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Question -

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



Answer -

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, = 2.50 ×10–2 Nm–1

Relative density of the soap solution = 1.20

Densityof 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 therelation:

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

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

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 + g + P

Therefore, the pressure inside the air bubble is 

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