why is air pressure lower at a higher elevation
Atmospheric pressure reduces with altitude for two reasons - both related to gravity. The gravitational attraction(*) between the earth and air molecules is greater for those molecules nearer to earth than those further away - they have more weight - dragging them closer together and increasing the pressure (force per unit area) between them. Molecules further away from the earth have less weight (because gravitational attraction is less) but they are also 'standing' on the molecules below them, causing compression.
Those lower down have to support more molecules above them and are further compressed (pressurised) in the process. (*) Strictly it is the gravitational force minus the effect of the Earth's spin (an effect that is greatest at the equator). The graph below gives an indication of how pressure varies non-linearly with altitude. (Apologies for using feet rather than metres but most values of altitude are still expressed in this ancient unit. )
Boiling point is the point at which vapour pressure equals atmospheric pressure.
In a liquid, some particles always have enough energy to escape to the gas phase. Gaseous particles are also returning to the liquid. The vapour pressure (from facweb. bhc. edu) As temperature increases, more particles have enough energy to escape to the gas phase. This increases the vapour pressure. When the vapour pressure equals atmospheric pressure, the liquid boils.
As elevation increases, atmospheric pressure decreases because air is less dense at higher altitudes. Because the atmospheric pressure is lower, the vapour pressure of the liquid needs to be lower to reach boiling point. Therefore, less heat is required to make the vapour pressure equal to the atmospheric pressure. The boiling point is lower at higher altitude. Here's a video that demonstrates the effect of atmospheric pressure on boiling point.
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