Zen and the Second Law of Thermodynamics (2)

In Zen and the Second Law of Thermodynamics I dismissed the claim that the atmospheric "greenhouse effect" violates the second law of thermodynamics, invoking the correct (in my view, and most others) interpretation of the Stefan-Boltzmann equation. Here I will demonstrate that there is an overriding reason that the law cannot be violated in the mechanism of the "greenhouse effect", which is that it doesn't apply to radiative transfer of heat from greenhouse gases in the atmosphere to the Earth's surface.

Before I get into specifics of the mechanism, I should say that it appears to me that it's not only some sceptics who misunderstand it, but some atmospheric scientists too. That misunderstanding has led to the postulation of the so-called tropospheric "hot spot", which has proved so elusive, and thus an embarrassment to the scientists, and free ammunition for critics of the hypothesis. I should also say that this article in no way supports the hypothesis (it's not a theory in the strict sense) of catastrophic anthropogenic global warming (CAGW). It does support the general theory of the "greenhouse effect", its fundamentals can be tested, and effects measured.

First, some seeming irrelevancies which are important to understand. I'm going to describe how a fluorescent lamp works, in order to shed some light on the subject (I know it's a horrible pun, but I can't resist 'em). Before you switch off (there I go again), bear with me - it's important.

In an incandescent lamp, the filament is heated to the point where it emits near-white light, at a temperature of about 4000°C. A fluorescent lamp or tube works by electrically heated filaments exciting mercury vapour atoms, which then emit ultra-violet light. The light is absorbed by suitable phosphors (chemical compounds coating the inside of the glass tube) which re-emit visible white (or near-white) light. Neither the mercury vapour, nor the surrounding phosphors are at a high temperature, in fact neither are hot enough to cause a burn or even discomfort. The heating of the glass tube is almost entirely due to the hot filaments, and where the tubes are long, the centre part never feels more than just warm to the touch. The point is that it's impossible to deduce the temperature of a source simply by measuring its radiation spectrum. In the case of the incandescent lamp, the calculation would be correct; in the case of the fluorescent lamp, totally wrong.

Why is this important when considering the "greenhouse effect"? Because the absorption and emission of long-wave infra-red radiation by greenhouse gases is very much like the absorption and emission of light by the fluorescent phosphor, and the emission is not like that of a hot filament. All gases absorb and emit radiation to some degree (whatever you may read). Nitrogen comprises about 78% of the atmosphere, and absorbs/emits very weakly in the infra-red, about 5000 times less than CO2, molecule-for-molecule, but, and it's a very big but, there's about 2,000 times as much of it in the atmosphere, so why is is ignored? Oxygen absorbs/emits more strongly, and is included with ozone (O3) in the relevant IPCC diagram, a fact unknown to many.

The strongest absorbers/emitters are the multi-atomic molecules, in descending order, water vapour, methane, and CO2. I can't place ozone in the list because all references I've seen lump it in with oxygen. I'd guess it's between water vapour and methane, but of course it's a very minor component of the atmosphere. These molecules absorb long-wave infra-red photons and store the energy in their internal molecular bonds, in the form of twisting or flexing. The external, or kinetic energy of the molecule, and therefore the temperature of the gas is unchanged. When the energy is released a very short time later, the resulting photon is of the same energy and frequency as that absorbed. There is therefore no change in gas temperature during the entire process. This is therefore not a thermodynamic process, and so the Second Law doesn't apply. There is however, a finite chance that the internal energy can be transferred to another gas molecule in a collision; in that case, there is a temperature increase, though this isn't a major part of the process.

The surface emission and subsequent absorption/emission by GHGs is a "pumped" process; when the pumping stops, the process stops. The Sun is the pump input of course; it heats the surface (the atmosphere a little), the surface warms, radiates to the atmosphere, the GHGs absorb and re-radiate a portion of that, maintaining the surface temperature. Simple evidence for this is the change in temperature of the surface and atmosphere from just before sunset onwards. When the sun is high, the surface is much warmer than the atmosphere. As sunset approaches, the surface cools rapidly, and radiation from the atmosphere drops even more rapidly. Within a few hours, the surface is much cooler than the air above. In colder weather, ground frosts predominate, demonstrating the temperature inversion. Radiation and temperature measurements prove the case.

In my view, the postulated tropospheric "hot spot" is a chimera; the upper troposphere doesn't have to warm up very much as a result of the "greenhouse effect", unless there's a much higher proportion of energy transfers via collision rather than absorption/emission. I'd suggest its absence proves nothing, and that its claimed existence might indicate a misunderstanding by climatologists who proposed it. Of course, I might be wrong, something they fail to admit, claiming that it's not the hypothesis that's shaky, but the data; decades of radio-sonde measurements to a precision at least one-tenth of the size of the claimed "hot-spot" temperature increase fail to show anything remotely like it.

The Stefan-Boltzmann equation can't be used to calculate the radiation from the temperature of greenhouse gases, nor deduce their temperature from radiation measurements, because they emit in specific bands, and not over an entire Planck curve, which is necessary for the relationship to be applied. The Earth is ascribed an "effective emission temperature", calculated using the measured radiation to space, and the Stefan-Boltzmann equation. It's called "effective" because it's notional only. Neither the surface, nor the greenhouse gases which radiate, are at anything approaching that temperature. Attempts to deduce anything from that notional temperature are simply invalid. Stefan-Boltzmann is a two-body equation, right enough, but each body is a single source of radiation, radiating towards the other. The Earth/atmosphere combination is not a "single body" radiating to space.

The claim invoking the Second Law of Thermodynamics is that heat flow must be from hotter to colder, and that "a cool body cannot hear a warmer body". In my previous post I showed that the first is inevitably true, that the warmer Earth heats the cooler atmosphere, and that the second is wilful misunderstanding of the process; radiation from the cooler atmosphere merely slows the rate of transfer from the surface. I've shown here that the Second Law can't even be justifiably invoked at all.

A Simpe Solution

In Zen and the Second Law of Thermodynamics I discussed claims of the non-existence of the so-called "greenhouse effect". Some of those claims use analogies or examples to "prove" the point. Most of these are misconceived at best and erroneous at worst. Most scientists and informed non-scientists accept the basic physics. I won't say "99%" or similar because I'm aware that 87.37% of statistics are made up on the spot, and in any case I don't know what the figure might be. This is not an "appeal to consensus" - the basic physics involved is well understood and founded on fundamental physical laws.

Here's such an analogy designed to "prove" that the infrared radiation ("back radiation") from the atmosphere to the Earth's surface either doesn't exist or cannot have the claimed effect. Not surprisingly, it's from one of the many authors of "Slaying the Sky Dragon" who thinks he's illustrated "perpetual feedback":

Say you have a blackbody plate (think of an electric heater) radiating 1000 W/m² toward another plate which, because of distance, absorbs half of that intensity, i.e., 500 W/m². At equilibrium, the receiving plate thus radiates 250 W/m² toward the 1000 W/m² plate. Question: Does the 1000 W/m² plate thereby rise to 1250 W/m²? If so, then, by raising the radiator's temperature without adding more energy, you've disproved the first law of thermodynamics. Effectively, you've made the radiator heat itself. Moreover, now at 1250 W/m², the radiator will heat the other plate still more, absorb another dose of back-radiated energy, and will reach 1562 W/m². And so on, ad infinitum.

This seems to prove a feedback causing a runaway heating in the system. However, the author (Alan Siddons) is confusing an infinite geometric series (with a finite sum) to a never-ending sequence of feedback. Let's look closer at the diagram. Something is missing (par for the course in these analogies). In this case it's the radiation lost from the system, and examining that will directly give us the equilibrium conditions.

At equilibrium, the two-plate system is receiving the equivalent of 1000 W/m² via the heated plate, so the system must lose that energy to the surroundings. If the heated plate is now radiating x W/m², then x/2 W/m² is being lost to the surroundings. The receiver is absorbing x/2 W/m², so must be radiating the same amount, with half of that radiation, x/4 W/m² lost to the surroundings. We have a simple expression to solve:

x/2 + x/4 = 1000   so 3x/4=1000  and x = 1,333.3

The heater radiates 1,333.3/2 = 666.7 (actualy 666.66 recurring) to the receiver, which radiates half, or 333.3 back:

Balance is restored and no runaway heating. But where does the "extra" radiation come from, which as claimed above "violates the First Law"? It comes from the heat energy stored in the system during the equilibrium process, and the amount depends on the specific heat of heater and receiver. There is no violation of the First Law, and no violation of the Second Law either. Net flow between the two plates is from hotter to cooler, with both plates heating up until overall equilibrium is restored. Al the heat energy in the system came from the heated plate, which has some of that returned to it from the receiver. The returned heat reduces the net heat lost from the heater, so because the input remains the same, it heats up until the heat lost from the system equals the heat input.

Does the cooler receiver "heat" the hotter heated plate? No, it simply replaces some of the energy radiated (and therefore lost) from the heater, so it's the continual 1000 W/m² energy input which does the heating. Mr. Siddons has himself said "a cooler body cannot heat a hotter body, it just slows the rate of cooing". This is a perfect example - initially the heater radiates 500 W/m² to the receiver, reducing to a net 666.7 - 333.3 or 333.3 W/m² at equilibrium, and the result is a hotter radiator, radiating a total of 1333.3 W/m².

The misconception arises from only considering the instantaneous input to the system and ignoring the heat stored during the equilibrium process, a common thread in such discussions. If you intend waving a big stick, make sure you've got hold of the right end of it first.

Zen and the Second Law of Thermodynamics

The Clausius expression of the Second Law of Thermodynamics:

No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

This is unequivocal, so how does the "Greenhouse Effect" in the atmosphere raise the temperature of the Earth's surface? The atmosphere is cooler than the surface, so the flow of heat must be from the surface to the atmosphere, and so it is. Yet a number of people claim that this is proof that the "Greenhouse Effect" does not exist; "A cooler body cannot heat a warmer body" they proclaim, while in fact no-one has even suggested that this is the case. Some even go so far as to claim the so-called "back radiation" from the atmosphere to the surface doesn't exist.

Such claims have no basis whatsoever. Atmospheric longwave infrared "back radiation" has been measured, and its spectrum plotted, routinely since the 1950s. A simple web search can reveal summaries of some of the hundreds of scientific papers on the topic. It is part of the fabric of atmospheric physics. To ignore or dispute the existence of the phenomenon can only be termed denialism. However, disputing the effect(s) of this radiation in detail is another matter entirely. Such arguments can be examined for scientific logic and therefore veracity.