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?

Answer 1

Height of mercury column = h_Hg = 76 cm = 0.76 m
Verticles height of air column = h_air =?
Density of mercury = ρ_Hg = 13600 kgm⁻³
Density of air = ρ_air = 1.29 kgm⁻³
According to the question:
Pressure due to air column = Pressure due to Hg column
ρ_air × h_air × g = ρ_Hg × h_Hg × g
h_air = `(ρ_("Hg")xx"h"_"Hg")/ρ_"air"`

h_air = `(13600xx0.76)/1.29`
= 8012.4 m