If you are referring to energy produced through combustion, such as heat energy from a gas stove or an open fire, then yes, people at higher elevations use more energy on average. One reason is because of the limited amount of oxygen in the air that restricts the rate of combustion, however the decreased atmospheric pressure at higher elevations also affects energy efficiency. A practical example that proves this is boiling water at a higher altitude; due to the drop in atmospheric pressure the higher you go, water molecules are not held together as tightly as they would be at sea level and therefore are more likely to free themselves from their liquid state into steam. This has two effects: one, it means water boils at a lower temperature at higher altitudes (around 208 F at 2000 feet), and two, it means that it takes more time and energy to reach the sea-level boiling temperature of 212 F. Unless one allows for an increased amount of time to boil food, then food that is ready at sea level is undercooked at higher altitudes. One way people compensate for this is by using a pressure cooker which raises the temperature at which water boils.
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