If hot air rises due to convection, why does it get colder when we climb mountains?
After some research, I found out that atmospheric pressure affects the temperature of the surroundings.
Another question arises: How does atmospheric pressure affect the surrounding temperature?
High pressure warm air is lifted at ground level (say at the equator) by even higher pressure air that has drifted from the cold air latitude part of the convection cell. As the air lifts upwards through a vertical column, it pushes outwards against lower pressure air (whose pressure is determined by altitude) around the sides of the column. In pushing outwards, it does work on the lower pressure air, and through collisional transfer of energy/momentum, the ascending air cools.
Before answering this question,I think this little fact help you understand what really is gonna happen
Gases are a phase of matter where all the atoms or molecules are moving independently of each other all the time. All these molecules move at a different speeds but if we take the average speed of all the molecules; we get the temperature of the gas. If a particular gas has a large number of fast molecules, the gas is hot. On the other hand, if a particular gas has mostly slow molecules, then the gas is cold.
The temperature of a gas is a measure of the speed of its molecules. Increasing the temperature of a gas increases the average speed (and therefore the kine tic energy) of the molecules.This causes the molecules to expand out
Coming to your question,When a gas expands it takes energy.This energy has to come from the internal energy of the gas.
From the ideal gas law- PV = nRT
You can get the decrease in pressure from an increase in volume, decrease in number of atoms or a decrease in temperature. Under the circumstances of constant volume and number of atoms, ,the decrease must come from a decrease in energy, reflected by a decrease in temperature.Withdrawing energy cools off the gas making the molecules move slowly.That is the reason why it is colder at high altitude
As you go up atmospheric pressure decreases so your blood in your body flows faster to compensate that thus I believe human bodies feel cold due to this. Now coming to convection, it is the process of warm air rising up and denser air falling down. Due to lower atmospheric pressure the air molecules do not gain much kinetic energy, which means the temperature is low. And vice versa. That’s how it can be claimed that atmospheric pressure affects sorrounding temperature.
To illustrate @johnforkosh's point, here is a brief example. In the absence of convection, let's first imagine a vertical tube filled with air, extending from the surface of the earth up to, say, 100 miles. At every height increment going upward from zero to 100 miles, the equation of state of the air (approximated by something called the ideal gas law) relates the pressure, temperature and density of the air in such a manner that when the pressure decreases, so does the temperature. Since the pressure in the atmosphere decreases exponentially with increasing altitude, so will the temperature. Near the earth's surface, this is fairly well-approximated by subtracting five degrees F per 1000 feet of altitude gain, which is why mountain peaks are colder than the valleys between them.
In the presence of convection, the atmosphere gets stirred up vertically which moves hot, low-density air away from the surface of the earth and up into higher altitudes. As it rises, the warm air encounters progressively lower pressure which causes it to expand and as it expands, it cools.
This simplified view ignores the effects of heat exchange between different bodies of air and between air and the ground (a condition called "adiabaticity"). When heat exchange is allowed, the situation becomes far more complicated, and entire chapters of books about atmospheric dynamics are devoted to it.
