If during the ascent to the altitude k the air pressure decreased by pgh, where p is the air density, then already at an altitude of about 8 km the atmospheric pressure would decrease to zero! But it is well known that airplanes can fly at high altitudes too. Is there a contradiction here?
there is no contradiction, the pressure of the atmosphere is not calculated by the formula n = pgh, the pressure of the atmosphere decreases even at high altitudes.
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