Question

Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $R$ to $3R$ at given temperature will be :

• A. $64\pi S{R}^2$
• B. $\frac{18\pi S{R}^2}{3}$
• C. $8\pi S{R}^2$
• D. $16\pi S{R}^2$

Answer 1

Answer: (A)

$64\pi S{R}^2$

Given, surface tension of the liquid iis $S$.
Workdone in blowing a soap bubble. So as to increase its radius from $R_1=R$ to $R_2=3R$ is given by
$W=S\cdot 8\pi [R_2^2-R_1^2]$
Where $S=$ surface tension
$W=S\cdot 8\pi \left[\right(3R{)}^2-\left(R{)}^2\right]$
$=S\cdot 8\pi [9R^2-R^2]$
$=S\cdot 8\pi \cdot 8R^2=64\pi R^{2}S$.