The pressure of air in a soap bubble of 0.7cm diameter is 8mm of water above the pressure outside. The surface tension of the soap solution is

The correct option is 68.66 dyne/cm.

Step-by-Step Explanation:

To find the surface tension of the soap solution, we can use the formula for the excess pressure inside a soap bubble.

A soap bubble has two liquid-gas interfaces (an inner surface and an outer surface). Thus, the excess pressure ($\mathrm{\Delta P}$) inside a soap bubble of radius $R$ is given by:
$\mathrm{\Delta P}=\frac{4T}{R}$
where $T$ is the surface tension of the soap solution.

We are given the following values in CGS units:
Diameter of the soap bubble, $d=0.7\text{cm}$
Radius of the soap bubble, $R=\frac{d}{2}=\frac{0.7}{2}=0.35\text{cm}$

The excess pressure is equivalent to the pressure exerted by a water column of height $h=8\text{mm}=0.8\text{cm}$:
$\mathrm{\Delta P}=h·\rho ·g$
where:
$\rho$ (density of water) $=1{\text{g/cm}}^3$
$g$ (acceleration due to gravity) $\approx 980.85{\text{cm/s}}^2$

Substituting the expression for $\mathrm{\Delta P}$ into the bubble pressure formula, we get:
$h·\rho ·g=\frac{4T}{R}$

Rearranging the equation to solve for surface tension ($T$):
$T=\frac{h·\rho ·g·R}{4}$

Now, substitute the values:
$T=\frac{0.8·1·980.85·0.35}{4}$

Calculating the numerator:
$0.8·1·980.85·0.35=274.638{\text{dyne/cm}}^2$

Now, divide by 4:
$T=\frac{274.638}{4}\approx 68.66\text{dyne/cm}$

Thus, the surface tension of the soap solution is 68.66 dyne/cm.