If the work done in blowing a soap bubble of volume ' V ' is ' W ', then the work done in blowing a soap bubble of volume ' 2 V ' will be

The work done is given as \(\mathrm{W}=\mathrm{T} \Delta \mathrm{A}\)
Volume of sphere is \(V=\frac{4}{3} \pi \mathrm{r}^3\)
Area of sphere is \(\mathrm{A}=4 \pi \mathrm{r}^2\)
\(\therefore \mathrm{A} \propto \mathrm{~V}^{\frac{2}{3}} \)
\( \therefore \mathrm{~W} \propto \mathrm{~V}^{\frac{2}{3}}\)
\(\frac{\mathrm{W}^{\prime}}{\mathrm{W}}=\frac{\mathrm{V}^{\frac{2}{3}}}{\mathrm{~V}^{\frac{2}{3}}} \)
\( \frac{\mathrm{~W}^{\prime}}{\mathrm{W}}=\frac{(2 \mathrm{~V})^{\frac{2}{3}}}{\mathrm{~V}^{\frac{2}{3}}} \)
\( \therefore \frac{\mathrm{~W}^{\prime}}{\mathrm{W}} =2^{\frac{2}{3}}=4^{\frac{1}{3}} \)
\( \therefore \mathrm{~W}^{\prime} =4^{\frac{1}{3}} \mathrm{~W}\) \(\ldots(\because \mathrm{V}=2 \mathrm{~V})\)