You may be using the term “radiation” incorrectly - radiation is a transmission of energy, like electromagnetic radiation (including visible light, X-rays, radio, gamma rays, etc). It’s not a source of energy, it’s how energy is transmitted.
I think what you meant is radioactive decay. Various types of radiation are usually produced by radioactive decay, but it’s not the same thing.
Wow. I think a brown font would have been better to describe a dying race and orange or red for hopelessness.
You’re omitting the “more atmosphere above you, raising the pressure” factor here.
No, a black font would be fine. There’s nothing but Blackness and Bleakness. Sob. Blackness and Bleakness. Black is the mood, black is the soul, and black is the Mind. Or whatever’s left of it. 
I may have spoken too soon in this last sentence. I retract it pending further research.
Wiki says otherwise. In the Timeline of the Far Future, we only have 2.3 billion years before the outer core freezes. This will shut down the magnetic field. It will be 7 billion years before the Sun expands sufficiently to consume the Earth. Not that it will really matter because the Earth can only support us for 600-800 million years or so due to the gradual brightening of the sun.
Yeah, but that’s a quibble. Wiki still supports watchwolf49’s conclusion that it’s OK for Leo to buy unripe bananas. He’ll have plenty of time to eat them before anything too bad happens. 
Right, 600-800 million years to be boiled off … 2.3 billion before the magnetic field weakens … less than 7 billion years before the planet is consumed by the surface of the sun … assuming the universe doesn’t wink out of existence before then … I think it’s safe to plant banana trees right now …
minor nitpick: I am not a comedian or a poet (IANACOAP), but the phrase should really be “green bananas”, as in “Don’t buy any green bananas!”. “Green bananas” is funnier, and “unripe bananas” is just clunky.
I’ll also point out that if Leo does survive to the time when the core cools and the magnetosphere fails, he’ll surely have “one foot in the grave and the other on a banana peel”.
What a droll fruit! Given the lack of genetic diversity of bananas and the state of politics lately, I fear humor will die out long before we lose our oil-laden brain-rotting bottom-heated atmosphere to the solar wind.
Boy- now I have to critique myself! That would’ve been funnier (I think!) if I’d quoted the right posts!
Some Googling suggests that this is a secondary effect - the principal one is the increase in air pressure with depth.
Here’s the Wiki article on the TauTona gold mine west of Johannesburg. It’s 3.5 km deep, at which depth the unconditioned air temperature is 55 C (131 F).
The adiabatic lapse rate is 9.8 C per 1000 meters, which means the temperature at a depth of 3.5 km should be 34.3 C higher than at the surface. Thus, with a surface temperature of 20.7 C (70 F) we could account for the mine’s elevated temperature entirely by the increase in air pressure.
It’s clear that this is not the only effect. The linked article says the rock face temperature is 60 C - 5 degrees higher than the air temperature.
An interesting suggestion … although the dry adiabatic lapse rate assumes there’s no thermodynamics going on … like dry air in the troposphere …
However, when we put air in a 60ºC container, it won’t matter the pressure, the air will become 60ºC rather quickly, like in the bottom of a mine shaft … also, we’re still absorbing the infrared portion of the solar radiation in the stratosphere, so here dry air will be increasing temperature with decreasing pressure …
Of course the dry adiabatic lapse rate has some effect … but I do believe the 60ºC walls have the far greater effect … plus I’m not sure about your 20ºC surface temperature that makes the math work out so nicely … I can’t say anything about the normal temps at 26ºS latitude in South Africa … but at 26ºN latitude in Mexico, 20ºC would be a chilly day indeed …
“They have it figured out”? Whomever “they” are you should probably reconsider listening to them.
“Oil in the atmosphere” … that’s a new one on me … hydrocarbons quickly oxidize in air … oxygen is nasty stuff …
This I know, which I made clear (honest!) in the post you are responding to. But I still do not know the answer to more urgent question, even though a correct-within-given-definition-of-Leo-lifetime answer was given:
What is the relative amount of potassium and its subsequent decay rate in ripe vs unripe bananas?
Awww … yes … there’s a few species of radionuclides that form in the upper parts of the atmosphere … potassium, oxygen, carbon … however I’m not sure enough of these are being sequestered in the mantel or core areas, and then decaying releasing that energy into the Earth … my point here is that any energy we do find in the Earth due to radioactive decay would be from decay that has already happened … any decay that is yet to happen would have no effect on the current energy level … and that most of the species have a half life shorter than 5 or 6 billion years, most of the decay that could happen has already happened …
I am glad I changed that to bananas at the last second … or I’d really be in trouble …
The adiabatic lapse rate is relevant only when you have a parcel of air that is changing altitude: it cools as it ascends because it is performing mechanical work on the rest of the atmosphere as it expands, or it warms as it descends because the atmosphere is performing mechanical work to compress it. If the air stagnates at the bottom of the mine, there is no mechanical work being done, so the only remaining temperature driver is the temperature of the rocks down there.
It would be counterproductive to simply ventilate the mine by forcing air from the surface down to the depths, since it would heat up on the way down. Instead, they employ air conditioning equipment to control temperature at the bottom of the mine. My guess is that there’s a refrigeration system on the surface that chills water/glycol that then gets pumped down to the depths for cooling. Liquids are pretty much incompressible, and so are not subject to the lapse rate in the same way that air is.
This is part of it, and would probably be all of it if the observer were on top of a tall, skinny tower poking up to high altitude without actually redirecting the ambient wind.
But the thing about mountains and mountain ranges is that they force air parcels to climb to go up over them, inducing adiabatic lapse - or vice versa, cold air that crosses a mountain range descends into a valley, warming as it descends simply because it’s being compressed. This is why the rim of the grand canyon can be balmy, while the bottom is sweltering, even on a day when both areas are receiving the same insolation. A similar situation exists when one drives from Boulder, CO (elevation 5400’) just a few miles west to Nederland (elevation 8200’). Nederland doesn’t sit on a mountain top piercing the sky, either; it’s in the Rockies, sure, but the sky-piercing peaks are all around it. And yet it’s generally a good bit cooler than Boulder.
In this time lapse video, you can see from the motion of the wisps of cloud that the air is moving down off of the mountain. But the cloud itself stays glued to the mountain top: as its leading edge moves downslope, the adiabatic temperature increase causes the condensed water droplets to evaporate, making the cloud disappear.
The principal “background” variation in temperature with altitude/elevation is not due to adiabatic processes. Although as you say mountainous terrain does cause parcels of air to rise and fall adiabatically and to change in temperature accordingly, the “background” variation in temperature with altitude is called the Environmental Lapse Rate (ELR). The ELR in the standard atmosphere (approximate average global conditions) is about -2°C (-3.5°F) per 1000 feet. As discussed above, the ELR is due to the fact that the atmosphere does not absorb much of the sun’s radiation, so most of the heat energy is added to the atmosphere from below.
Based on the average ELR, you’d expect the bottom of the Grand Canyon at 5000’ lower to be 15-20°F warmer, which is just what you find. This fundamental background variation in temperature with altitude is not attributable to an adiabatic process of air rising or falling.
I think we’re in agreement that both phenomena exist:
[ul][li]solar heat is added to the atmosphere primarily at ground level, which is why the air gets colder as you move straight up through open air;[/li]
[*]adiabatic lapse explains why ground level at high elevations tends to be colder than ground level at low elevations.[/ul] In the case of the Grand Canyon, the rim is not simply 5000 feet straight up in open air; there is ground at the rim, collecting heat and locally warming the air at the same rate as the ground at the floor of the canyon. In the absence of any air movement (which would induce adiabatic lapse), shouldn’t we then expect approximately the same ground-level temperature at the rim as is observed at ground level on the canyon floor?