Question

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

• A. $2.5 \times 10^{-6} J$
• B. $1 \times 10^{-7} J$
• C. $8 \times 10^{6} J$
• D. $5 \times 10^{-6} J$

Answer 1

Answer: (D)

As, we know that the surface energy of a soap bubble,
$W=A T$
So, $W'=2 A'T \,\left[A'=2 A\right]$
Since, a soap bubble has double surface area.
Given, surface tension of soap water solution,
$T=\frac{1}{10 \pi} N / m$ and diameter of soap bubble $=5\, mm$
Now, $W'=2\left(\pi D^{2}\right) T=2 \times \pi \times 25 \times 10^{-6} \times \frac{1}{10 \pi}$
$\Rightarrow W'=5 \times 10^{-6} J$