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Question: If hot air rises, why is it cold on the mountaintops?
If you drop an object into water it will float if it has a lower density than that of the water. Otherwise, it will sink. Maybe you have seen this in your bathtub. The hot air has a lower density than the density of the surrounding cold air. This is the reason why hot air rises.
Atmospheric pressure is the measure of the weight of the air above. The atmospheric pressure always decreases with increasing the altitude. As hot air rises into regions of lower atmospheric pressure, it expands (or spreads out) into a larger voume. This is similar to blowing up a balloon. The ballooon expands because the air pressure inside the balloon is higher than the pressure outside.
For the expansion, the hot air needs "extra" energy known as "work". In other words, molecules of the rising air need more energy to move apart or expand. The only possible source of energy available to do this "work" is the thermal energy of the rising air. This means, as the rising air reaches into the regions of lower pressure, part of its thermal energy is used to expand the air into a larger volume. As the expanding air loses its thermal energy, it cools. In the end, the rising air will eventually reach the same temperature as the air around it. At this point the air will cease its expansion and rising. This cooler air stays in the atmosphere until the changing climate conditions move it back down.
This process is known as adiabatic cooling. This means the air rises, expands, and becomes cooler, but no thermal energy is transferred (gained or lost) from the adjacent air. This adiabatic cooling plays an extremely important part of our weather patterns.
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