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. $24 \pi T r^{2}$

Answer 1

Answer: (B)

Initially area of soap bubble
$A_{1}=4 \pi r^{2}$
Under isothermal condition radius becomes $2 r$,
Then, area $A_{2} =4 \pi(2 r)^{2}$
$=4 \pi \cdot 4 r^{2}$
$=16 \pi r^{2}$
Increase in surface area
$\Delta A =2\left(A_{2}-A_{1}\right) $
$=2\left(16 \pi r^{2}-4 \pi r^{2}\right)=24 \pi r^{2}$
Energy spent
$ W =T \times \Delta A $
$=T \cdot 24 \pi r^{2} $
or $ W =24 \pi T r^{2} J$