A test tube with a length of L = 1 m was filled with atmospheric air under a pressure of P0 = 10 ^ 5 Pa

A test tube with a length of L = 1 m was filled with atmospheric air under a pressure of P0 = 10 ^ 5 Pa, closed with a light movable piston and immersed in a vessel with liquid to a depth of H = 40 m. What part of the tube length a = x / L will be filled with gas? The temperature is constant, the saturated vapor pressure is low, Pmax = 1.26 g / cm (glycerin), g = 10m / s2.

The pressure at depth is determined by the formula:

p = ρ * g * h, where ρ is the density of the fluid g is the acceleration of gravity h is the depth.

Then the pressure at a given depth will be:

p = 1267 * 10 * 40 = 506800 Pa.

Since atmospheric pressure is present, the gas will be under pressure:

p2 = 100000 + 506800 = 606800 Pa.

At constant temperature, the equality is true:

v1 / v2 = p2 / p1;

x / L = p1 / p2 = 100000/606800 = 0.16.

Answer: At depth, it will be filled with gas 0.16 of the original length of the tube.