Naked Science Forum
General Science => Question of the Week => Topic started by: Sally Le Page on 06/07/2021 09:47:04
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Wayne sent us this question:
"We've always learned that heat rises. Why is it usually colder in the mountains? Shouldn't their higher elevation make them warmer?"
What do you think?
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Air temperature in the Troposphere( the lowest atmospheric layer), is driven by being heated by the ground, which was, in turn heated by the Sun. Higher altitudes, being further from the ground are heated less by this effect. Now while it is true that air near a mountain is close to the ground of the Mountain, that air is always being mixed with air that comes from the much larger regions where air at that altitude is much further from the ground.
As far as heat rising goes. Yes, warmer air, in general, will rise in colder air, But in doing so, it has to climb against gravity, and it can't do this for free, it has to give up some of its heat energy in doing so. So even warm air rising from the surface will not be as warm at altitude as it was near sea level.
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Temperature is a measure of how fast the molecules are moving.
If you throw a ball up in the air, it slows down as it gets higher.
The same thing happens to air molecules.
They bounce off eachother and the ground etc so they don't all fallout of the sky but the idea is essentially the same, if they go up, they gain gravitational energy at the expense of kinetic energy.
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As air rises, it expands, due to lower pressure. As it expands, it cools (even if it expands horizontally, with no increase in height).
Query: How much of this cooling is due to the expansion, and how much due to "climbing against Earth's gravity"?
- I would expect that the gravitational effect would be small, since every cubic meter of air that rises from ground level is replaced by another cubic meter of very similar density, so it doesn't require a lot of energy to lift air to the troposphere (not like climbing a mountain, or firing a cannon shell into the troposphere, where you do lose a lot of energy on the way up...)
- However, atoms/molecules of a gas are attracted to each other by inter-molecular forces. It takes work to increase the average distance between these particles, and this energy comes from their speed. So expanding gases cool. If a cubic meter of air rises and becomes 1 cubic meters, it will cool down.
So which has the bigger effect on air being cooler at the top of mountains: Climbing against gravity, or expanding against inter-molecular forces?
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Solar radiation transfers very little heat directly to the atmosphere below 40,000 ft. Heating is caused mainly by conduction and re-radiation from the solid (or liquid) surface to the lowest layer of air, which expands and rises in smooth convection or as "thermals" - discrete vortices formed where there is more significant surface contrast.
The ambient pressure decreases with height (there being less weight of air above) so each parcel of rising hot air expands, pushing the ambient air aside as it does so. The work done in displacing the ambient air comes from the kinetic (heat) energy of the parcel, which cools as a result. The rate of cooling with altitude is termed "lapse rate", generally around 3 deg C per 1000 ft depending on the moisture content.
Above 40,000 ft (way higher than any mountain) the solar radiation input exceeds the lapse rate and the temperature of the stratosphere actually increases with altitude. The inversion of the temperature gradient means that there is very little convective activity around 40,000 ft, so jet travel is generally more comfortable than in propellor-driven aircraft at 15 - 20,000 ft.
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You asked and we answered on our show! You can listen to what atmospheric physicist Simon Clark had to say here:
https://www.thenakedscientists.com/podcasts/question-week/if-heat-rises-why-it-colder-mountains
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Hi all.
So BC
Temperature is a measure of how fast the molecules are moving.
If you throw a ball up in the air, it slows down as it gets higher.
The same thing happens to air molecules.
They bounce off eachother and the ground etc so they don't all fallout of the sky but the idea is essentially the same, if they go up, they gain gravitational energy at the expense of kinetic energy.
So maybe the bold highlighted part isn't quite right. maybe it should be;
they gain gravitational energy because they have an increase in kinetic energy, by displacement due to convection !
this occurs due to an change in density in an non inertial reference frame.
momentum is also created in the atmosphere in this process.