Why does water boil faster on the top of a mountain?

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Water boils at a lower temperature (therefore faster) at high altitudes because the atmospheric pressure it lower. A liquid will begin to boil when its vapor pressure equals atmospheric pressure. The vapor pressure of water increases with temperature. The normal boiling point, 100 degrees C or 373K, is the temperature at which the vapor pressure equals 1.00 atm pressure, the normal pressure at sea level. 

Atmospheric pressure decreases with altitude because the weight of the air above decreases.

When the atmospheric pressure is lower, the vapor pressure of water will reach atmospheric pressure at a lower temperature. We might say that the water boils "faster" because it reaches boiling at a lower temperature, but at the lower temperature it will cook food more slowly.

At pressures higher than atmospheric pressure the boiling point of water is higher. A pressure cooker reduces cooking time by keeping water in the liquid phase at temperatures above 100 degrees C.

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