• # question_answer The radius of a soap bubble is R and surface tension is T, keeping the temperature constant, the extra energy needed to double the radius of the soap bubble by blowing, will be: A)  $32\pi {{R}^{2}}T$                        B)  $24\pi {{R}^{2}}T$ C)  $16\pi {{R}^{2}}T$                        D)  $8\pi {{R}^{2}}T$

Energy needed to double the radius $E=T.2\Delta A$ $=T.2\left\{ 4\pi r_{2}^{2}-4\pi r_{1}^{2} \right\}$ $=T.2\times 4\pi \{r_{2}^{2}-r_{1}^{2}\}$ $=T.2\times 4\pi \{{{(2R)}^{2}}-{{(R)}^{2}}\}$ $=8\pi T.\{4{{R}^{2}}-{{R}^{2}}\}$ $=24\pi {{R}^{2}}T$