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Why are the tops of mountains covered with snow, but not at the bottom? There is always snow even on high peaks in very hot areas. It has to be very cold at the top of the mountaintop so that the snow doesn't melt. But why are they so cold?

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The effect cited by Arturo don Juan is called the adiabatic lapse rate in atmosphere and it is approximately $9.8 °C/km$ or $5.38 °F/1,000 ft$ (dry air). If the humidity of air is higher, then the lapse rate is lower.

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To answer the question in your title, it's because it really is much colder up there. It's colder up there because atmospheric pressure decreases as you increase altitude, which is a result of gravity.

Source

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