Question

The radius $R$ of the soap bubble is doubled under isothermal condition. If $T$ be the surface tension of the soap bubble, the work done in doing so is given by

• A. $32\pi R^{2}T$
• B. $24\pi R^{2}T$
• C. $8\pi R^{2}T$
• D. $4\pi R^{2}T$

Answer 1

Answer: (B)

The surface energy of a bubble
$E$ = Tension $\times$ Surface area
For soap bubble
$E=2T\times A$
$=2T\times 4\pi R^2$
Here, $R$ = radius of the bubble
If the radius is doubled then we have
$E^{\prime }=2T\times 4\pi {\left(2R\right)}^2$
$E^{\prime }=32\pi R^{2}T$
Work done = $E^{\prime }-E$
$\Rightarrow 32\pi R^{2}T-8\pi R^{2}T=24\pi R^{2}T$