Author : D J Cotton
Well here's a summary then WIlliam ...
The Second Law of Thermodynamics never mentions thermal equilibrium or heat transfers from hot to cold. It is all about evolving towards thermodynamic equilibrium which is quite a different thing, involving mechanical equilibrium as well, and thus gravitational potential energy.
The Maxwell-Boltzmann distribution is derived theoretically for a non-gravitational field. Hence it is not strictly correct when a state of thermodynamic equilibrium (or close to such) exists and you are considering molecules at different altitudes, although it will apply in any horizontal plane.
It is a red herring to postulate a gas that does not absorb any solar radiation and re-emit it. If such an atmosphere did exist it would still exhibit a thermal gradient but, by the assumption made, it would be just as if it weren't there at all as far as radiation is concerned. Of course if it got too cold near the top, some would solidify and collapse.
It is energy from the Sun (mostly absorbed in the atmosphere) which heats the surface of Venus, for example, and actually raises its temperature from about 732K to 737K during the course of its 4-month-long daytime. But the whole temperature profile in the troposphere has to rise 5 degrees also for this surface warming to happen, and then indeed the surface is warmed by conduction from the base of the troposphere.
All planetary temperatures in tropospheres and even beneath any surface are determined by the gravito-thermal effect, and they have nothing to do with any greenhouse radiative forcing or sensitivity to carbon dioxide.
When they drilled the KTB borehole down to 9Km depth in Germany they were surprised at how much water they found underground. This then helps confirm that the gravito-thermal effect is also apparent in solids and liquids. At 9Km depth it was 270C, far hotter than they expected, with a thermal gradient in the outer crust at least 20 times as steep as the mean gradient to the centre of the core. That's because specific heat increases very significantly with the hotter temperatures in the mantle and core.
If you plotted just the temperatures between, say, 9Km and 4Km you would find that the near linear plot extrapolates quite well to the actual mean minimum daily temperatures at the surface.
Why is it so?