Question

What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10^–2 N m^–1? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01 × 10⁵ Pa).

Answer 1

Excess pressure inside the soap bubble is 20 Pa;

Pressure inside the air bubble is

Soap bubble is of radius, r = 5.00 mm = 5 × 10^–3 m

Surface tension of the soap solution, S = 2.50 × 10^–2 Nm^–1

Relative density of the soap solution = 1.20

∴Density of the soap solution, ρ = 1.2 × 10³ kg/m³

Air bubble formed at a depth, h = 40 cm = 0.4 m

Radius of the air bubble, r = 5 mm = 5 × 10^–3 m

1 atmospheric pressure = 1.01 × 10⁵ Pa

Acceleration due to gravity, g = 9.8 m/s²

Hence, the excess pressure inside the soap bubble is given by the relation:

Therefore, the excess pressure inside the soap bubble is 20 Pa.

The excess pressure inside the air bubble is given by the relation:

Therefore, the excess pressure inside the air bubble is 10 Pa.

At a depth of 0.4 m, the total pressure inside the air bubble

= Atmospheric pressure + hρg + P’

Therefore, the pressure inside the air bubble is