Name: Capillary Rise
Uploaded: 2019-07-19
Duration: 10 min 29 s
Description: Have you ever seen what happens to a celery stalk dipped in red-coloured water? We notice that after a day or two, the leaves turn reddish! Let's learn the r...

Question

Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of the soap solution is 30 dyne/cm. $(π = 3.142)$

Accepted Answer

Whenever a liquid film is expanded, the work done gets stored as energy in the film. Hence the increase in energy of the film is equal to the work done.

The soap bubble expands hence the surface area increases.

The increment in the surface area * the surface tension T is the extra energy and hence equal to the work done.

Note that the bubble has two areas, inner and outer, Since the thickness of the film in negligible, both the radii can be assumed as equal.

Work done= (Increase in the surface ares of bubble) $\times$ Surface Tension

Formula for it as given below

$W = T Δ A$

$A_{1} = 4 {πr}_{1}^{2} = 4 π \times 1^{2} = 4 π {cm}^{2}$

$A_{2} = 4 {πr}_{2}^{2} = 4 π \times 2^{2} = 16 π {cm}^{2}$

$Δ A = A_{2} - A_{1} = (16 - 4) π = 12 π {cm}^{2}$

Since soap bubble has two surfaces

$w = 2 T \times Δ A$

$= 2 \times 30 \times 12 π$

$w = 2.26 \times 10^{3} e r g$

The work done is increasing the radius of the soap bubble is $2.26 \times 10^{3} e r g$

Embibe Experts Solutions for Chapter: Surface Tension, Exercise 1: Maharashtra Board-2018

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