A soap bubble of radius ' $R$ ' is blown. After heating a solution, a second bubble of radius ' $2…
A soap bubble of radius ' $R$ ' is blown. After heating a solution, a second bubble of radius ' $2 \mathrm{R}$ ' is blown. The work required to blow the $2^{\text {nd }}$ bubble in comparison to that required for the $1^{\text {st }}$ bubble is
exactly double.
slightly more than 4 times.
slightly less than 4 times.
slightly less than double.
Solution
$\begin{aligned}
\mathrm{W}_1 & =8 \pi \mathrm{R}^2 \mathrm{~T}_1 \\
\mathrm{~W}_2 & =8 \pi(2 \mathrm{R})^2 \mathrm{~T}_2=32 \pi \mathrm{R}^2 \mathrm{~T}_2 \\
\therefore \quad \frac{\mathrm{W}_1}{\mathrm{~W}_2} & =\frac{\mathrm{T}_1}{4 \mathrm{~T}_2}
\end{aligned}$
When $\mathrm{T}_1=\mathrm{T}_2, \mathrm{~W}_2=4 \mathrm{~W}_1$
But as work is done, temperature increases and surface tension decreases.
$\therefore \quad \mathrm{W}_2 < 4 \mathrm{~W}_1$