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

Given:

Diameter of the soap bubble $d=5 \mathrm{mm}$.

The surface tension of the soap water solution is $T=\frac{1}{10\pi }$

The expression for the free energy of the surface layer is given by,$E=T\left(2 \mathrm{A}\right)=T4\pi R^2=T\left(2\frac{4\pi d^2}{4}\right)$

(Since the soap has two surfaces)

$F=\frac{1}{10\pi }\times 2\pi \times {\left(5\times {10}^{-3}\right)}^2=5\times {10}^{-6} \mathrm{J}$