Why does water boils at lower temperature at higher altitudes?

Pressure decreases with increasing elevation. Thus at higher altitudes, there is less pressure as compared to the ground level. Boiling point is the temperature when the pressure of the substance equals the atmospheric pressure. When there is less atmospheric pressure, obviously the boiling point will also be low.

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Boiling point is the point at which water undergo a phase change from liquid to gas. A liquid becomes a gas because it has enough kinetic energy to break the intermolecular forces which hold the molecules together as a liquid. One way to increase this kinetic energy is to heat up the molecules by raising the temperature. 

The reason that water boils at a lower temperature at a higher altitude is because the pressure exerted upon it from the atmosphere is less at higher altitudes and so it is less "held together". For example, imagine the air as blankets, and the lowest part (sea level) has the most blankets of air stacked on top of one another. This pressure is greatest at the bottom than at the top. Similarly, when you are underwater, and dive deeper you can feel your goggles being pushed more into your head than when you come up, because the water increases more pressure on you the farther down you dive. 

So, at a higher altitude, there is lower pressure, which means a smaller force holding the water molecules together. This means that the water requires less energy to overcome the intermolecular forces keeping the water molecules in the liquid phase.

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