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Warm air is less dense than cold air. Heat is energy, so the warm air molecules are more energetic and move about more, increasing the distance between molecules - thus less dense.

Density is not weight as some have implied. Density is Mass/Volume.

Atmospheric pressure =(density)(accel due to gravity)(height of atmosphere)

The last two terms are constant regardless of temperature of air. Warmer air has less density and thus the pressure due to this air is less.

Alternatively, you could picture two columns of air from the ground to the top of the atmosphere having the same volume. If one has cold air and the other warm, the cold air column, being more dense, will have more mass of air within it since the volume is constant. The greater mass will weigh more due to gravity.

Source(s):Degrees in Physics and Mechanical Engineering
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Q: Why is the atmospheric pressure lower beneath the mass orf warm air than beneath the mass of cold air?
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