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 x 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 x 10⁵ Pa).

Answer 1

Given ,

surface tension of the soap bubble (S) = 2.5 × 10^-2 N/m

radius of soap bubble (R) = 5mm = 5× 10^-3 m

Excess pressure inside the soap bubble = 4S/R

= 4 × 2.5 × 10^-2 /5 × 10^-3

= 20 Pa

Excess pressure inside the air bubble = 2S/R

= 2 × 2.5 × 10^-2 /5 × 10^-3

= 10 Pa

pressure inside the air bubble = atmospheric pressure + pressure due to soap solution + Excess pressure inside the bubble

= 1.01 × 10^5 Pa + dgh + 10 Pa

= 1.013 × 10^5 + (1.2 × 10³×9.8 × 0.4) + 10

= 1.05714 × 10^5 Pa

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