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That is correct. If you think of the air as being a column of molecules, you can visualize that the mass of molecules in that column is forced downward by gravity. A 1cm square column extending upward to the top of the atmosphere weighs approximately 2.2 pounds. At an altitude further up the column where fewer molecules comprise a lesser mass they would exert proportionately less force. Another way to measure the weight of this column of air is by the pressure it exerts at a given point.

Temperature also has an effect on the pressure of air due to a change in the density of the air mass, thus two columns of air at at the same altitude might have different pressures because their temperatures are different. Generally, cold air has a higher pressure than warm air at the same altitude.

The decrease in pressure as altitude increases is called the pressure lapse rate, and has been tabulated for a "standard atmosphere" (one where the pressure and temperature at sea level are 29.92 in Hg (inches of Mercury) and 15 deg C respectively). Obviously, this varies in real world conditions but is approximately 1 in Hg per 1000 ft. The term lapse rate also applies to temperature changes with altitude and is approximately 2 deg C per 1000 ft on average depending upon the the moisture content of the air.

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