What is the depth of the cave if the air pressure in it is 770 mm Hg and on the surface

What is the depth of the cave if the air pressure in it is 770 mm Hg and on the surface of the earth the pressure is 750 mm Hg? Air temperature 0.

The pressure at depth h is described by the formula:

p = ρ * g * h, ρ is the density, g is the acceleration of gravity, h is the depth. Then:

Δp = ρ * g * Δh, where Δh is the depth of the cave.

Δh = (p1 – p2) / g * ρ.

Let us express Δp in pascals:

Δp = (770 – 750) = 20 mm Hg = 20 * 133.3 = 2700 Pa.

The density of air at zero temperature is 1.275 kg / m ^ 3. Then we get:

Δh = 2700/10 * 1.275 = 209 m.

Answer: the desired depth of the cave was 209 m.