Question

What is the excess pressure inside a bubble of soap solution of radius 5 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10^-2 N/m? If an air bubble of the same dimension were formed at a 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

Radius of the soap bubble, r = 5mm

= 5 × 10³m

Surface tension of the soap solution,

S = 2.5 × 10^-2 N/m

Since the soap Bubble has two surfaces,

Excess pressure, P = 4S/r

P = 20 Pa

Excess pressure inside the soap bubble is 20 Pa

Radius of air bubble, r = 5 mm = 5 × 10^-3

Depth, h = 40 c = 0.4 m

Density of soap solution, ρ = 1.2 × 10^-3 kg/m²

Atmospheric pressure, P_o = 1.01 × 10⁵ Pa

g = 9.8 m/s²

Excess pressure inside air bubble,

P₁ = 25/r

⇒ P₁ = 

P₁ = 10Pa

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

P_Total = P_o + ρgh + P₁

P_Total = 1.01 × 10⁵ + 1.2 × 10³ × 9.8 × 0.4 + 10

⇒ P_Total = 1.057 × 10⁵Pa

∴ The pressure inside the air bubble is 1.06 × 10⁵Pa.