Q. 203.6( 9 Votes )

# 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 × 10^{5} Pa).

Answer :

Excess pressure inside the soap bubble:

Excess pressure inside the air bubble:

Where,

S is the surface tension of the soap solution.

r is the radius of the soap bubble.

r’ is the radius of the air bubble.

Total Pressure inside the air bubble at a depth of 0.4 m= P_{1}

P_{1} = P_{0} + hρg + P’

Where,

‘P_{0}’ is the atmospheric pressure

Given,

Radius of the soap bubble, r = 5.0 mm = 5 × 10^{-3} m

Surface tension of the soap solution, S = 2.50 × 10^{-2} N / m

Relative density to the air of the soap solution, ρ = 1.2 × 10^{3} kg /m^{3}

The height at which the air bubble is formed, h = 40 cm = 0.4 m

Radius of the air bubble, r’ = r = 5 × 10^{-3} m

Acceleration due to gravity = 9.8 m/s^{2}

The atmospheric pressure, P_{0} = 1.01 × 10^{5} Pa

Therefore,

Excess pressure inside the soap bubble

⇒

⇒ P = 20 Pa

Excess pressure inside the air bubble,

⇒

⇒ P’ = 10 Pa

The total pressure inside an air bubble at the depth of 0.4 m, P_{1}

P_{1} = 1.01 × 10^{5} Pa + (0.4 m × 1.2 × 10^{3} kg/m^{3} × 9.8 m/s^{2} ) + 10 Pa

P_{1} = 1.057 × 10^{5} Pa

__The excess pressure inside the soap bubble is 20 Pa, the excess pressure inside the air bubble 10 Pa and the total pressure inside the air bubble is 1.057 × 10 ^{5} Pa__

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