Question

Determine the energy stored in the surface of a soap bubble of radius $2.1\text{cm}$ if its surface tension is $4.5\times {10}^{-2}\text{N/m}$.

• A. $3.6\pi \times {10}^{-4}\text{J}$
• B. $0.6\pi \times {10}^{-4}\text{J}$
• C. $1.6\pi \times {10}^{-4}\text{J}$
• D. $2.6\pi \times {10}^{-4}\text{J}$

Answer 1

The correct option is C $1.6\pi \times {10}^{-4}\text{J}$

Given,
Radius of soap bubble, $R=2.1\text{cm}=2.1\times {10}^{-2}\text{m}$
Surface Tension, $T=4.5\times {10}^{-2}\text{N/m}$
We know that, number of free surfaces for soap bubble, $n=2$
Surface energy $=$ Surface tension $\times$ surface area $\times$ number of free surfaces
$\Rightarrow E=T\times A\times n$
$=4.5\times {10}^{-2}\times 4\pi (2.1\times {10}^{-2}{)}^2\times 2$
$[$ surface area $=4\pi R^2]$
$=1.6\pi \times {10}^{-4}\text{J}$