If the surface tension of a liquid is $T$,the gain in surface energy for an increase in liquid surface by $A$ is

The surface tension of the soap water solution is $\frac{1}{10 \pi} \text{ N m}^{-1}$. The free energy of the surface layer of a soap bubble of diameter $5 \text{ mm}$ will be:

Let $W_1$ be the work done in blowing a soap bubble of radius $r$ from a soap solution at room temperature. The soap solution is now heated and a second soap bubble of radius $2r$ is blown from the heated soap solution. If $W_2$ is the work done in forming this bubble,then:

The radius of a soap bubble is $r$, and the surface tension of the soap solution is $T$. Without increasing the temperature, how much energy is required to double its radius (in $\pi r^2 T$)?

$A$ liquid drop having surface energy $E$ is sprayed into $512$ droplets of same size. The final surface energy is (in $E$)

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is