Physics - Fluid Question with Solution | TestHub

The surface energy of a bubble
$E$ = Tension $\times$ surface area
$E=T\times A$
For soap bubble
$E=2T\times A$
$E=2T\times 4\mathrm{\pi }{R}^2$
Here, $R$ = radius of the bubble
If the radius is doubled then we have
$E^{\mathrm{\prime }}=2T\times 4\mathrm{\pi }{R}^2$
$E^{\mathrm{\prime }}=2T\times 4\mathrm{\pi }{\left(2R\right)}^2$
$E^{\mathrm{\prime }}=32\mathrm{\pi }{R}^{2}T$

Work done = $E\text{'}-E$

$\Rightarrow 32\pi R^{2}T-8\pi R^{2}T=24\pi R^{2}T$