If two bodies have
the same average kinetic energy of their atoms, the will have the same temperature no matter how large [i.e. how much mass] the bodies are.
A mercury thermometer is going to register the same reading for a highly radiative gas like CO2 as it is for a barely radiative gas like N2 when they have
the same average kinetic energy in the molecules.
Molecules of one mass don't have
the same average kinetic energy as more massive or less massive molecules.
In equilibrium, molecules of one mass have
the same average kinetic energy as molecules of a different mass.
If those two containers have the same temperature, they have
the same average kinetic energy per particle (for a monatomic gas).
Over a sufficiently long period of time, it follows from the equipartition theorem and other principles of statistical mechanics that every molecule in a gas will have
the same average kinetic energy, the same average potential energy, and the same total energy, as any other molecule.
Not exact matches
As implausible as it might seem at first, the
average kinetic energy of the molecules that make it 17 km will be the
same as the
average KE of the molecules at the bottom.
On
average, just as many molecules move up, with exactly the
same velocity /
kinetic energy profile, as move down, with zero
energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the
same temperature.
That's not necessarily the
same kinetic energy as any individual molecule will have at any given time — it's the
average that's the temperature.
What's stated is that eventually the
average kinetic energy (the temperature) of all molecules will be the
same throughout the gas.
He appears to think it's fine that molecules in the upper shell have more total
energy, on
average, than molecules in the lower shell so long as
average kinetic energy is the
same.
This is something that you have denied was possible on the ground that (allegedly) a gas can't have a lower density, the
same average molecular
kinetic energy, and yet the
same temperature.
Within each region of the atmosphere that contains CO2, and within each region of the Earth surface, some molecules have above
average kinetic energy and some have below
average kinetic energy; the temps of the regions are proportional to the means of the
kinetic energies in those regions, but the molecules are not all the
same.