We’re still discussing Willis Eschenbach’s ‘Steel Greenhouse’.
How come the warming EFFECT of putting the shell around the sphere is real but Eschenbach’s “back radiation” EXPLANATION of how it comes about is wrong?
Simply put, it’s because the effect doesn’t violate the 2nd Law of Thermodynamics, but the explanation does.
In Part 1 and Part 2 we established some fairly basic principles of thermodynamics that we can now put to use in analysing Eschenbach’s explanation of why and how the radiating central sphere needs to warm with the steel shell surrounding it:
“In order to maintain its thermal equilibrium, the whole system must still [after the steel shell is placed around the sphere] radiate 235 W/m2 out to space. To do this, the steel shell must warm until it is radiating at 235 watts per square metre. Of course, since a shell has an inside and an outside, it will also radiate 235 watts inward to the planet. The planet is now being heated by 235 W/m2 of energy from the interior, and 235 W/m2 from the shell. This will warm the planetary surface until it reaches a temperature of 470 watts per square metre. In vacuum conditions as described, this would be a perfect greenhouse, with no losses of any kind.”
The first part of this paragraph simply describes the necessary conditions for reaching a new dynamic equilibrium upon putting the steel shell up around the radiating sphere. Nothing mysterious about it at all.
But then (in the bolded part) Eschenbach starts ‘explaining’ how he sees this new state of dynamic equilibrium to be accomplished.
And this is where any connection to basic, ordinary physics – and hence, to the real world – appears to be lost.
Let’s parse what he’s saying:
- Of course, since a shell has an inside and an outside, it will also radiate 235 watts inward to the planet.
Now will it indeed? Says who? The people adhering to the ‘bidirectional flow’ concept of radiative heat transfer do. This concept was however only ever meant to be a theoretical, descriptive model. It is not observed reality. It is a SUGGESTION, an ASSUMPTION, of how things might work, and nothing else. I feel the need here to reiterate the words of quantum theory master Niels Bohr:
“There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature IS. Physics concerns what we can SAY about nature …”
Nature reveals to us the unidirectional transfer of energy as ‘heat’ from a hot object to a cold one. This spontaneous transfer (or, specifically, its effect) can be directly observed, measured, detected, sensed. It is, then, by definition, a real, directly verifiable physical phenomenon.
However, in order to deconstruct this phenomenon, to describe exactly what goes on in detail when energy is transferred from a hot to a cold object as heat (in our case, radiative heat), to describe (and – hopefully – be able to explain) the inner nature of a heat transfer, so to say, we have to resort to mental models. Because then we enter the realm of the invisible, the unobservable. We cannot possibly say in this case how nature really IS. We can only guess and theorise about it, say something ABOUT nature based on what it does in fact reveal to us.
The ‘bidirectional flow’ concept of radiative heat transfer (originally Pierre Prévost’s ‘radiative theory of exchanges’ (1791)) is such a mental model (a stubborn one at that!), an attempt to describe in an orderly and (‘macroscopically’) understandable, instructive fashion what might happen on a microscopic (quantum) level when we observe energy being transferred as radiative heat across a vacuum between two surfaces at different temperatures.
That doesn’t mean we KNOW that what this model describes is reality, the real situation, that the suggested outline of what’s going on is what actually physically happens. It is merely a (convenient, useful) model of how it perhaps could happen.
Note, we can only ever physically observe (detect) the actual ‘heat’ being transferred. And temperatures changing as a result. Nothing else. Everything else is pure theory. People tend to forget (or ignore, or deny) this.
Let’s find out, then, if this model in the end turns out to be a good description of reality. What’s Eschenbach saying next?
- The planet is now being heated by 235 W/m2 of energy from the interior, and 235 W/m2 from the shell.
Well, yeah, if you are one of those believing that there is in fact “back radiation” constituting a real flux (transfer) of energy from the warm shell to the (even warmer) sphere, then the sphere will necessarily receive (and absorb) ‘235 W/m2 of energy from the interior, and 235 W/m2 from the shell’.
- This will warm the planetary surface until it reaches a temperature of 470 watts per square metre.
What Eschenbach is doing here is this: He takes the heat flux equivalent from the nuclear power source inside the sphere (235 W/m2) and ADDS to this the “back radiation” flux from the shell (235 W/m2). From this he simply ends up with [235+235=] 470 W/m2. And acquires a corresponding blackbody temperature for the sphere surface amounting to 301.7K, ~1.19 times the absolute temperature of the shell temperature and of the initial temperature of the sphere itself.
Can he do this?
Of course he can’t.
I will, however, in the following try to show that the ultimate problem here is not Eschenbach’s use of the ‘bidirectional flow’ model. It is the ‘bidirectional flow’ model itself.
The first catch with a ‘two-stream’ concept such as this becomes apparent as soon as one attempts to apply it to a decidedly thermodynamical problem, one which strictly deals with the transfer of energy between systems to change ‘internal energies’ and ‘temperatures’ of those systems.
The ‘bidirectional flow’ model aims to portray a single heat transfer as a ‘net’ of TWO separate and opposite ‘energy transfers’ in one.
Such a conceptual idea doesn’t square well (it is in fact completely and directly at odds) with basic thermodynamic principles, principles that are firmly founded on what we can actually observe in nature. We simply do not observe a two-stream energy transfer between two objects. Anywhere. At any time.
The ‘bidirectional flow’ model hence conveys a certain mental embroidering of reality that goes beyond what reality itself reveals, a mere attempt at making sense of a phenomenon that by its inscrutable nature alone would appear to boggle a human mind.
It is so very easy at this point to lose one’s focus, to let words and mental visualisations cloud one’s actual vision.
So I want you to hold on to this fundamental knowledge, based on observed reality:
- A thermodynamic ‘energy transfer’ between two systems (or a system and its surroundings) is always unidirectional. There is only ONE transfer of energy going on between two systems at any one time. Furthermore, such an ‘energy transfer’ can only come in two varieties: as ‘heat’ [Q], a spontaneous transfer of energy by virtue of a temperature difference between the two systems, always and only from the warmer to the cooler system; or as ‘work’ [W], by one system doing work on the other.
- By the 1st Law of Thermodynamics [ΔU = Q – W], a transfer of energy to or from a system (as ‘heat’ [Q] or ‘work’ [W]) changes the ‘internal energy’ [U] – and thus normally the temperature – of that system. This effect (changing system internal energies and thus temperatures) is exclusive to the two varieties of thermodynamic energy transfer. If a thermodynamic process brings about a change in a system’s ‘internal energy’ [U] (and thus temperature), you have transferred energy to or from it as ‘heat’ [Q] and/or ‘work’ [W]. There is no other way. Transfer heat TO it or let its surroundings do work ON it, the internal energy increases. And temperature rises. Transfer heat FROM it or let IT do work on its surroundings, the internal energy DEcreases. And temperature drops.
Eschenbach and the rGHE “back radiation” proponents seem utterly oblivious to these simple facts of thermodynamics. Or they completely ignore them (sweep them under the rug) and hope that no one will notice.
So where, ultimately, does the ‘bidirectional flow’ concept go wrong? What specifically in the end makes splitting up a unidirectional ‘heat’ transfer into two separate and opposing ‘energy’ transfers violate the 2nd Law of Thermodynamics?
I will try my best to explain:
q = σ(Tsphere4 – Tshell4)
According to the ‘bidirectional flow’ concept of radiative heat transfer, the radiative heat is simply the ‘net’ of the two opposing flows (fluxes) of radiative energy between the two objects involved in the heat transfer. In other words, neither of the two temperature terms on the righthand side are in themselves supposed to be ‘heats’; rather, they are considered ‘radiative emission fluxes’. Only the ‘net’ – the vector sum – of the two apparently constitutes what is called a ‘radiative heat transfer’. So, the ‘bidirectional flow’ concept tries to separate between ‘radiative emission fluxes’ and ‘radiative heat fluxes’. ‘Energy’, apparently, moves both ways, but ‘heat’ moves only one.
Awkward, perhaps, but a fair enough principle. As long as you manage to stick to it. But does the ‘bidirectional flow’ concept really pull off the task of keeping the opposing ‘radiation fluxes’ and the resulting (net) ‘heat flux’ apart as separate entities all the way? That’s the question.
Well, already from the onset it starts losing some of its sense and coherence. Because two separate, opposing fluxes could never make one unidirectional flux in between them. The first flux would simply transfer energy from the warmer system to the cooler and the second flux from the cooler system to the warmer. The ‘heat’, then, could only ever be the ‘net result‘ of this two-way transfer: Since the cool object transfers less energy by radiation to the warmer object than the other way around, then after each cycle of radiative exchange there will be an energy surplus (an increase in ‘internal energy’) in the cooler object (large flux IN minus small flux OUT) and an energy deficit (a decrease in ‘internal energy’) in the warmer object (small flux IN minus large flux OUT), meaning, the cooler object would warm and the warmer object would cool. There has been a net transfer of energy from the warmer to the cooler object. This would be the ‘heat’. Not itself an actual flux, that is. Just a net result of two (opposing) fluxes.
Peculiar? Maybe. Maybe not. At least such a view doesn’t appear to violate any laws of thermodynamics. Yet.
But this is precisely where the problem starts emerging. For the ‘bidirectioners’.
The size, the magnitude, of this net transfer of energy (q, the ‘heat’) in a radiative heat transfer between two systems at different temperatures depends very much on the size, the magnitude, of that temperature difference between them. It’s right there in the Stefan-Boltzmann radiative heat transfer equation above. So, large difference, large net transfer of energy, large q; small difference, small net transfer of energy, small q. If the difference is zero, then q is also zero. Because then each object transfers as much energy to the other as the other transfers to it. According to the ‘bidirectional flow’ concept …
This too I presume we can all agree on.
Further, the q is, at the same time, the net energy loss of the warmer object per unit time per unit area (J/s/m2) AND the net energy gain of the cooler object per unit time per unit area. Which means it is simultaneously the Qout (the energy lost as ‘heat’) of the warmer object AND the Qin (the energy gained as ‘heat’) of the cooler object. The warmer object being the central sphere or the surface of the Earth, the cooler object being the surrounding shell or the atmosphere.
I hope this is also clear to everyone.
However, the warmer object (the sphere, Earth’s surface), as we all know by now, does not only have a Qout. It doesn’t just lose energy. It also itself has a Qin. Coming from ‘behind’, so to say, from its power/heat source, basically its very own ‘hot reservoir’. Through a different, separate heat transfer:
Figure 1. QH is the Qin of the sphere, its energy input or gain. QC is the Qout of the sphere, its energy output or loss. To keep the sphere system in a dynamic equilibrium, the sphere’s internal energy, and thus temperature, in a steady state, these two ‘heats’ must be of equal size (as much energy coming IN as what goes OUT at any time).
The point here is that as the temperature difference between the sphere and the shell grows less (from the shell warming), then q (equal to QC in Figure 1; the sphere’s Qout, energy lost as ‘heat’ to the shell, the cold reservoir) also naturally becomes smaller.
At the same time, the sphere’s Qin (equal to QH in Figure 1; energy gained as ‘heat’ from the hot reservoir) remains the same as before.
It should go without saying, then, that in this situation, the energy gained by the system (the sphere) can no longer be matched by the energy lost: Qin is now larger than Qout. Which means the ‘net heat’, the Q in the First Law equation (defined as ‘the energy transferred to the system as heat’, basically the balance between the system’s heat IN and heat OUT), is no longer zero, like it was in the initial state of dynamic equilibrium, before the shell started warming. It would now be positive again, as it was during the original heating of the sphere.
And so, some of the energy constantly provided to the sphere by the internal power source would once again pile up inside the sphere’s mass (not as much energy can escape as what comes in), increasing its U and hence its T. Towards a new dynamic equilibrium, reached only when the sphere’s Qout once more matches its Qin.
Basic thermodynamics. Basic energy accounting.
q needs to be preserved. The sphere thus needs to warm.
The problem for the ‘bidirectioners’ appears just here. According to the ‘bidirectional flow’ concept, the radiative emission fluxes are simply dependent on each object’s surface temperature, so as long as the sphere’s blackbody surface stays at 255K, it will always send out a ‘radiative emission flux’ of 240 W/m2, matching the ‘heat flux’ equivalent from its internal power source. So as much energy escapes the surface of the sphere per unit time as radiation as what enters at the core of the sphere per unit time.
So how come, as the shell warms, the sphere warms also, if its radiative output stays the same as always?
Because as the shell warms, the q (the ‘radiative HEAT flux’ from the sphere to the shell) decreases, which means the sphere’s Qout decreases. And according to the ‘bidirectional flow’ concept, how does the q decrease if the radiative emission flux from the sphere stays the same? By the opposing radiative emission flux from the shell increasing, of course:
q = σ(Tsphere4 – Tshell4)
(The larger the Tshell4 term with the sphere temp kept constant, the smaller the q. Simple as that.)
So if q needs to be preserved (and it does), then the Tsphere4 term needs to increase correspondingly.
But how does the sphere’s surface temperature rise? It can only happen by a direct increase in its internal energy (+U). Energy from somewhere will have to pile up.
But from where?
We know already that the energy in from the power source at its core is constant, it never changes. No help there. We also know that the emissive power of the sphere (its radiative output) is completely and only due to its surface temperature. In the ‘bidirectional flow’ model. So unless it actually cools, its output rate will not diminish. No help there either.
That leaves only one alternative.
Only the now ‘extra’ energy in from the shell is available to pile up at/below the surface of the sphere. The “back radiation” flux from the warming shell. That’s the only difference. The only ‘new’ energy.
In the ‘bidirectional flow’ model.
So in effect, an extra ‘heat input’ has been added to the sphere that wasn’t there before the shell came into place. A ‘radiation flux’ merely, you say. No, ‘radiative heat‘. A physical transfer of energy to the sphere, directly and all by itself increasing its ‘internal energy’, thus raising its temperature and, consequently, its corresponding ‘radiative emission flux’ out. Back towards the shell. [235+235=] 470 W/m2.
That’s a transfer of energy as ‘heat’. By thermodynamic definition.
From cool shell to warm sphere …
This is what Eschenbach is saying:
q (the sphere’s Qout) needs to be conserved. And he’s correct. Simply because its Qin is conserved. q needs to match the Qin in order for the sphere’s Q (‘net heat IN/OUT’) to remain at zero; Q=0 means ΔU=0 and so no further temperature rise.
He then says that as the shell warms, q naturally decreases, forcing the sphere to warm also to make it grow back to where it was. And he’s still correct.
What he then does is simply using the ‘bidirectional flow’ model to explain how this further warming of the sphere comes about. And within the framework of this particular view of the world, he would actually still be correct. For there it is specifically the “back radiation” from the shell to the sphere that makes the ‘internal energy’ of the sphere increase. It is the “back radiation” from the shell being absorbed by the sphere as ‘extra’ energy, in addition to the energy from the internal power source, that raises its surface temperature and thus enables it to radiate out more energy than before, than with only the internal power source providing the energy.
So Eschenbach, when he claims that, at the new dynamic equilibrium, the shell radiates 235 W/m2 to space from its outer surface and 235 W/m2 to the sphere from its inner surface, forcing the sphere to radiate 470 W/m2 to the shell to maintain its Qout (sphere>shell q) at 235 W/m2 ([470–235=] 235 W/m2), to match the steady 235 W/m2 input equivalent from the internal power source, then he is well within his rights to do so.
The ‘bidirectional flow’ model allows him to; in fact, demands him to …
So the basic problem with Eschenbach’s explanation of the ‘Steel Greenhouse’ (and with the climate establishment’s common explanation of the rGHE (see below)) lies not so much with Eschenbach himself, but rather with that fundamental idea of a ‘bidirectional flow’ in a radiative heat transfer, the model concept of a two-way radiative flux exchange making up a ‘net sum’ called the ‘heat’.
It is a problematic concept to say the least. Any physical explanation ending up violating the 2nd Law of Thermodynamics is …
The ‘bidirectional flow’ model in effect allows you to pretend that there are two separate, simultaneous heat transfers going on between the sphere and the shell, one where the sphere gets to add to the internal energy of the shell, thus warming it, and one where the shell gets to add to the internal energy of the sphere, thus warming it. This model basically treats both terms on the righthand side of the radiative heat transfer equation as real, separate, thermodynamically working ‘radiative heat fluxes’ (as if the two objects were thermally isolated from one another):
q = σ(Tsphere4 – Tshell4)
The thing is, even though we know from basic thermodynamic principles that this cannot be, ‘heat’ by definition flows only one way between systems and in nature invariably and exclusively from hot to cold, the fundamental flaw lying at the heart of this (admittedly, deeply ingrained) conceptual idea only becomes a real and obvious problem as you connect a system to both a (steady) hot and a cold reservoir, essentially when you both (constantly) heat and insulate it at the same time. At other times* we need not worry too much about it. We can sort of avoid having to be directly confronted with it. The concept ‘works’. It ‘explains’ stuff. It is ‘practical’. (So why discard it?)
*Normally, in radiative heat transfer textbooks, the bodies in question are either all unpowered and simply start at different temperatures, moving towards thermal equilibrium between each other, or they are somehow kept at constant temperature (meaning, the power input varies). I can’t recall having seen any example where a central object surrounded by a passive insulating shell is rather heated by a constant power input (meaning, the temperature is free to change). This would be the instance where the inherent flaw in the ‘bidirectional flow’ concept emerges as a direct explanatory problem.
But in the case of such a three-body arrangement (where the central system is constantly heated by the first system and insulated by the third), adhering to the ‘bidirectional flow’ explanation of things, the only reason the central system warms beyond the equilibrated state with its heat source (its hot reservoir) alone, is the additional energy input from the “back radiation” flux from the insulating layer, its heat sink (its cold reservoir). The cool system heating the warm system. There is no way around it. This is the corollary of the ‘bidirectional flow’ concept. You are simply forced to break the 2nd Law of Thermodynamics.
The situation with the heated central sphere and the surrounding steel shell insulating it (Eschenbach’s ‘Steel Greenhouse’) is the exact equivalent to the rGHE “back radiation” idea of how the surface of the Earth warms beyond its pure solar radiative equilibrium temperature; also a three-body setup, sun > sfc > atm:
Figure 2. (Derived from Stephens et al. 2012.)
Evidently, the Sun here could itself only possibly warm the surface as far as 165 W/m2 (232K), so you need the addition of the 345 W/m2 down from the cooler atmosphere to warm it to 289K, radiating a corresponding blackbody emission flux of 398 W/m2. In other words: The entire rise in surface temperature from 232 to 289K (57 degrees) is specifically due to the absorption of the atmospheric extra radiative energy input to the surface, the DWLWIR (“back radiation”) ‘flux’, and nothing else. Note that there is NO restriction whatsoever to the outgoing radiation from the surface at any point in the cycle. As per the ‘bidirectional flow’ concept. The warming, then, is ONLY caused by more energy coming IN, not in any way by less energy going OUT. Increased energy input. More ‘heat’ to the surface. And that extra heat is NOT from the hot Sun, but from the cool atmosphere …
- If you somehow insulate a constantly heated object, then the object WILL equilibrate at a higher temperature than if you DIDN’T insulate it.
- However, it is NOT energy from the insulating layer doing the extra warming. Cold cannot heat hot. It is STILL only the energy from the power source constantly heating the object that can make it warmer.
– – –
- What the insulating layer does, though, is warming – by absorbing the heat flux from the object it insulates – to a temperature beyond the heated object’s original surroundings, the ultimate heat sink now outside the insulating layer.
- This increases the temperature ‘potential’ facing the central heated object, which in turn reduces the DIFFERENCE between the temperature ‘potential’ of the heated object itself and that of its surroundings, compared to what it used to be before the insulating layer started warming.
- Since it is the difference in system temperature ‘potentials’ that generates a ‘heat flux’ between the systems, the size of this difference matters: The larger the difference, the larger the heat flux. And the smaller the difference, the smaller the heat flux.
- If the INCOMING heat flux (the Qin) to an object is kept constant, but its OUTGOING counterpart (the Qout) is reduced, the object will naturally warm, from the Qin energy not being able to escape as fast as before, thus partially piling up inside of it instead. Until we reach a new (and higher) surface temperature to restore the balance.
– – –
- An insulating layer simply impedes the energy ESCAPING the heated/powered central object as heat, thus indirectly forcing it to warm further. The insulating layer, however, does this merely through its temperature being higher than the heated object’s original surroundings. It doesn’t do it by radiating some of the heated object’s own emitted energy back to it as recycled ‘heat’ to be absorbed a second time to warm it some more. This would violate the laws of thermodynamics.
– – –
- The source of today’s ubiquitous and deep-seated belief that a warm surface can warm even further from simply absorbing “back radiation” from a cool atmosphere is the (archaic) ‘bidirectional flow’ concept of radiative heat transfer …
Next up: How do you heat a planetary surface, then? If not by the Earth’s own thermal radiation, a result of its temperature rather than a cause of it … How does the atmosphere insulate the surface?