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

Answer: (D)

$24 \, \pi \, Tr^2$

Answer 2

Initially area of soap bubble $A_{1}=4 \pi r^{2}$ Under isothermal condition radius becomes $2 r$. Then, area $A_{2}=4 n(2 r)^{2}$ $=4 n .4 r^{2}$ $=16 \pi r^{2}$ 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 $W =T \times \Delta A$ $=T .24 \pi r^{2}$ or $W =24 \pi T r^{2} J$