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 soap solution, the energy spent in doing so is

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

Answer 1

The correct option is D

$24\pi \sigma r^2$

Surface area of bubble of radius $r=4\pi r^2$
Surface area of bubble of radius $2r=4\pi (2r{)}^2=16\pi r^2$
Therefore, increase in surface area $=16\pi r^2-4\pi r^2=12\pi r^2$
Since a bubble has two surfaces, the total increase in surface area $=24\pi r^2$
$\therefore$ Energy spent = work done $=24\pi \sigma r^2$
Hence, the correct choice is (d).