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Question
At sea level, the atmospheric pressure is 76 cm of Hg. If air pressure falls by 10 mm of Hg per 120m of ascent, what is the height of a hill where the barometer reads 70 cm Hg. State the assumption made by you.
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Solution
Atmospheric pressure, P = 76 cm Hg
Rate at which pressure falls = 10 mm of Hg per 120 m of ascent = 1 cm of Hg per 120 m of ascent
Let h be the height of the hill.
Pressure at hill, P' = 70 cm Hg
Total fall in pressure = P − P' = (76 − 70) cm Hg = 6 cm Hg
Now, fall in pressure is 1 cm Hg for every 120 m increase in height
Thus, if the fall in pressure is 6 cm Hg, increase in height shall be (6 × 120)m = 720 m
∴ Height of the hill = 720 m
The calculation assumes a linear relationship between the altitude and the atmospheric pressure, meaning the rate of pressure drop is constant over the entire height of the hill.
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