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 × 105 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= P1


P1 = P0 + hρg + P’


Where,


‘P0’ 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 × 103 kg /m3


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/s2


The atmospheric pressure, P0 = 1.01 × 105 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, P1


P1 = 1.01 × 105 Pa + (0.4 m × 1.2 × 103 kg/m3 × 9.8 m/s2 ) + 10 Pa


P1 = 1.057 × 105 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 × 105 Pa


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