10.20 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).
10.20 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).
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1 Answer
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Soap bubble radius, r = 5.0 mm = 5 m
Surface tension of the soap bubble, S = 2.50 N/m
Relative density of soap solution = 1.20, hence density of soap solution, = 1.2 Kg/
Air bubble formed at a depth, h = 40 cm = 0.4 m
1 atmospheric pressure = 1.01 Pa
Acceleration due to gravity, g = 9.8 m/
We know, the excess pressure inside the soap bubble is given by the relation:
P = = Pa = 20 Pa
Hence, the excess pressure inside the air bubble is given by the relation, P' = = 10 Pa
At a depth of h, the total pressure inside the air bubble = Atmospheric press
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