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81.

Problem 17.57 (RHK)

A soap bubble in air has a radius of 3.20 cm. It is then blown up to a radius of 5.80 cm. We can use 26.0 mN/m (constant) for the surface tension of the bubble. (a) We have to find the initial pressure difference across the bubble film. (b) Pressure difference across the film at the larger size. (c) Work done on the atmosphere in blowing up the bubble. (d) Work done in stretching the bubble surface.

Solution:             Click For PDF Version

Gauge pressure inside a bubble of radius r is

(a)

As the radius of the bubble film initially is 3.20 cm,

 

 

(b)

As the radius of the bubble film finally is 5.80 cm,

(c)

Work done on the atmosphere in stretching the radius of the bubble from r to is

Therefore,

On substituting the values for the atmospheric pressure,, we find

(d)

Work done in stretching each bubble surface is