Question

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

• A. $6\pi \sigma r^{2}$
• B. $24\pi \sigma r^{2}$
• C. $12\pi \sigma r^{2}$
• D. $9\pi \sigma r^{2}$
• E. $18\pi \sigma r^{2}$

Answer 1

Answer: (B)

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 $=\sigma \left[8 \pi \left(2 r\right)^{2} - 8 \pi r^{2}\right]$
$=\sigma \left(32 \pi r^{2} - 8 \pi r^{2}\right)$
$=24\pi \sigma r^{2}$