The other night I was hanging out with a grade-school science teacher. She was talking about how she told her students that heat rises. One of her students objected. He, being from Bolivia, observed that it’s much colder in the mountains. The teacher said that was a very good observation, and that she and the class should endeavor to answer it.
She never did say what they came up with.
So, if heat rises, why is it so cold in the mountains?
Adiabatic cooling is one reason. Air that rises will cool down due to the drop in pressure. So if cool air is blown up there via wind or other processes then it will become even cooler.
Isn’t the air thinner and drier in the mountains? Perhaps it can’t hold heat as well as in the valleys. I live in the Rocky Mountains at 3,500 feet and as soon as the sun goes down the air temperature drops dramatically.
This is what I’ve always understood as well.
Thinner air can’t hold the heat. You can get one hell of a sunburn though.
“If heat rises, Heaven might be hotter than Hell.” - Stephen Wright
More specifically: if air is allowed to expand, it does mechanical work that extracts energy from it (as opposed to heat transfer, which extracts thermal energy from it). So as warm air at low altitudes is forced by prevailing winds to move upslope, it experiences a decrease in pressure, expands, and cools.
Suppose you have air at sea level, 14.7 psi, 70 degrees F, and the wind carries it up the slope of a mountain to an elevation of 10,000 feet, where ambient pressure is 10.2 psi. The equation for adiabatic expansion (with temps on an absolute scale, in this case Rankine) is:
P[sub]1[/sub][sup]-0.4[/sup] * T[sub]1[/sub][sup]1.4[/sup] = P[sub]2[/sub][sup]-0.4[/sup] * T[sub]2[/sub][sup]1.4[/sup]
14.7[sup]-0.4[/sup] * 529[sup]1.4[/sup] = 10.5[sup]-0.4[/sup] * T[sub]2[/sub][sup]1.4[/sup]
T[sub]2[/sub] = 22 F
So that 70F sea-level air you just shoved up to 10,000 feet is now at 22 degrees F. That’s without transferring any heat to or from it. Beyond that, it’s influenced substantially by local climate. In mid-summer, places like the summit of Pikes Peak (14,000+ feet) and Trail Ridge Road (12,000+ feet) through Rocky Mountain National Park are typically in the 40’s and 50’s.
Hot air only rises if it is warmer than a body of air surrounding it. So a hot air balloon will rise in cooler air, or a body of air heated over a warmed area of land or sea will rise, so long as it is small relative to the extend of air around it. But if you have a very extended body of air, there is nothing to rise inside of. As noted above, even a body of hot air rising will expand as it rises, and the pressure drops, and will eventually stop rising. Large bodies of rising air are basically what makes weather. But you don’t get an en-mass rising of the entire atmosphere, rather parts of it that are heated relative to their surrounds rise, and then cool off and fall down. Add in a bit of Coriolis force magic and you have your basic low and high pressure systems and the main weather mechanisms. If you are in a heated bit of moving air, well the hot air does rise to heat you. But you are as likely to be in a bit of falling cool air that will cool you. That is weather for you. (Coriolis force turns the rising and falling air into mostly horizontal movements, but the basic idea remains.)
Interestingly, the temperature does not continue to drop the higher you go. Above about 80,000 feet it starts to rise again. Not that there is a lot of air up there to appreciate this with, but rise it does,
Is this why bicycle pumps get hot?
I believe that’s just a function of friction
Air compression does produce heat, this how a Diesel engine works. it compresses the air fuel mixture to a point where it is hot enough to self ignite.
Bike pumps do have a significant amount of friction that produces heat but part is from the compression of air.
Air compression, mostly. See fire piston.
A related (sort of) question: Why is it that when you use compressed air to clean your keyboard, the can becomes too cold to hold onto?
The can contains liquid which boils away to produce the vapor that squirts out of the nozzle. In any body of liquid or gas that seems to be at a single temperature, the molecules actually exist at a range of individual kinetic energies; the average energy level manifests itself as the bulk temperature of the fluid that you can feel. So when you squeeze the trigger on the can, here’s what happens:
-vapor escapes from the can
-the pressure inside the can drops
-the hotter molecules of liquid become vapor, leaving the colder molecules of liquid remaining in liquid form
Since the hottest liquid molecules are transformed into vapor and get shot out of the can, the average energy level of the liquid drops, leaving you with an icy cold can.
The heat is almost entirely due to adiabatic compression. Run through the equation in my previous post for ambient air compressed to 90 psi gauge (104.7 psi absolute), and you find that the outlet temperature is near 470F. Your hand-operated bicycle pump doesn’t get terribly hot because it’s pissing away some of that heat to atmosphere; you give it time to do so because you’re pretty slow when the pressure gets that high. But if you’ve got a motorized air compressor, you’ll find that the outlet tube leading from the pump to the tank does indeed get screamin’ hot (capable of third-degree burns if you sustain contact with it) when it’s operating at high pressure.
Because (as Ludovic noted in post #2), by the time warm air has risen to mountain altitudes, its density - and thus its temperature - have decreased significantly. The decrease is 5.5 degrees F per 1000 ft (= 10 degrees C per kilometer) - so you’d expect air that started at, say, 80F at 1000’ to be below freezing at the top of a 10,000’ mountain.
As others have indicated, “heat rises” is not particularly accurate. Fluid that is less dense rises, and gases (including air) become less dense as they are heated, so a parcel of heated air can reach a density less than that of the surrounding air, and consequently rise.
While Machine Elfs answer is certainly more precise, I would tell a grade schooler that the air is like a blanket and the mountains are mostly above it.
This is related to what I came to mention. Air and haze block radiation, and the air at high altitudes is thin and seldom hazy. During the day that can make for vicious sunburn issues at high altitude. At night it means the ground cools quickly, which cools the air around it. Thus the temperature starts out a lot cooler in the morning, so it doesn’t get as hot during the day. But it still gets plenty hot, relatively hotter than most sea level locations. That is to say the ground temperature increases much more than the normal atmospheric temperature for that altitude. This makes for strong convective activity, and can make for spectacular soaring and impressive thunderstorms.
And this is why I was in college before I started thinking of teachers and classrooms as a place to learn. Even in high school, the priority was still to dumb things down and end the conversation before we had to deal with anything that might be challenging to anyone. If I wanted to learn anything real, I had to hit the library at lunch and read through class.
Kids can handle it, you know. I wouldn’t throw the algebra at grade-schoolers… but you could program a web-based calculator that would let them input values and see how the results change - the way Machine Elf gave us all a simple example of 70 F cooling to 22 F by 10,000 feet. Adiabatic heating and cooling can be demonstrated in a classroom setting to back up the math. The connection between heat gain/loss and work done in expanding/contracting can be explained to grade-schoolers.
Will there be much left to learn in high school and college? Sure. But we don’t have to give them an answer that’s not true to tide them over until they’re “ready.”
I’m fine with simplifying answers for little kids - “when air rises a great distance, it expands and cools” - but outright lies do them a disservice. A lot of kids won’t take physics in high school or thermodynamics in college; when those kids reach adulthood, I would rather they remember “when air rises a great distance…” than “air is like a blanket…”.
You guys lost me, I thought atmospheric density had a direct effect on how quickly the earths surface cools.