Question

A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing

• A. $3 \pi Tr^2 $
• B. $6 \pi Tr^2 $
• C. $12 \pi Tr^2 $
• D. $24 \pi Tr^2 $

Answer 1

The Correct Option is D

Initially area of soap bubble, $A_1 = 4 \pi r^2$
Under isothermal condition radius becomes 2r.
$\therefore $ Area $A_2 = 4 \pi (2r)^2 = 16 \pi r^2$
Increase in surface area
$\Delta A = 2 (A_2 - A_1 ) $
$= 2(16 \pi r^2 - 4 \pi r^2) $
$= 2 4\pi r^2$
Energy spent,
$W = T \times \Delta A$
$ = T . 24 \pi r^2 $
$= 24 \pi T r^2\, J $