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Question
Suppose the density of air at Madras is ρo and atmospheric pressure is P0. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10 km above Madras. If we use the equation Po − P = ρogz, will we get a pressure more than the actual or less than the actual? Neglect the variation in g. Does your answer change if you also consider the variation in g?
Solution
Using the equation Po − P = ρogz, we get:
P = Po − ρogz
The pressure calculated by using this equation will be more than the actual pressure because density at a height of 10 km above Madras will be less than ρo.
Yes, the answer will change if we also consider the variation in g. Because g decreases with height, it will have the same effect on pressure as that of density.
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