Guest post By Tom Vonk (Tom is a physicist and long time poster at many climate blogs. Note also I’ll have another essay coming soon supporting the role of CO2 – For a another view on the CO2 issue, please see also this guest post by Ferdinand Engelbeen Anthony)
If you search for “greenhouse effect” in Google and get 1 cent for statements like…
“CO2 absorbs the outgoing infrared energy and warms the atmosphere” – or – “CO2 traps part of the infrared radiation between ground and the upper part of the atmosphere”
…you will be millionaire .
Even Internet sites that are said to have a good scientific level like “Science of doom” publish statements similar to those quoted above . These statements are all wrong yet happen so often that I submitted this guest post to Anthony to clear this issue once for all.
In the case that somebody asks why there is no peer reviewed paper about this issue , it is because everything what follows is textbook material . We will use results from statistical thermodynamics and quantum mechanics that have been known for some 100 years or more . More specifically the statement that we will prove is :
“A volume of gas in Local Thermodynamic Equilibrium (LTE) cannot be heated by CO2.”
There are 3 concepts that we will introduce below and that are necessary to the understanding .
- The Local Thermodynamic Equilibrium (LTE)
This concept plays a central part so some words of definition . First what LTE is not . LTE is not Thermodynamic Equilibrium (TE) , it is a much weaker assumption . LTE requires only that the equilibrium exists in some neighborhood of every point . For example the temperature may vary with time and space within a volume so that this volume is not in a Thermodynamic Equilibrium . However if there is an equilibrium within every small subvolume of this volume , we will have LTE .
Intuitively the notion of LTE is linked to the speed with which the particles move and to their density . If the particle stays long enough in a small volume to interact with other particles in this small volume , for example by collisions , then the particle will equilibrate with others . If it doesn’t stay long enough then it can’t equilibrate with others and there is no LTE .
There are 2 reasons why the importance of LTE is paramount .
First is that a temperature cannot be defined for a volume which is not in LTE . That is easy to understand . The temperature is an average energy of a small volume in equilibrium . Since there is no equilibrium in any small volume if we have not LTE , the temperature cannot be defined in this case.
Second is that the energy distribution in a volume in LTE follows known laws and can be computed .
The energy equipartition law
Kinetic energy is present in several forms . A monoatomic gas has only the translational kinetic energy , the well known ½.m.V² . A polyatomic gas can also vibrate and rotate and therefore has in addition to the translational kinetic energy also the vibrational and the rotational kinetic energy . When we want to specify the total kinetic energy of a molecule , we need to account for all 3 forms of it .
Thus the immediate question we ask is : “If we add energy to a molecule , what will it do ? Increase its velocity ? Increase its vibration ? Increase its rotation ? Some mixture of all 3 ?”
The answer is given by the energy equipartition law . It says : “In LTE the energy is shared equally among its different forms .”
As we have seen that the temperature is an average energy ,and that it is defined only under LTE conditions , it is possible to link the average kinetic energy <E> to the temperature . For instance in a monoatomic gas like Helium we have <E>= 3/2.k.T . The factor 3/2 comes because there are 3 translational degrees of freedom (3 space dimensions) and it can be reformulated by saying that the kinetic energy per translational degree of freedom is ½.k.T . From there can be derived ideal gas laws , specific heat capacities and much more . For polyatomic molecules exhibiting vibration and rotation the calculations are more complicated . The important point in this statistical law is that if we add some energy to a great number of molecules , this energy will be shared equally among their translational , rotational and vibrational degrees of freedom .
Quantum mechanical interactions of molecules with infrared radiation
Everything that happens in the interaction between a molecule and the infrared radiation is governed by quantum mechanics . Therefore the processes cannot be understood without at least the basics of the QM theory .
The most important point is that only the vibration and rotation modes of a molecule can interact with the infrared radiation . In addition this interaction will take place only if the molecule presents a non zero dipolar momentum . As a non zero dipolar momentum implies some asymmetry in the distribution of the electrical charges , it is specially important in non symmetric molecules . For instance the nitrogen N-N molecule is symmetrical and has no permanent dipolar momentum .
O=C=O is also symmetrical and has no permanent dipolar momentum . C=O is non symmetrical and has a permanent dipolar momentum . However to interact with IR it is not necessary that the dipolar momentum be permanent . While O=C=O has no permanent dipolar momentum , it has vibrational modes where an asymmetry appears and it is those modes that will absorb and emit IR . Also nitrogen N-N colliding with another molecule will be deformed and acquire a transient dipolar momentum which will allow it to absorb and emit IR .
In the picture left you see the 4 possible vibration modes of CO2 . The first one is symmetrical and therefore displays no dipolar momentum and doesn’t interact with IR . The second and the third look similar and have a dipolar momentum . It is these both that represent the famous 15µ band . The fourth is highly asymmetrical and also has a dipolar momentum .
What does interaction between a vibration mode and IR mean ?
The vibrational energies are quantified , that means that they can only take some discrete values . In the picture above is shown what happens when a molecule meets a photon whose energy (h.ν or ђ.ω) is exactly equal to the difference between 2 energy levels E2-E1 . The molecule absorbs the photon and “jumps up” from E1 to E2 . Of course the opposite process exists too – a molecule in the energy level E2 can “jump down” from E2 to E1 and emit a photon of energy E2-E1 .
But that is not everything that happens . What also happens are collisions and during collisions all following processes are possible .
- Translation-translation interaction . This is your usual billiard ball collision .
- Translation-vibration interaction . Here energy is exchanged between the vibration modes and the translation modes .
- Translation-rotation interaction . Here energy is is exchanged between the rotation modes and the translation modes .
- Rotation-vibration interaction … etc .
In the matter that concerns us here , namely a mixture of CO2 and N2 under infrared radiation only 2 processes are important : translation-translation and translation-vibration . We will therefore neglect all other processes without loosing generality .
The proof of our statement
The translation-translation process (sphere collision) has been well understood since more than 100 years . It can be studied by semi-classical statistical mechanics and the result is that the velocities of molecules (translational kinetic energy) within a volume of gas in equilibrium are distributed according to the Maxwell-Boltzmann distribution . As this distribution is invariant for a constant temperature , there are no net energy transfers and we do not need to further analyze this process .
The 2 processes of interest are the following :
CO2 + γ → CO2* (1)
This reads “a CO2 molecule absorbs an infrared photon γ and goes to a vibrationally excited state CO2*”
CO2* + N2 → CO2 + N2⁺ (2)
This reads “a vibrationally excited CO2 molecule CO2* collides with an N2 molecule and relaxes to a lower vibrational energy state CO2 while the N2 molecule increases its velocity to N2⁺ “. We use a different symbol * and ⁺ for the excited states to differentiate the energy modes – vibrational (*) for CO2 and translational (⁺) for N2 . In other words , there is transfer between vibrational and translational degrees of freedom in the process (2) . This process in non equilibrium conditions is sometimes called thermalization .
The microscopical process (2) is described by time symmetrical equations . All mechanical and electromagnetical interactions are governed by equations invariant under time reversal . This is not true for electroweak interactions but they play no role in the process (2) .
Again in simple words , it means that if the process (2) happens then the time symmetrical process , namely CO2 + N2⁺ → CO2* + N2 , happens too . Indeed this time reversed process where fast (e.g hot) N2 molecules slow down and excite vibrationally CO2 molecules is what makes an N2/CO2 laser work. Therefore the right way to write the process (2) is the following .
CO2* + N2 ↔ CO2 + N2⁺ (3)
Where the use of the double arrow ↔ instad of the simple arrow → is telling us that this process goes in both directions . Now the most important question is “What are the rates of the → and the ← processes ?”
The LTE conditions with the energy equipartition law give immediately the answer : “These rates are exactly equal .” This means that for every collision where a vibrationally excited CO2* transfers energy to N2 , there is a collision where N2⁺ transfers the same energy to CO2 and excites it vibrationally . There is no net energy transfer from CO2 to N2 through the vibration-translation interaction .
As we have seen that CO2 cannot transfer energy to N2 through the translation-translation process either , there is no net energy transfer (e.g “heating”) from CO2 to N2 what proves our statement .
This has an interesting corollary for the process (1) , IR absorption by CO2 molecules . We know that in equilibrium the distribution of the vibrational quantum states (e.g how many molecules are in a state with energy Ei) is invariant and depends only on temperature . For example only about 5 % of CO2 molecules are in a vibrationally excited state at room temperatures , 95 % are in the ground state .
Therefore in order to maintain the number of vibrationally excited molecules constant , every time a CO2 molecule absorbs an infrared photon and excites vibrationally , it is necessary that another CO2 molecule relaxes by going to a lower energy state . As we have seen above that this relaxation cannot happen through collisions with N2 because no net energy transfer is permitted , only the process (1) is available . Indeed the right way to write the process (1) is also :
CO2 + γ ↔ CO2* (1)
Where the use of the double arrow shows that the absorption process (→) happens at the same time as the emission process (←) . Because the number of excited molecules in a small volume in LTE must stay constant , follows that both processes emission/absorption must balance . In other words CO2 which absorbs strongly the 15µ IR , will emit strongly almost exactly as much 15 µ radiation as it absorbs . This is independent of the CO2 concentrations and of the intensity of IR radiation .
For those who prefer experimental proofs to theoretical arguments , here is a simple experiment demonstrating the above statements . Let us consider a hollow sphere at 15°C filled with air . You install an IR detector on the surface of the cavity . This is equivalent to the atmosphere during the night . The cavity will emit IR according to a black body law . Some frequencies of this BB radiation will be absorbed by the vibration modes of the CO2 molecules present in the air . What you will observe is :
- The detector shows that the cavity absorbs the same power on 15µ as it emits
- The temperature of the air stays at 15°C and more specifically the N2 and O2 do not heat
These observations demonstrate as expected that CO2 emits the same power as it absorbs and that there is no net energy transfer between the vibrational modes of CO2 and the translational modes of N2 and O2 . If you double the CO2 concentration or make the temperature vary , the observations stay identical showing that the conclusions we made are independent of temperatures and CO2 concentrations .
Conclusion and caveats
The main point is that every time you hear or read that “CO2 heats the atmosphere” , that “energy is trapped by CO2” , that “energy is stored by green house gases” and similar statements , you may be sure that this source is not to be trusted for information about radiation questions .
Caveat 1
The statement we proved cannot be interpreted as “CO2 has no impact on the dynamics of the Earth-atmosphere system” . What we have proven is that the CO2 cannot heat the atmosphere in the bulk but the whole system cannot be reduced to the bulk of the atmosphere . Indeed there are 2 interfaces – the void on one side and the surface of the Earth on the other side . Neither the former nor the latter is in LTE and the arguments we used are not valid . The dynamics of the system are governed by the lapse rate which is “anchored” to the ground and whose variations are dependent not only on convection , latent heat changes and conduction but also radiative transfer . The concentrations of CO2 (and H2O) play a role in this dynamics but it is not the purpose of this post to examine these much more complex and not well understood aspects .
Caveat 2
You will sometimes read or hear that “the CO2 has not the time to emit IR because the relaxation time is much longer than the mean time between collisions .” We know now that this conclusion is clearly wrong but looks like common sense if one accepts the premises which are true . Where is the problem ?
Well as the collisions are dominating , the CO2 will indeed often relax by a collision process . But with the same token it will also often excite by a collision process . And both processes will happen with an equal rate in LTE as we have seen . As for the emission , we are talking typically about 10ⁿ molecules with n of the order of 20 . Even if the average emission time is longer than the time between collisions , there is still a huge number of excited molecules who had not the opportunity to relax collisionally and who will emit . Not surprisingly this is also what experience shows .
Anthony, Tom makes several mistakes in this piece, equal time for a rebuttal?
I guess you overstretch the principle of local thermal equilibrium.
Suppose you put some water into a microwave oven. The water is in LTE. Then you switch on the microwave generator. For a while there is no LTE, there is more absorption by the water than emission. Eventually, there will be LTE again, but at quite a different temperature.
Replace the microwave oven by the black body radiation of earth’s surface. Without CO2 and other infrared active gases, and forgetting collision induced absorption of N2 or O2, there is no absorption in the atmosphere. Near room temperature you even may forget about N2 and O2 vibrations. Then, the temperature is determined by the kinetic energy of the molecules. Its value is governed by collisions of the gas moelcules with the earth’s surface, in fact by the temperature of the earth’s surface (plus a temperature gradient of roughly 1 Celsius per 100 m change of altitude on the basis of the so-called dry-adiabatic limit).
Add CO2 or H2O to the atmosphere, there is no LTE for a while, as parts of the black body radiation is absorbed by CO2 and H2O. Eventually, a new equilibrium is established.
The main difference to the old temperature gradient is that everywhere the new temperatures are somewhat higher than the old ones, just as in the microwave oven example. Now add further CO2 generated by burning of fossile fuels…
It’s been a few years since i studied physical chemistry. But something here doesn’t seem to add up.
“The LTE conditions with the energy equipartition law give immediately the answer : “These rates are exactly equal .” This means that for every collision where a vibrationally excited CO2* transfers energy to N2 , there is a collision where N2⁺ transfers the same energy to CO2 and excites it vibrationally . There is no net energy transfer from CO2 to N2 through the vibration-translation interaction .”
I believe this would only hold true if there was no net production or loss of either type of the two molecules CO2* and N2(+). This asumes there are no collisions like:
N2(+) + N2 = N2(0.5+) + N2 (0.5+)
Or similar collision of N2(+) with a non-exited CO2 molecule. A collision where the kinetic energy is split between two (or more) molecules, leading to a decay in number of molecules at N2(+) or near N2(+) kinetic energy levels. Which will eventually lead to the molecules reaching a Maxwell-Boltzmann kinetic enegy distribution.
Is there no such decay in kinetic energy levels for a system containing only CO2 and N2?
If there is such a decay then additional CO2* can be formed by IR absorption and feed the N2(+) which in turn decays into several N2(Y+) and CO2/y+) (where Y<1) and the distribution of these N2(y+) and CO2(Y+) defines the temperature.
As far as I can tell, the points raised in “caveat 1” seems be saying that while this treatment may be valid for a volume of gases in LTE, that never happens in the real world.
Any volume of gases with incoming IR cannot be in LTE unless precisely matched with outgoing LTE, and since the the missing N2-N2 collisions (and O2 of course) will prevent much of the outgoing IR from existing, the gas in not in LTE.
Jeez guys, for those that are taking Tom to task about what he didn’t show, did you expect an entire advanced chem semester in one article? The way I took this lesson, is to bring people up to speed about how CO2 acts when excited by infrared heat. And then touched on the interaction between CO2 and N2. I don’t believe this was supposed to be an all encompassing comprehensive article explaining the entire radiative chemical processes of our atmosphere. Obviously, there’s more going on up there than this.
Tom, once again, thanks for putting this in terms easily expressed. I’d often thought the energy emissions of CO2 were equally outward as they were back to earth, but as I’ve alluded to earlier, chemistry never really held much of an interest to me during my college years.
CO2 and H2O cool the atmosphere (at most levels):
http://rtweb.aer.com/lblrtm_frame.html
The follow on is that while they cool the atmosphere, they warm the surface even more,
warming which is subsequently shared to the atmosphere via convection.
The significant principal appears to me that additional CO2 broadens the
absorption bands meaning energy which left earth from the surface or troposphere,
(at a higher T) now would leave earth from the stratosphere
(at a lower T) thus, ‘All other things being equal’ less energy should leave earth.
‘All things’ usually not equal, and negative feedbacks (which IPCC seems to preclude)
seem to me as likely as positive feedbacks (which IPCC seems to ‘guarantee’).
But more likely still would be net zero feedbacks which would leave us with a small warming, which is what we’ve observed for the last third to half century.
That being said, the actual measurements of outgoing IR seem much more variable,
with no clear trend, making one wonder if CO2 is just not significant compared
to other factors governing energy loss to space:
http://www.climate4you.com/images/OLR%20Global%20NOAA.gif
Great presentation! Back to text book basics. I understand it because 60 years ago I used the rigid-rotator, harmonic-oscillater approximation to calculate classical thermodynamic functions, as a function of temperature. I doubt there are many post modern “climatetoligist” who have done that. My statistical analysis tends to confirm your conclusions. http://www.kidswincom.net/CO2OLR.pdf.
The main difference to the old temperature gradient is that everywhere the new temperatures are somewhat higher than the old ones, just as in the microwave oven example.
Is that microwave oven in a vast freezer? How does the potential to hold more energy work when it is bordered by an area with an unlimited potential to adsorb it.
I would suggest the author edit some of the sentence structures and grammar before posting on such a hot topic. It detracts from his attempt to state his case. Further, I am not at all convinced that the treatise presented here is a strong case against increased CO2 (from any source) adding to the heating of the Earth’s atmosphere.
As a skeptic, my central issue is that I am not convinced that our noisy planet, with its intrinsic short and long term temperature variability from natural sources, can be adequately measured in such a way to detect anthropogenic CO2’s warming affect.
From the comments I have read so far I think everyone is missing the very important point you made in defining the initial conditions:
Essentially you are setting the initial conditions to equilibrium and THEN detail your proof FOR THAT CONDITION.
Initial conditions:
1. LTE requires only that the equilibrium exists in some neighborhood of every point…temperature may vary with time and space within a volume so that this volume is not in a Thermodynamic Equilibrium . However if there is an equilibrium within every small subvolume of this volume , we will have LTE .
2. …a temperature cannot be defined for a volume which is not in LTE
3. …the energy distribution in a volume in LTE follows known laws and can be computed .”
I hope that clears up the misunderstandings.
We’ve all seen the “proof” starting with a=1 and b=2, going through a series of seemingly valid algebraic manipulations, and ending with the conclusion that a=b. The trick, of course, is to hide a divide-by-zero operation somewhere in the proof.
Ton Vonk has made some similar errors.
First, throughout the article, he uses “temperature” when he is actually talking about “heat”. Except that sometimes, “temperature” really does mean temperature, so he can come to some seemingly valid conclusions that are completely wrong. I suspect that untangling “heat” and “temperature” throughout this essay would clearly show some of the places where he has gone off the rails.
Second, he treats the “energy equipartition law” as if it were an iron-clad law of physics that holds exactly at all scales of size and time. This is simply not true.
The equipartition law, like all such empirical laws, is a statistical approximation that becomes less and less accurate as the population of gas molecules becomes smaller. Yet this article treats it as if it must be obeyed exactly by any random pair of molecules. Also, this law can be temporarily violated by transient responses.
Let’s put one molecule of CO2 in a chamber with 78 molecules of N2 and 21 of O2 (to pull some random numbers out of thin air). Hit that lone CO2 with a 15 micro-meter photon of infrared light and let it absorb the photon. Instantly, the equipartition law is violated, because the CO2 molecule has gained more vibrational energy, which increases the total vibrational energy of the gas sample relative to the rotational and translational energy. Before long, the excessively vibrating CO2 molecule will bump into another molecule. Depending on the exact geometry of the collision, both could use that excess vibration to rebound with excess translational or rotational energy, or some combination. Both molecules then go on to collide with other molecules, and the energy increase eventually distributes throughout the volume, re-establishing local equilibrium, and re-establishing the energy partition. In the end, there is an infinitesimally higher heat energy content of our gas sample, and consequently an infinitesimally higher temperature.
So, yes, CO2 absorbing infrared light does indeed increase the temperature of the atmosphere.
The question that is usually un-asked, let alone satisfactorily answered, is “how much?”
DocWat says:
August 5, 2010 at 5:26 am
My above entry would have looked better if the system had not erased my left and right carrots from the equations.I blame Bugs Bunny.
To make my position clear: I come at this after many years of seeing creationists mis-use basic physics such as entropy and the laws of thermodynamics to “prove” that evolution can’t happen. And just as many years of arguing against those mis-uses. I don’t know much about climatology, but I know a LOT about how to spot bad arguments.
The opening paragraphs of this article give me the same tingling-down-the-back-of the-neck feeling as those creationist arguments about thermodynamics. It doesn’t feel right. The slightly patronizing writing style, the drastic simplifying of a very complex subject, the theme of ‘armchair genius uses basic facts to prove a major field of science wrong’ — all just like any pseudo-scientific creationist tract.
I have been a skeptic on AGW for several years and will likely remain so for years yet to come. But this article strikes me as bad science. Bad science on one side is no more justified than bad science on the other.
The whole of this unfortunately fallacious argument is based on a false premise: that we have LTE. We don’t.
Nowhere in the atmosphere is at equilibrium (except in the sense of a dynamic equilibrium with continuous energy flows).
What we have are ensembles in which the various components (sunlight, thermal radiation, oxygen, nitrogen, water, greenhouse gases, etc.) and their various energy modes (translational, rotational, vibrational, directional, polarisation, chemical, etc.) all have slightly different thermodynamic temperatures (except for the incoming, scattered and reflected sunlight, which has a radically different temperature from the rest). What we call “the” temperature of the gas is just an average.
We do not have equipartition. It is the departures from equipartition that drive the system.
There are many other minor mis-statements in the article (for example, infra-red does interect with the translational modes; conservation of momentum requires it), but the crucial error is in the assumption of equilibrium. At equilibrium, nothing can warm anything else, by definition. If you have warming, you don’t have equilibrium.
This essay is all fine and good. But i have a question.
OK .. we know that CO2 can transfer no net energy to O2 or N2, but what about H2O?? Where does water fall within your essay??
We all know that Water Vapor is the most important Greenhouse Gas. Thus, while your essay addresses the main “gas” characters in the atmosphere, it does not address the role of water vapor.
Can you expand on this??
Someone posted on Roy Spencer’s blog a nice point.
“You just can’t have a “hot” CO2 molecule beside a “cold” N2″ molecule for more than a microsecond.” [That is about the right number but it can even less time than this].
The greenhouse theory and the textbooks are written like the N2 and the O2 molecules play no role at all. Our thermometres tell us that they do.
The fact that there is lapse rate where temperatures decline from 288K at the surface to 220K at 10 kms high (and the temperature then stays stable at 220K for the next 10 kms) tells us what really happens.
“These rates are exactly equal .” This means that for every collision where a vibrationally excited CO2* transfers energy to N2 , there is a collision where N2⁺ transfers the same energy to CO2 and excites it vibrationally . There is no net energy transfer from CO2 to N2 through the vibration-translation interaction .
Of course there is a net energy transfer from CO2 to N2, as in every equilibrium reaction: if you add something at one side of the equation, that pushes the reaction to the other side. In this case, you add energy to a CO2 molecule as it captures an IR foton. That increases the total energy content of the (micro)system: energy can’t be destroyed (except for energy-mass transfers, which isn’t the case here)… The increased energy content either is re-emitted by the CO2 molecule or redistributed over all the existant molecules by collisions. In the first case, half of it is directed to the surface. In the second case, the temperature of the mass increases. In the atmosphere, the warmer gas lifts up, causing an increase of the surface temperature due to the lapse rate.
Therefore in order to maintain the number of vibrationally excited molecules constant , every time a CO2 molecule absorbs an infrared photon and excites vibrationally , it is necessary that another CO2 molecule relaxes by going to a lower energy state .
That is true if there is no net radiation energy coming in as in your example. But (as Tyndal proved over 100 years ago): put a beam of IR, including the right frequency, through a volume of pure N2 and nothing happens. Put some CO2 in the same volume, and part of the IR is absorbed, increasing the temperature of the volume of gas. This proves beyond doubt that your reasoning doesn’t hold for a dynamic process where one of the components changes (either the amount of IR or the amount of CO2…).
Sorry I haven’t read all of the comments, so someone might have already said this.
I agree that IR does not heat the atmosphere. The heating affect is from the redirection of the IR. CO2 absorbs some IR traveling from earth to space and reradiates in some random direction. Some significant percentage is aimed back at the ground which can be warmed by IR.
So, a system at Local Thermodynamic Equilibrium doesn’t change temperature. Isn’t that the definition of Local Thermodynamic Equilibrium? I’m not sure I learned anything here.
DocWat says:
August 5, 2010 at 5:23 am
“What I really don’t understand is why water and CO2 are better, by a factor of 20, at this as N2 and O2 ”
Here is a very rough analogy. Recall the small hand exercise thing shaped like a V with a spring. Squeeze the handles, let go, and the thing springs back to its original shape. Think of your squeezing as the absorption and spring-back part as the release of that energy. Think of this as a CO2 molecule. Now cut two 25 cm long pieces, one blue and one green, from wood broom handles. Blue can be N2 and green can be O2. There is nothing to squeeze together. No squeeze – no energy absorbed. So, think of the nitrogen and oxygen gases (major components of earth’s atmosphere) as having no role to play in this little game. Only molecules with particular characteristics (read the post for them), and CO2 is one such, can play in this game.
This is an amazing exercise in disinformation: how to thoroughly muddle the waters while pretending to clarify.
All the greenhouse physics is hidden in caveat 1 and the weasel-y reference to “much more complex and not well understood aspects.”
Here’s a better “thought experiment” for you. Shine light on a black rubber sphere, uniformly, from all sides, until it gets hot. How hot? If the incoming energy flux is Iin, then it will get hot enough to radiate out at a rate Iup = Iin, in equilibrium.
Suppose that most of the radiation that makes up the flux Iup is not visible, but infrared. Now put the sphere inside a larger glass sphere, made of a glass that is transparent in the visible but partly absorbing in the infrared. So Iin watts/m2 still comes through, but not all the Iup makes it out. A fraction is absorbed and–in equilibrium–reradiated in all directions: some out, some back in. As a result of this, the total Iout is not equal to Iup anymore. Let us say it is equal to 0.8*Iup. So what happens?
Well, since in equilibrium we need to balance things, we need the total radiation out to equal the radiation in,
Iout = Iin
but Iout is only 80% of the radiation emitted upwards by the sphere,
Iout = 0.8*Iup
so we end up with
Iup = Iin/0.8 = 1.25 Iin
which means the “earth” has to radiate more with the glass in place, which means it has to get hotter.
Now tell me exactly what part of “CO2 traps part of the infrared radiation in the atmosphere” you think is untrue.
Sorry, just need to weigh in one more time.
When transferring translational energy, start by thinking about classical systems and let’s start with the simplest classical system – spheres. Imagine billiard balls. Imagine one billiard ball moving toward another and the vector that the moving billiard ball is travelling passes exactly through the center of the stationary billiard ball. When they collide some of the energy of the moving billiard ball will be transferred to the stationary billiard ball and both will be moving. In a completely frictionless environment with perfectly rigid balls the greatest energy possible will be transferred to the stationary ball and both balls will continue in the same direction as the original vector of originally moving ball. The amounf of energy transferred is also dependent upon the relative masses of the two balls.
Now, imagine that the center of the stationary ball is not exactly on the vector of the moving ball. the distance between the center of mass of the stationary object and the infinite line described by the direction of motion of the moving ball is called the impact parameter, usually denoted as b. The impace parameter can take on any value from 0 to infinity. The first case we considered was the b=0 case. The maximum interesting value of b is b r1+r2 then the balls don’t collide. With 0 < b < r1+r2 we have an interesting case where the amount of energy transferred is now determined by more than just the relative masses of the particles and the two objects also change direction after collision.
Now, if we replace one of the balls with two balls connected by a rigid stick, when the collision occurs the moving ball will put energy, in general, into BOTH translation AND rotational degrees of freedom of what I'll call the rigid rotor. If we're talking about macroscopic objects both the translational and rotational degrees of freedom and the energies that each of the modes can take on are continuous: i.e., the translational and rotational energies can take on any continuous value.
Now, replace the rigid stick with a spring. Our imagined collision between what I'll now call the vibrotor (which is not moving translationationally, rotationally, or vibrationally) and a moving sphere results in a vibrotor that IS moving, rotating, and vibrating. And, again, if the objects are macroscopic, all of the modes can take on any continuous value.
In the case of CO2 and N2 molecules, all of the translations are still rigorously classical – they can take on any real value. However, both the rotations and vibrations are classical and can only take on certain discrete values. For instance, as mention above, there are well known excitation modes in CO2 with an energetic value equivalent to 15 um radiation. If an object (for example, an N2 molecule) is going to collide with a CO2 molecule and excite it with to an excited state that N2 molecule has to have translational energy equivalent to at least 15 um radiation and the impact must occur with exactly the right impact parameter for the reaction to occur. Far more likely is for the transfer of translational (and rotational) energy from the N2 molecule to end up in translational and rotational degrees of freedom in the CO2 molecule.
I think Tom makes the common mistake that chemists see physicists make here, and that is assuming that microreversibility applies on the macroscopic scale. That's rarely true. As a physicist he's probably more used to seeing the term detailed balance, which is essentially the same thing, though in fact microscopic reversibility is technically a broader term. And, as misroscopic reversibility applies in laser cavities, as mentioned, we are still forced in almost all practical cases to find laser gain media with extremely long-lived states which are typically only available through non-radiative processes (i.e., the initially excited state does NOT re-emit!) in order to get a useful laser – but that's a digression (but Tom brought up the laser!).
Tom points out that re-excitation of CO2 vibrations occurs all of the time in an N2:CO2 laser. Quite right, but the effective internal temperature in the laser cavity is extremely higher than, for instance, 15C, so that there is in fact plenty of translational energy available at well above the vibrational excitation energy. At 15C this reverse step is in fact almost never going to occur due to the fact that all other energy transfer options are so much more likely and with much higher transition probabilities and that so few of the N2 molecules have energy significantly in excess of the equivalent of 15 um to overcome the impact parameter issues (i.e., most imapct parameters are going to be greater than 0).
There’s a throwaway remark in the article “Even Internet sites that are said to have a good scientific level like “Science of doom” publish statements similar to those quoted above .” I wonder if anyone could point me at some specific examples of this from “Science of doom”?
Thanks.
I’d think the heat capacity of a CO2 molecule vs water vapor would be of importance. No?
“In the case that somebody asks why there is no peer reviewed paper about this issue , it is because everything what follows is textbook material.”
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The fact that today’s “science” of AGW is quite murky and has a disgusting odor therefore suggests that scientists of all stripes are not policing their turf well at all, and are themselves therefore very complicit in the “political” shenanigans that have been going on for the past 30 years. If it ain’t the math it must be the money. Why else would so many do so little to stop so few from making a mockery of their profession? For the right price, you can get anyone to do or say anything you want; especially in today‘s world. Now we know how Lot felt.