First slide

Surface tension and surface energy

Question

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

Moderate

A

$2 π D^{2} T$
B

$6 π D^{2} T$
C

$4 π D^{2} T$
D

$8 π D^{2} T$

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 soap bubble, there are two free surfaces)
$= 2 \times (4 π D^{2} - π D^{2}) T = 6 π D^{2} T$

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