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

The surface tension $(T)$ of a liquid is equal to the work $(W)$ required to increase the surface area of the liquid film by unity at constant temperature. As per key idea, tension $=\frac{\text { work done }}{\text { surface area }}$ Or $T=\frac{W}{\Delta A}$ Since soap bubble has two surface and surface area of soap bubble is $4 \pi R^2$ where $R$ is radius of bubble. then $W=T \times 2 \times 4 \pi \dot{R}^2$ Given $R=2 R$ therefore $\quad W=T \times 2 \times 4 \pi \times(2 R)^2$ $W=32 \pi R^2 T$