Question

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

• A. $6 \pi \sigma r^2 $
• B. $3 \pi \sigma r^2 $
• C. $24 \pi \sigma r^2 $
• D. $12 \pi \sigma r^2 $
• E. $9 \pi \sigma r^2 $

Answer 1

Answer: (C)

Energy spent $=$ Work done $=T \Delta A$
Here, $A$ is total surface area
$\therefore A=8 \pi r^{2}$ for soap bubble
Hence, energy spent $=\sigma\left[8 \pi(2 r)^{2}-8 \pi r^{2}\right]$
$=\sigma\left(32 \pi r^{2}-8 \pi r^{2}\right)$
$=24 \pi \sigma r^{2}$