It’s a little disappointing to hear that teachers are still breaking out the old “heat rises” saw. You don’t say what grade your friend teaches, but the kids are probably old enough to understand the concept that warm air is less dense than cooler air at comparable pressures. And that, rather than a misleading two-word adage, could definitely lead to an interesting class discussion about why it gets colder at high elevations.
I think she said 5th. Yeah, that’s probably old enough for a more involved discussion.
Heat doesn’t “rise”. Gravity pulls the heavier, denser cold air down which forces the lighter, less dense warmer air up. If that air becomes colder and heavier, it will be drawn down and replace relatively warmer, less dense air below it.
The natural state of everything would be absolute zero (0 Kelvin, −273.15° Celsius, −459.67° Fahrenheit) if “something” didn’t transfer it’s heat to “something” else.
Compressing molecules of air in a bicycle pump raises their tempurature which transfers heat to the cylinder of an air pump. The friction between the shaft/piston seal and the cylinder wall also warm the air. The heat is transfered to the air surrounding the cylinder. The heat is also transfered to your hand if you touch the cylinder.
The Earth has a molten core. The deeper you dig (100’s of feet, not in your garden) the warmer it gets. The sun’s radiation transfers heat as it strikes the planet or passes thru it.
Expansion of molecules creates a cooling effect. Moving air is cooler than stationary air.
So why is it colder in the mountains? The air is thinner, which is cooler. The mountain mass retained less heat, which is cooler. The wind is generally blowing (moving) which is cooler. Less direct sunlight reaches the mountain’s sides, so one side may be much cooler while the other side is much warmer.
But the bottomline is that everything is headed for absolute zero unless there is something that transfers heat to it. So the question should be - What is available in a mountainous region that could transfer heat?
“Heat” does not rise. Warm air may rise, heat goes where the laws of thermodynamics tell it to go (paraphrasing from memory).
Don’t ever tell your professor that “heat” rises. You may get this…in class…in front of everyone.
5.5 degrees F per 1000 ft. is the dry adiabatic lapse rate, by the way. If you’re in average air (meaning average amount of moisture present) the lapse rate is around 3.5 degrees per 1000 ft. This is the lapse rate used by aviation to approximate temperatures aloft.
So in your example the temperature on the top of the mountain would be more like 48 degrees F.
I’m skeptical that adiabatic expansion has anything to do with the answer. If you had a 20 mile tall insulated room, and let the temperature in it come to equilibrium, the air throughout the room will be at the same temperature, not colder at the top. Otherwise, you could have a tube with a vacuum in it going from the bottom to the top, and radiation would take energy from the warm bottom to the cold top. You’d be able to use this flow of energy to do work, making a perpetual motion machine.
Space is cold, and the Earth is warm, and outlierrn’s “simplified” explanation is pretty accurate.
The DALR (dry adiabatic lapse rate) applies until the air is fully saturated (i.e. reaches its dewpoint - 100 % RH). Here’s an article that explains this.
It’s fair to note that the altitude at which the dewpoint is reached (i.e. the height of cloudbase) may well be below the tops of decent sized mountains.
I thought it’s because air doesn’t absorb sunlight, the ground does. The ground heats the air. The air nearest the ground is the warmest.
The adiabatic lapse rate is a bad example because it refers to a temperature change of a parcel of air as it rises or sinks. While following the parcel up into the mountains gives us a story that is related to the atmosphere, it’s not why the atmosphere is cooler up there to begin with.
The environmental lapse rate (ELR) of 3.56F per 1,000ft describes the temperature gradient through the first 39000 ft of the atmosphere and would be a better description, but it’s still just a description of how things are and doesn’t tell us why.
The “why” has already been said. The air in the mountains is thinner because the air in the atmosphere presses down on itself and accumulates at the bottom. More air at the bottom means denser air which means more molecules bouncing into each other which means more energy which means higher temperature. Thinner air in the mountains means less dense air which means which means less molecules bouncing into each other which means less energy which means lower temperature.
Ground heat can play a role, as can other factors, but there would still be an ELR without ground heat due solely to the pressure gradient.
And it’s that pressure gradient that’s responsible for the fact that air cools as it rises.
No, for the reasons I gave in my last post.
Of course. With the quiescent air in that scenario, there’s no particular reason the temperatures would differ anywhere in the enclosure. But if you add in some vertically-oriented fans to force the air to circulate between altitudes (mimicking naturally occuring winds that drive air masses across mountain ranges, or the vertical circulation that occurs in thermal updrafts/downdrafts), you will develop a temperature differential between higher and lower regions inside your giant room. Given that the pressure at the top of your room is lower than at the bottom (as it must be, since gravity is in effect), thermodynamics says this must happen: as air from the top is driven downward by the fans, it will increase in temperature, even in the absence of heat transfer - and as air from the bottom is driven upward by the fans, it will likewise decrease in temperature.
In the real world, an external energy source (the sun) is responsible for the prevailing winds that move air masses around; in your 20-mile-tall room, externally-powered fans are responsible for moving the air around and producing those temp differences. If your heat engine is truly capable of providing mechanical work when exposed to hot/cold sinks, then it would work in the real world, where there definitely is a temperature difference between 0 and 20 miles of altitude; clearly this is not perpetual motion.
First sentence is correct, but the rest is not. Temperature is a manifestation of the per-molecule average energy level. If two air masses each have the same per-molecule energy level, then they have the same temperature, regardless of any difference in density. Take a sea-level mass of air at 70 degrees, an an Everest-level mass of air also at 70 degrees, and put them in contact with each other across a thin-but-sturdy membrane that maintains the pressure differential: there will be no heat transfer between the two air masses.
No, for the reasons I gave in my last post, you won’t get temperature equilibrium. Temperature is a measure of energy and there will be more energy where there are more molecules.
I don’t understand the part about the vacuum tube. If there’s nothing inside it, it won’t warm up or cool down, how are you taking advantage of the high and low temperature difference? You could put a fluid in it and open the top and the air would be drawn up toward the lower pressure, but gravity pulls it back down and it ends up stabilizing in what is called hydrostatic equilibrium.
That is not correct. Temperature is related to the average kinetic energy of the molecules. The overall density of the molecules does not matter. It is possible to have a not-dense gas that is very hot.
This is the key point that all the other explanations skipped over. The sun heats the ground and the ground heats the air. This in itself is the main reason why the air is cooler higher up.
It’s also true that the equilibrium temperature gradient will approximately equal the lapse rate associated with the reduction in pressure of a rising parcel of air.
You are right - adiabatic expansion does not cause the temperature gradient. But if you heat the floor of the room, the temperature gradient in the column (up to some mixing height) will be determined by adiabatic expansion.
The existence of temperature inversions in the stratosphere and thermosphere must be taken into account. I think the stratospheric inversion is explained by the higher absorptivity of the ozone molecules that are found within the eponymous layer to UV radiation and the thermosphere inversion is somehow related to the ionosphere and its interaction with the higher frequency (x-ray and gamma-ray) radiation, as well as matter (as opposed to radiation).
I have a very vague hunch that in Mars, for instance, a planet which has no oxygen and hence no ozone in its atmosphere, as well as no magnetosphere/ionosphere, there should be no temperature inversions; please correct me if I’m wrong…I’ll check myself later on. =)
For a given latitude, high-altitude locales receive just as much insolation as low-altitude locales - yet they are typically colder. Lhasa, Tibet is at about the same latitude as San Antonio, Texas, but it’s at 11,000 feet, whereas SA is at about 650 feet. Lhasa has summertime highs in the low 70’s, SA in the mid-90’s.
Why is Lhasa cooler?
The same reason it’s colder in winter. Sunlight falling on the ground at angle heats less than falling perpendicularly.