At the foot of the mountain, the barometer shows a pressure of 760 mm Hg. Art.

At the foot of the mountain, the barometer shows a pressure of 760 mm Hg. Art. and at the top-722 mm Hg. Art. determine the height of the mountain.

P1 = 760 mm Hg
P2 = 722 mm Hg. Art.
ρ = 1 kg / m ^ 3.
g = 9.8 m / s ^ 2.
Δ h -?
Let’s translate the pressure in pascals, in 1 mm Hg. st = 133 Pa.
P1 = 760 mm Hg. st * 133 = 101080 Pa.
P2 = 722 mm Hg. st * 133 = 96026 Pa.
Δ P = P1-P2.
P1 = ρ * g * h1, h1 = P1 / ρ * g.
P2 = ρ * g * h2, h2 = P2 / ρ * g.
Δ h = h1 – h2.
Δ h = P1 / ρ * g – P2 / ρ * g = Δ P / ρ * g.
Δ h = (101080Pa – 96026 Pa) / 1 kg / m ^ 3 * 9.8 m / s ^ 2 = 515.7 m.
Answer: the height of the mountain is Δ h = 515.7 m.