Question
Sun January 13, 2013 By: Shabnakp
 

what is the excess pressure inside a bubble of soap solution of radius 5 mm .Give surface tension of soapis 2.5*10^-2 n/m. if an air bubble of same diamension is formed at depth of 40cm.inside the container containing the soap solution.what is the pressure inside tha bubble. density of soap solution is 1.2

Expert Reply
Sun January 13, 2013
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, S = 2.50 × 10–2 Nm–1
Relative density of the soap solution = 1.20
?Density of the soap solution, ? = 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 the relation:
P = 4S/r
   = (4 x 2.5 x 10 -2)/(5 x 10-3)
= 20 Pa
Therefore, the excess pressure inside the soap bubble is 20 Pa.

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

P =2S/r
  = (2 x 2.5 x 10-2)/ (5 x 10-3)
  =10 Pa
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 + h?g + P’
= 1.01 × 105 Pa+  0.04 x 1.2 × 103 kg/m3x 9.8 + 10
=1.057 x 10 5Pa
=1.06 x 105Pa
Ask the Expert