Question

Assuming the density of air to be 1.295 kg per m cube, find the fall in barometric height in mm of Hg at a height of 107 m above the sea level. Take density of mercury =13.6× 1000 kg per m cube. (I know how to solve this. But I need someone to explain me the process.)

Answer 1

AnswEr

GivEn that, density of air to be 1.295 kg/m³. Height of the cube above the sea level is 107 m. Also, Density of mercury is 13.6× 1000 kg/m³.

We know the required formula for decrease in the pressure of air, that is,

⇒ ρ g h

Substituting the values :

⇒ 1.295 × g × 107

⇒ 13.6 × 10³ × g

Now, for calculating the decease in barometric height of mercury, we'll multiply the same eqn by H.

⇒ 13.6 × 10³ × g × H

⇒ H of mercury = air density × height of air / density of mercury

⇒ ρ × g × h of air = ρ × g × H of mercury

⇒ ρ g h / (13.6 × 10³ × g)

⇒ 1.295 × 107/13.6 × 10³

⇒ 0.010 m of Hg

⇒ 10 mm of Hg.

∴ Fall in barometric height in mm of Hg at a height of 107 m above the sea level is 10 mm of Hg.