No.,Short answer- the two coils are of different temperatures and so radiating at different frequencies and wavelengths. The cooler coil will accept the radiation of the warmer coil but not vice versa.
Yeah, that's what I thought you would say. Well, as a physics professor I can tell you that you are dead wrong about that. There is nothing that will, or can, prevent the warmer coil from absorbing radiation from the cooler one. Exactly how much they absorb depends on their absorptivity at the frequencies in question, but those frequencies don't change that much from 600 C to 700 C. For galvanized iron the absorptivity is about 0.9. So the two coils will absorb roughly the same proportion of the radiation incident on them, i.e. all but about 10%.
The reason the 2nd law isn't violated is that the energy radiated at any frequency increases very rapidly with temperature. Because of that, the warmer coil emits a lot more energy than the cooler coil. So the cooler coil will receive much more energy from the warmer one than the warmer one receives from the cooler, and the net flow of heat will be from warmer to cooler.
If you don't accept that, write another physics professor at a major university and ask them the same question. See what they say. Heck, write Judith Curry or Richard Lindzen. If they don't tell you essentially the same thing I did, I'll send you a case of beer.
Seriously, if you are going to question the greenhouse theory on *physical* grounds, make sure you have the physics right. Otherwise, you're only going to look like a fool.
If the Earth is receiving constant radiation from the sun, and then recieves and absorbs additional radiation from another source ( back radiation from GHG) then the surface temperature must rise. The additional radiation would not slow the cooling but it must raise the temperature. This is why the back radiation would act like a perpetual motion machine of the second kind. This just doesn't occur in nature.
No, you're forgetting that the surface is also radiating, and therefore losing heat that way, as well as by conduction, convection, and evaporation. The temperature won't rise unless it absorbs heat energy at a greater rate than it loses it. That's why we talk about the "heat budget".
But I can see why you think of this as a perpetual motion machine and as a feedback mechanism, because if it worked that way, the temperature would run away and the extra heat energy produced that way could be used to drive a heat engine. It doesn't, because when GHGs are increased, the temperature only rises until the net outflow again balances the net inflow.
There are three thoughts on the Greenhouse theory- 1 the theory is real and accounts for 33C of temp, 2 the theory is real but the effect is negligible, 3 the effect doesn't exist.
I don't think there is a middle ground. If the effect accounts for 33C, then the effect is huge. Any significant increase in CO2 levels should have profound effects. CO2 levels have increased about 40% since pre industrial. But all we have seen are normal temperature variations, with temp sometimes behaving contrary to the theory. A lot of other things haven't happened according to theory also.
The effect accounts (according to theory) for most (at least) of the 33C but it's not all due to CO2 alone. A *lot* of that 33 degrees is due to the effect of water vapor. Without CO2 though, the temperature would be so low that there wouldn't be enough water vapor in the atmosphere to make a difference.
You're right that a lot of things haven't happened according to "theory", but that theory is a simulation model run on a computer that isn't based on just the greenhouse theory, but the greenhouse theory combined with a ton of assumptions and simplifications to make the computations feasible. The models are tuned to hindcast the recent climate history, which only works if the recent climate is representative of the real long-term climate with all its natural variability once all the external forcings like variations in the solar constant are accounted for.
Curry's blog has a lot of good discussion about the models and the reasons why they're unreliable. I think a lot of what she says is plausible - without knowing the magnitude or time scale of "internal" climate variability, we really have no way of determining how much, if any, of the recent warming is due to manmade CO2.
There is also the fact that it takes time for the surface temperature to "catch up" with increases in GHGs, due to the heat being sequestered in the ocean. How long? That paper I linked to on the end Pleistocene transition suggests the time could be in the hundreds of years. I don't think we have a good idea of the difference in timescale between what they call "transient climate response" and when the equilibrium is reached.