Question

If the difference between pressure inside and outside of a soap bubble is $6mm$ of water
and its radius is $8mm$. What is the surface tension in dynes per $cm$.

• A. $117.6$
• B. $256$
• C. $378$
• D. $450$

Answer 1

The correct option is A $117.6$

Because of surface tension, drops and bubbles have a tendency to contract and compress the fluid inside. Bubble will compress the air inside. Hence inside pressure is greater than the outside one. $P_i>P_o.$

By Laplace's law for bubbles, $P_i-P_o=\frac{4T}{r}$

We know how a mercury barometer works. If it is used for measuring pressure, then the pressure is given by $P=h\rho g$, where h is the height of mercury in the tube and $\rho$ is its density.

The same formula $P=h\rho g$ is applicable for any other liquid used in place of mercury.

Although water is never used, we can imagine it.

Everything is in CGS units.

$h=6mm=0.6cm,$ for water $\rho =1g/cc,$ in CGS, $g=980cm/s^2$

$\therefore P_i-P_o=\Delta P=h\rho g=0.6\times 1\times 980$

$r=8mm=0.8cm$

$P_i-P_o=980\times 0.6=\frac{4T}{0.8}$

$\therefore T=\frac{980\times 0.6\times 0.8}{4}=117.6$ $dyne/cm$