Comment on If hot air rises, why is it colder at the top of a mountain?
lurker2718@lemmings.world 2 months agoWhile I agree in general, one point is a bit to simplified in my opinion
In other words, there are fewer air molecules per cubic foot (volume of air). The molecules are farther apart and can hold less heat energy. Because “heat” is what we say when we mean molecules are moving around.
Less molecules mean less heat, it has nothing to do with the temperature, if you just decrease the density by removing half the molecules, you have the same temperature.
It cools down because it expands adiabatically. Consider a very thin balloon filled with air which is warmer than the surrounding. This now rises up, but as it does, the pressure decreases, causing the balloon to expand. During this expansion, the balloon transfers energy away from itself, because it has to push away air, to make room for expanding in the surrounding. This work cools the air inside the balloon. Assuming the air inside is dry, it would cool around 10 °C per km it rises. Now if you think about it, the balloon just stopped the inside from mixing with the outside. If you look at a large “piece” of air, it does not mix very fast, so you can remove the balloon and just consider what happens with warm air heated from the ground.
Now this does not mean, it has to be cooler when higher up. The same points hold, inside a house, but there it is often warmer when higher.
The best explaination is when looking where the heat comes from and goes too from the air. The atmosphere is mostly heated from the surface of earth, so the bottom and cooled from the upper layers. So naturally it gets hotter where it is heated. The question is now by how much? There are three modes of heat transfer in the atmosphere: radiation, conduction and convection. The first two are very slow. Connection is fast but has limits. Consider the piece of air, if it rises, it cools. So at some place it may be the same temperature as the surrounding air, so it stops rising. This means the convection works only when the air gets cooler by 10 °C/km going up (~6.5°C when the air is moist and precipation happens). So this temperature gradient is observable very often.
Turun@feddit.de 2 months ago
But does the energy to expand the balloon not just come from the pressure? Pressure has units of energy per volume btw.
lurker2718@lemmings.world 2 months ago
I think it is actually the other way around. You can consider the air inside the balloon to have internal energy from the heat. And additionally you have to make room for the balloon in the atmosphere, so you have removed the atmosphere from the volume the balloon takes, which also needs energy. If you consider both you arrive at the concept of enthalpy (H = U + pV), which is very useful for reactions in the atmosphere as pressure is constant. For this example it is not that useful as outside pressure changes when the balloon rises.
Another way to see it, the pressure has no “real” energy. In a ideal gas, the only energy comes from the kinetic or movement energy of the atoms. Each time a gas molecule is hits the balloon envelope it transfers some momentum. The cumulative effect of the constant collisions is the pressure of the gas. If the balloon is now expanding slowly, each collisions also tranfers some energy, in sum building the work the system has to do to the atmosphere. Leading to a decrease in internal, so “real” energy in the balloon. This corresponds to a decrease in temperature.
Turun@feddit.de 2 months ago
I see! Thank you very much!
If we assume the balloon model and the sides expand then each collision of a molecule inside the balloon with the outer wall will leave it with less speed and therefore lower energy and therefore a lower temperature.
As a consequence, gas expanding in a vacuum does not cool off, because it has nothing to transfer the energy to!