A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If $\sigma$ is the surface tension of soap solution, the energy spent in doing so is $x\left(4\pi \sigma r^2\right)$  .Find $x$

Surface area of bubble of radius $r=4\pi r^2$ .Surface are of bubble of radius $2r=4\pi {\left(2r\right)}^2=16\pi r^2.$ Therefore, increases in surface area $=16\pi r^2-4\pi r^2=12\pi r^2$  . since a bubble has two surface, the total increase in surface are  $=24\pi r^2$
Energy spent  = work done  $=24\pi \sigma r^2$