From Forbes, replying to the question "If Heat Rises, Why Is It So Cold In The Mountains?":
Gas also get cooler as its pressure drops, which it does as it rises up where there is less air pressing down on it. So when warm air rises, it cools off. That’s pretty significant here.
But there’s an even more important force at work: Earth radiates heat (infrared light) into space. Down near sea level, heat from the sun hits the ground and is trapped under 100 km (at least) of insulating air and clouds that intercept escaping heat and re-radiate it back toward the ground. The higher up you go, however, the less any of this can happen. Above a certain level, the atmosphere loses heat to space faster than is can be warmed either directly (by sunlight) or indirectly (from the ground) so it gets colder and colder.
Up to a point.
The first sentence over-simplifies to the point of being totally wrong. The effect of reducing density by half and pressure by three-quarters (i.e. at 10 km up) would be to cool some air which has risen from the ground to about negative 100 C (if I understand this correctly). What actually happens is sunlight hits the ground and warms it up; this warms the air; warmer air is less dense so it rises; energy cannot be created or destroyed, so thermal energy is converted to potential energy. That's how the lapse rate formula is derived, then you adjust it for latent heat of evaporation/condensation = 6.5 degrees per km altitude. The effect of lower pressure/expansion neatly cancels out; higher up, it requires less work to rise further.
Air, being mainly NO2 and O2 doesn't emit much radiation. Neither does CO2, for that matter, it just absorbs 5.14% of infra red and warms up slightly and then warms up the 2,499 air molecules around it (see footnote). So the first assumption must that the atmosphere would warm to the same temperature as the surface. If you assume no atmosphere (like on the Moon), you can calculate the likely temperature of the surface quite easily and accurately, based purely on incoming sunlight = effective temperature +/- adjustments.
So our first assumption is that earth's atmosphere would be 255K (the effective temperature of Earth's surface based on incoming sunlight alone). And its average temperature is indeed about 255K, but then you have to adjust for the lapse rate, so it's 33 degrees warmer at the surface - and 33 degrees colder at the top of the troposphere, approx. 10 km up.
The second paragraph is pure Alarmism (see footnotes).
The final sentence is a nod to the fact that the greenhouse effect does NOT explain why it is so cold on mountains. If you look at the temperatures at the top of mountains which halfway up the troposphere (5km to 6km height), the temperature is what you'd expect based on incoming sunlight alone, you can cheerfully ignore all the air, of which there is still a heck of a lot (nearly half by mass). If the greenhouse effect existed, it would be warmer than that.
But let's climb further, to the top of Mount Everest, near the top of the troposphere. Its effective and actual temperature would also be 255K (assuming no atmosphere) but its actual temperature is a darn sight colder than that. According to the greenhouse 'trapping' effect, its temperature would be at least 255K, plus a smidge for the greenhouse effect of the small amount of air above it (about 25% by mass). In actual fact, there appears to be a negative greenhouse effect. Which can't exist, by definition.
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Footnote - first the article says radiation energy is 'trapped' (plausible) and then they say it is re-radiated. Which one is it? It can't be both.
The Alarmists like to do demonstrations where they fill a tube with CO2, place a heat source at one end and measure the amount of radiation that gets through to the other end - it's very little, which indicates 'trapping'. If it were re-radiating, then at least half would get through. So 'trapping' seems more plausible and CO2 absorbs 5.14% of the radiation from the surface and warms up a smidge, that warms up the air around it by 1/2,500 of a smidge, which is a small number, certainly less than one degree. And the gravito-thermal effect greatly outweighs this at the top of Mount Everest.
Then there's this: "Above a certain level, the atmosphere loses heat to space faster than is can be warmed either directly (by sunlight) or indirectly (from the ground) so it gets colder and colder."
Nope. The atmosphere doesn't lose thermal energy to space. The only way it could do is to emit radiation, which it doesn't (to any great extent). The point is, the air up there was never that warm in the first place - see explanation of lapse rate.
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