with any “greenhouse gases (due to the greenhouse effect (due to backradiation))”… it is a result of the conversion of translational mode (kinetic) energy in the z-axis DOF (Degree Of Freedom) to gravitational potential energy with altitude (and vice versa). That changed z-axis DOF kinetic energy then equipartitions to the other 2 linearly-independent DOF upon subsequent collisions of the atmospheric atoms or molecules, per the Equipartition Theorem. This is why temperature decreases as altitude increases (and vice versa).
The climatologists didn’t have a choice in conflating their wholly-fictive “greenhouse effect (due to backradiation)” with the Kelvin-Helmholtz Gravitational Auto-Compression Effect… they know that “backradiation” does not and cannot exist because energy does not and cannot spontaneously flow up an energy density gradient. Even the pyrgeometers they use to ‘measure’ “backradiation” utilize the same misuse of the Stefan-Boltzmann (S-B) equation as the climatologists use in their Energy Balance Climate Models (EBCMs) to conjure “backradiation” out of thin air. But they had to show an effect for their “greenhouse effect (due to backradiation)”, so they glommed onto the adiabatic lapse rate.
In short, they’ve confused idealized blackbody objects and real-world graybody objects, using the idealized blackbody form of the S-B equation upon real-world graybody objects in their Energy Balance Climate Models (EBCMs). That assumes emission to 0 K, which artificially inflates radiant exitance of all calculated-upon objects, and forces the climatologists to carry those incorrect values through their calculation and cancel them on the back end to get their equation to balance.
Thus, they subtract a wholly-fictive “cooler to warmer” energy flow from the real (but too high because it was calculated for emission to 0 K) “warmer to cooler” energy flow.
That wholly-fictive “cooler to warmer” energy flow is otherwise known as “backradiation”. That implies rampant and ongoing violations of 2LoT in the Clausius Statement sense. Of course, fundamental physical laws aren’t violated… if one claims their physical process does violate a fundamental physical law, their physical process is physically impossible. But that’s what the climatologists do.
The S-B equation for graybody objects isn’t meant to be used by subtracting a wholly-fictive ‘cooler to warmer’ energy flow from the real (but too high because it was calculated for emission to 0 K) ‘warmer to cooler’ energy flow, it’s meant to be used by subtracting cooler object energy density from warmer object energy density to arrive at the energy density gradient, which determines radiant exitance of the warmer object. This is true even for the traditional form of the S-B equation, because temperature is a measure of radiation energy density, per Stefan’s Law.
————————-
Temperature (T) is equal to the fourth root of radiation energy density (e) divided by Stefan’s Constant (a) (ie: the radiation constant), per Stefan’s Law.
e = T^4 a
a = 4σ/c
e = T^4 4σ/c
T^4 = e/(4σ/c)
T = 4^√(e/(4σ/c))
T = 4^√(e/a)
where:
a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4
where:
σ = (2 π^5 k_B^4) / (15 h^3 c^2) = 5.6703744191844294539709967318892308758401229702913e-8 W m-2 K-4
where:
σ = Stefan-Boltzmann Constant
k_B = Boltzmann Constant (1.380649e−23 J K−1)
h = Planck Constant (6.62607015e−34 J Hz−1)
c = light speed (299792458 m sec-1)
σ / a = 74948114.502437694376419756266673 W J-1 m (W m-2 / J m-3)
————————-
The traditional Stefan-Boltzmann equation for graybody objects:
q = ε_h σ (T_h^4 – T_c^4)
[1] ∴ q = ε_h σ ((e_h / (4σ / c)) – (e_c / (4σ / c)))
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))
[2] ∴ q = (ε_h c (e_h – e_c)) / 4
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4
[3] ∴ q = (ε_h * (σ / a) * Δe)
Canceling units, we get W m-2.
W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)
One can see from the immediately-above equation that the Stefan-Boltzmann (S-B) equation for graybody objects is all about subtracting the energy density of the cooler object from the energy density of the warmer object.
You will note that σ = (a * c) / 4… the S-B Constant equals Stefan’s Constant multiplied by the speed of light in vacua divided by 4.
[4] ∴ q = (ε_h * ((a * c) / a) * Δe) / 4 = (ε_h * c * Δe) / 4
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 * ΔJ m-3) / 4
————————-
The Stefan-Boltzmann equation in energy density form ([3] above):
σ / a * Δe * ε_h = W m-2
σ / a = 5.6703744191844294539709967318892308758401229702913e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 = 74948114.502437694376419756266673 W m-2 / J m-3.
Well, what do you know… that’s the conversion factor for radiant exitance (W m-2) and energy density (J m-3)!
It’s almost as if the radiant exitance of graybody objects is determined by the energy density gradient, right?
Energy can’t even spontaneously flow when there is zero energy density gradient:
σ [W m-2 K-4] / a [J m-3 K-4] * Δe [J m-3] * ε_h = [W m-2]
σ [W m-2 K-4] / a [J m-3 K-4] * 0 [J m-3] * ε_h = 0 [W m-2]
… it is certainly not going to spontaneously flow up an energy density gradient.
Just as water cannot spontaneously flow when there is zero pressure gradient, and it most certainly cannot spontaneously flow up a pressure gradient (ie: uphill).
^^^^^^^^^^
vvvvvvvvvv
Note 2LoT in the Clausius Statement sense:
“Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.”
‘Heat’ [M1 L2 T-2] is definitionally an energy [M1 L2 T-2] flux (note the identical dimensionality), thus equivalently:
“Energy can never flow from a colder to a warmer body without some other change, connected therewith, occurring at the same time.”
That “some other change” typically being external energy doing work upon the system energy to pump it up the energy density gradient, which is what occurs in, for example, AC units and refrigerators.
Remember that temperature is a measure of energy density, equal to the fourth root of radiation energy density divided by Stefan’s Constant, per Stefan’s Law, thus equivalently:
“Energy can never flow from a lower to a higher energy density without some other change, connected therewith, occurring at the same time.”
Or, as I put it:
“Energy cannot spontaneously flow up an energy density gradient.”
My statement is merely a restatement of 2LoT in the Clausius Statement sense, but you’ll note my statement takes all forms of energy into account… because all forms of energy follow the same rules.
^^^^^^^^^^
vvvvvvvvvv
Do remember that a warmer object will have higher energy density at all wavelengths than a cooler object:
https://web.archive.org/web/20240422125305if_/https://i.stack.imgur.com/qPJ94.png
… so there is no physical way possible by which energy can spontaneously flow from cooler (lower energy density) to warmer (higher energy density). ‘Backradiation’ is nothing more than a mathematical artifact due to the climatologists misusing the S-B equation.
The above completely destroys AGW and CAGW, because they are predicated upon the existence of “backradiation” (radiation spontaneously flowing up an energy density gradient) as the causative agent for the climatologists’ claimed “greenhouse effect”.
Also new to me! Why is this mentioned nowhere? I am reading everything about climate change every day since 2007 and nowhere was this mentioned!
Good old Bill Gates. If O2 is a greenhouse gas, he is clearly right. We need to cut down every tree and green thing that produces it (to make room for his vast farm holdings).
But what shall we do about that pesky Nitrogen?
This analysis is all wrong but on the right track. The GHE is a radiative process by definition, and thus to argue O2 and N2 are the real GHGs is nonsense. What really happens is that 99% of the IR absorbed by GHGs in the lower troposphere is thermalized (because on average all molecules in the air at each altitude are the same temperature and this happens because the 1% GHGs warm the other 99% non-GHGs to achieve this). This means that only 1/2 of 1% of the GHG-absorbed IR is left to radiate to the surface. Worse, as each GHG has a path to extinction, above a certain altitude, none of the downward IR makes it back to the surface, which is to say the GHE disappears (for this or that GHG). Net/net the GHE is 99% conduction, and 1% radiation (1/2 going down) mostly limited to the lower troposphere. At the tropopause where the air is thin GHGs can radiate more and there they serve to cool the atmosphere. But this activity is not part of the GHE. To sum up: close to the surface GHGs warm the air (not the surface) and higher up GHGs cool the atmosphere by radiating thermal energy to outer space.
What explains the 288K surface temperature? Answer: adiabatic effects. Merely take the 216K at the average troposphere height 12 km up and work your way down to the surface using the lapse rate and voila you get 288K. Actually, you get more than 288k unless you use a blend of the wet and dry lapse rates. But in reality, the problem of climate science is not to answer why the surface is so hot, but rather why isn’t it hotter, as adiabatic effects more than explain the 288K. So, it’s a good thing that the GHE is so tiny. The bigger the GHE the more it pushes the 288K surface temperature higher than it is.
Tufts University found the same results with Argon( not a greenhouse gas) as with CO2 in a test tube experiment-
“Climate change in a shoebox: Right result, wrong physic”
https://pubs.aip.org/aapt/ajp/article-abstract/78/5/536/1040040/Climate-change-in-a-shoebox-Right-result-wrong?redirectedFrom=fulltext
What’s true is that active gases in the IR mid to far spectrum are the only way for the atmosphere to keep cooling itself by radiating into space.
In conjunction with convection/advection, they carry on an AC like cooling of the atmosphere with a pretty good efficiency since according to the NASA, they emit some 170 W/m² (and 160 W/m² from the top of the troposphere according to the IPCC) into space while absorbing only 17W/m² from what is emitted by the surface.
The cooling efficiency of the troposphere by active gases in the IR spectrum is (160-17)/160 = 89%.
Furthermore, this cooling is regulated since the active gases emission variation into space dE is related to the surface temperature variation dT by the (simplified) empirical (observed) law :
dE/dT = 2,4 W/m²/K
All of this stuff is free and effective :
– no need to destroy the planet with solar panels, wind farms, no need to destroy our civilization with absurd regulations against agriculture, genuine meat, pets, transportation, energy production, housing industry, etc.
– instead, we need to sack all the climate nutcases in charge and shutdown the institutions they belong to.
Keep calm and carry on.
[…] From NoTricksZone […]
I’ve been saying this exact thing for awhile now, and I even have the maths to back it up.
https://www.patriotaction.us/showthread.php?tid=2711
What one has to do is to calculate the Specific Lapse Rate of each constituent atomic or molecular species in the atmosphere:
Idealized dry gas molar heat capacity lapse rate:
If we take ϒ = 1.404, g = 9.80665 m s-2, R = 8.31446261815324 J mol-1 K-1 and M = 28.9647 g mol-1, then:
dT / dh = -0.4/1.404 * (((28.9647 g mol-1) * 9.80665 m s-2) / 8.31446261815324 J mol-1 K-1) = -9.7330377706482238008458858152373 K km-1
The stated molar isobaric heat capacity for dry air is Cp = 7/2 R
7 / 2 * 8.31446261815324 J mol-1 K-1 = 29.10061916353634 J mol-1 K-1
∴ Molar Heat Capacity / 7 * 2 = Specific Gas Constant
dT / dh = -0.4/1.404 * (((Molar Mass) * 9.80665 m s-2) / Specific Gas Constant) = Specific Lapse Rate
The below data is taken from the model atmosphere I constructed in my paper at:
https://www.patriotaction.us/showthread.php?tid=2711
… to calculate the Specific Lapse Rate below:
Symbol: Molar Mass: Molar Heat Capacity: Specific Lapse Rate (SLR):
H2 | 2.01588 g mol-1 | 28.82 J mol-1 K-1 | 0.6859482857817 K km-1
He | 4.002602 g mol-1 | 20.7862 J mol-1 K-1 | 1.8883738683977 K km-1
H2O | 18.01528 g mol-1 | 75.327 J mol-1 K-1 | 2.3453681364178 K km-1
CH4 | 16.04246 g mol-1 | 35.69 J mol-1 K-1 | 4.4080355942551 K km-1
N2 | 28.0134 g mol-1 | 29.12 J mol-1 K-1 | 9.4339738283240 K km-1
CO | 28.0101 g mol-1 | 29.1 J mol-1 K-1 | 9.4393555726775 K km-1
Ne | 20.1797 g mol-1 | 20.7862 J mol-1 K-1 | 9.5205114453312 K km-1
O2 | 31.9988 g mol-1 | 29.38 J mol-1 K-1 | 10.680770320623 K km-1
N2O | 44.0128 g mol-1 | 38.6 J mol-1 K-1 | 11.181816712950 K km-1
CO2 | 44.0095 g mol-1 | 36.94 J mol-1 K-1 | 11.683426182319 K km-1
O3 | 47.9982 g mol-1 | 39.22 J mol-1 K-1 | 12.001569302138 K km-1
NO2 | 46.0055 g mol-1 | 37.2 J mol-1 K-1 | 12.127952596066 K km-1
SO2 | 64.0638 g mol-1 | 39.87 J mol-1 K-1 | 15.757493460485 K km-1
Ar | 39.948 g mol-1 | 20.7862 J mol-1 K-1 | 18.846929895790 K km-1
SF6 | 146.06 g mol-1 | 93 J mol-1 K-1 | 30.187357269247 K km-1
Kr | 83.798 g mol-1 | 20.95 J mol-1 K-1 | 39.225663804284 K km-1
I2 | 253.80894 g mol-1 | 54.43 J mol-1 K-1 | 45.728742264382 K km-1
Xe | 131.293 g mol-1 | 21.01 J mol-1 K-1 | 61.282460659191 K km-1
=====
Note the calculated Dry Adiabatic Lapse Rate above: -9.7330377706482238008458858152373 K km-1
The negative sign means temperature decreases with altitude. Usually we leave it off.
(N2) 9.433973828324 K km-1 * 0.780761158 +
(O2) 10.680770320623 K km-1 * 0.20944121395198 +
(Ar) 18.84692989579 K km-1 * 0.00934 +
(CO2) 11.683426182319 K km-1 * 0.00043 +
(Ne) 9.5205114453312 K km-1 * 0.0000182 +
(He) 1.8883738683977 K km-1 * 0.000005222 +
(CH4) 4.4080355942551 K km-1 * 0.0000018 +
(Kr) 39.225663804284 K km-1 * 0.000001 +
(H2) 0.6859482857817 K km-1 * 0.00000055 +
(NO2) 12.127952596066 K km-1 * 0.00000033698 +
(N2O) 11.18181671295 K km-1 * 0.00000033671 +
(Xe) 61.282460659191 K km-1 * 0.0000000869565217391 +
(CO) 9.4393555726775 K km-1 * 0.00000008 +
(SO2) 15.757493460485 K km-1 * 0.000000015 +
(O3) 12.001569302138 K km-1 * 0.0000000003 +
(I2) 45.728742264382 K km-1 * 0.00000000009 +
(SF6) 30.187357269247 K km-1 * 0.0000000000115 =
(N2) 7.36568033074394 +
(O2) 2.23699350189356 +
(Ar) 0.176030325226679 +
(CO2) 0.00502387325839717 +
(Ne) 0.000173273308305028 +
(He) 0.00000986108834077279 +
(CH4) 0.00000793446406965918 +
(Kr) 0.000039225663804284 +
(H2) 0.000000377271557179935 +
(NO2) 0.00000408687746582232 +
(N2O) 0.00000376502950541739 +
(Xe) 0.00000532890962253648 +
(CO) 0.0000007551484458142 +
(SO2) 0.000000236362401907275 +
(O3) 0.0000000036004707906414 +
(I2) 0.00000000411558680379438 +
(SF6) 0.000000000347154608596341 = 9.78397288330931 K km-1
Above, I’ve adjusted relative concentrations to arrive at 1,000,000 ppm. You’ll note the model atmospheres you find online exceed 1,000,000 ppm, which is impossible and which skews results.
The differential of only 0.050935112661 K km-1 between the 9.7330377706482238008458858152373 K km-1 calculated result and the 9.78397288330931 K km-1 derived result shows we’re pretty close. The first result’s calculation makes assumptions that could skew the result, so it’s a good bet the second result is more precise… but then, the second result still isn’t exact because there are more than 17 gases in the atmosphere.
Then one can calculate for any given change in concentration of any given constituent atomic or molecular species of the atmosphere:
===============
If the climate alarmists were serious about reducing temperature, they’d advocate for removing all Ar… it serves no biological purpose, it’s used in industry so we need stocks of it, it has a higher concentration than CO2 and thus would be easier to remove, its removal wouldn’t destroy all life on the planet (as CO2’s total removal would) and its removal would lower the lapse rate (and thus cool the surface) by:
=====
(Ar) 18.846929895790 K km-1 * 5.105 km * 0.000001 = 0.000096213577118008 K ppm-1
(Ar) 18.846929895790 K km-1 * 5.105 km * 0.009340 = 0.8986348102821 K
But wait! We also have to account for the atoms and molecules which that Ar displaces. We’ll do the calculations for the three most-prevalent atomic or molecular species.
N2 | 28.0134 g mol-1 | 29.12 J mol-1 K-1 | 9.4339738283240 K km-1
(N2) 9340 ppm * 0.780761158 ppm = 7292.30921572 ppm
(N2) 780761.158 ppm + 7292.30921572 ppm = 788053.46721572 ppm
(N2) 9.433973828324 K km-1 * 5.105 km * 0.780761158 = 37.6017980884478 K
(N2) 9.433973828324 K km-1 * 5.105 km * 0.78805346721572 = 37.9529988825939 K
(N2) 37.9529988825939 K – 37.601798088447 K = 0.351200794146905 K warming
O2 | 31.9988 g mol-1 | 29.38 J mol-1 K-1 | 10.680770320623 K km-1
(O2) 9340 ppm * 0.20944121395198 ppm = 1956.18093831149 ppm
(O2) 209441.21395198 ppm + 1956.18093831149 ppm = 211397.394890292 ppm
(O2) 10.680770320623 K km-1 * 5.105 km * 0.20944121395198 = 11.4198518271666 K
(O2) 10.680770320623 K km-1 * 5.105 km * 0.211397394890292 = 11.5265132432324 K
(O2) 11.5265132432324 K – 11.4198518271666 K = 0.106661416065799 K warming
CO2 | 44.0095 g mol-1 | 36.94 J mol-1 K-1 | 11.683426182319 K km-1
(CO2) 9340 ppm * 0.00043 = 4.0162 ppm
(CO2) 430 ppm + 4.0162 ppm = 434.0162 ppm
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.00043 = 0.0256468729841176 K
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.0004340162 = 0.0258864147777892 K
(CO2) 0.0258864147777892 K – 0.0256468729841176 K = 0.0002395417936716 K warming
0.8986348102821 K – 0.351200794146905 K – 0.106661416065799 K – 0.0002395417936716 K = 0.440533058275724 K decrease in lapse rate
Removing all Ar would decrease the lapse rate (and thus surface temperature) by 0.440533058275724 K.
=====
Conversely, removing all CO2 would only reduce the lapse rate (and thus surface temperature) by:
=====
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000001 = 0.0000596438906607385 K ppm-1
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000430 = 0.0256468729841176 K
But wait! We also have to account for the atoms and molecules which that CO2 displaces. We’ll do the calculations for the three most-prevalent atomic or molecular species.
N2 | 28.0134 g mol-1 | 29.12 J mol-1 K-1 | 9.4339738283240 K km-1
(N2) 430 ppm * 0.780761158 = 335.72729794 ppm
(N2) 780761.158 ppm + 335.72729794 ppm = 781096.88529794 ppm
(N2) 9.433973828324 K km-1 * 5.105 km * 0.780761158 = 37.6017980884478 K
(N2) 9.433973828324 K km-1 * 5.105 km * 0.78109688529794 = 37.6179668616258 K
(N2) 37.6179668616258 K – 37.6017980884478 K = 0.016168773178002 K warming
O2 | 31.9988 g mol-1 | 29.38 J mol-1 K-1 | 10.680770320623 K km-1
(O2) 430 ppm * 0.20944121395198 = 90.0597219993514 ppm
(O2) 209441.21395198 ppm + 90.0597219993514 ppm = 209531.273673979 ppm
(O2) 10.680770320623 K km-1 * 5.105 km * 0.20944121395198 = 11.4198518271666 K
(O2) 10.680770320623 K km-1 * 5.105 km * 0.209531273673979 = 11.4247623634523 K
(O2) 11.4247623634523 K – 11.4198518271666 K = 0.00491053628570093 K warming
Ar | 39.948 g mol-1 | 20.7862 J mol-1 K-1 | 18.846929895790 K km-1
(Ar) 430 ppm * 0.00934 = 4.0162 ppm
(Ar) 934 ppm + 4.0162 ppm = 938.0162 ppm
(Ar) 18.84692989579 K km-1 * 5.105 km * 0.00934 = 0.898634810282194 K
(Ar) 18.84692989579 K km-1 * 5.105 km * 0.009380162 = 0.902498939966408 K
(Ar) 0.902498939966408 K – 0.898634810282194 K = 0.0038641296842139 K warming
0.0256468729841176 K – 0.016168773178002 – 0.004910536285700930 K – 0.0038641296842139 K = 0.000703433836200771 K.
Removing all CO2 would decrease the lapse rate (and thus surface temperature) by 0.000703433836200771 K.
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“No one is advocating for removing all CO2 from the atmosphere! That’s just ridiculous! That would kill all life on the planet!”, someone will invariably state.
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Ok, let’s assume they draw CO2 down from 430 ppm to 280 ppm (150 ppm decrease). That would reduce the lapse rate (and thus surface temperature) by:
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000001 = 0.0000596438906607385 K ppm-1
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000430 = 0.0256468729841176 K
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000280 = 0.0167002893850068 K
(CO2) 11.683426182319 K km-1 * 5.105 km * 0.000150 = 0.00894658359911077 K
But wait! We also have to account for the atoms and molecules which that CO2 displaces. We’ll do the calculations for the three most-prevalent atomic or molecular species.
N2 | 28.0134 g mol-1 | 29.12 J mol-1 K-1 | 9.4339738283240 K km-1
(N2) 150 ppm * 0.780761158 = 117.1141737 ppm
(N2) 780761.158 ppm + 117.1141737 ppm = 780878.2721737 ppm
(N2) 9.433973828324 K km-1 * 5.105 km * 0.780761158 = 37.6017980884478 K
(N2) 9.433973828324 K km-1 * 5.105 km * 0.7808782721737 = 37.6074383581611 K
(N2) 37.6074383581611 K – 37.6017980884478 K = 0.00564026971329668 K warming
O2 | 31.9988 g mol-1 | 29.38 J mol-1 K-1 | 10.680770320623 K km-1
(O2) 150 ppm * 0.20944121395198 = 31.416182092797 ppm
(O2) 209441.21395198 ppm + 31.416182092797 ppm = 209472.630134073 ppm
(O2) 10.680770320623 K km-1 * 5.105 km * 0.20944121395198 = 11.4198518271666 K
(O2) 10.680770320623 K km-1 * 5.105 km * 0.209472630134073 = 11.4215648049407 K
(O2) 11.4215648049407 K – 11.4198518271666 = 0.00171297777410118 K warming
Ar | 39.948 g mol-1 | 20.7862 J mol-1 K-1 | 18.846929895790 K km-1
(Ar) 150 ppm * 0.00934 = 1.401 ppm
(Ar) 934 ppm + 1.401 ppm = 935.401 ppm
(Ar) 18.84692989579 K km-1 * 5.105 km * 0.00934 = 0.898634810282194 K
(Ar) 18.84692989579 K km-1 * 5.105 km * 0.00935401 = 0.899982762497618 K
(Ar) 0.899982762497618 K – 0.898634810282194 K = 0.00134795221542394 warming
0.00894658359911077 K – 0.00564026971329668 K – 0.00171297777410118 K – 0.0013479522154239 K = 0.00024538389628901 K.
Reducing CO2 from 430 ppm to 280 ppm would decrease the lapse rate (and thus surface temperature) by 0.00024538389628901 K.
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Less than 1/1000th of a degree. For trillions of dollars wasted. When they could just remove all Ar and absolutely lower surface temperature by 0.440533058275724 K for far less money… but monetizing Ar emission isn’t as lucrative as CO2 emission, now is it?
“But what about the ‘greenhouse effect (due to backradiation)’?”, someone may ask? It doesn’t exist, because “backradiation” doesn’t exist, as I show at the link above. Energy does not and cannot spontaneously flow up an energy density gradient.