First slide

Surface tension

Question

If T is the surface tension of soap solution, the amount of work done is blowing a soap bubble from a diameter D to a diameter 2D is

Moderate

A

$2 {πD}^{2} T$
B

$4 {πD}^{2} T$
C

$6 {πD}^{2} T$
D

$8 {πD}^{2} T$

Solution

Work done = (Increase in surface area) x Surface tension
= $2 \times [4 π {(\frac{2 D}{2})}^{2} - 4 π {(\frac{D}{2})}^{2}] \times T$
[Since, for sap bubble, there are 2 free surfaces]
= 2 $\times (4 {πD}^{2} - {πD}^{2}) T = 6 {πD}^{2} T$

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