The volume of a gas bubble that floats to the surface from the bottom of the lake has doubled.

The volume of a gas bubble that floats to the surface from the bottom of the lake has doubled. How deep is the lake? The temperature is considered constant.

Initial data: V1 (volume of a gas bubble at the lake surface) = 2V2 (volume of a gas bubble at the bottom of the lake).

Permanent: Patm. (normal atmospheric pressure) = 101 325 Pa; ρ (water density) = 1000 kg / m3; g (acceleration due to gravity) = 9.81 m / s2.

The depth of the lake is determined from the equality: Р1 / V1 = P2 / V2.

(Patm. + Ρ * g * h) / 2V2 = Patm. / V2.

Patm. + ρ * g * h = 2 * Patm ..

ρ * g * h = Patm ..

h = Patm / (g * h) = 101325 / (9.81 * 1000) = 10.33 m.

Answer: The depth of the lake is 10.33 m.