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.