Why does a potato boil faster at higher altitude?

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If you are cooking a potato by boiling it in water, the water will boil faster at a higher altitude because the boiling point of water is lower. However, it will take the potato longer to cook since it will be surrounded by water that's boiling at a lower temperature. 

Water boils at 100 degrees C at sea level because at that temperature the molecules, on the average, have enough energy to overcome the forces of attraction to each other and overcome the pressure of the atmosphere to escape the liquid phase. At higher elevations atmospheric pressure is lower so less energy is required for the water molecules to enter the atmosphere in the gas phase. 

The vapor pressure of water, which is the pressure being exerted on the surface by molecules in the gas phase, increases with temperature. When the vapor pressure reaches the pressure of the atmosphere the water boils. At sea level, where the pressure is around 1 atm or 760 torr, this happens at 100 degrees C. This is called the normal boiling point. At lower atmospheric pressure this occurs at a lower temperature. The temperature of boiling water won't increase until all of the liquid has turned to water vapor.

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