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Question
Atmospheric pressure at sea level is 76 cm of mercury. Calculate the vertical height of the air column exerting the above pressure. Assume the density of air 1.29 kgm−3 and that of mercury is 13600 kgm−3. Why the height calculated by you is far less than the actual height of the atmosphere?
Solution
Height of mercury column = hHg = 76 cm = 0.76 m
Verticles height of air column = hair =?
Density of mercury = ρHg = 13600 kgm−3
Density of air = ρair = 1.29 kgm−3
According to the question:
Pressure due to air column = Pressure due to Hg column
ρair × hair × g = ρHg × hHg × g
hair = `(ρ_("Hg")xx"h"_"Hg")/ρ_"air"`
hair = `(13600xx0.76)/1.29`
= 8012.4 m
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