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  4. Pressure inside two soap bubbles are 1.06 and 1.08 atm. Ratio between their volumes is

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Q. Pressure inside two soap bubbles are $1.06$ and $1.08$ atm. Ratio between their volumes is

Mechanical Properties of Fluids

Solution:

Excess pressures $\left(\Delta P_{1}\right) P_{i}-P_{0}=1.06-1=0.06$ atm
$\left(\Delta P_{2}\right) P_{i}-P_{0}=1.08-1=0.08$ atm
$\Delta P=\frac{4 S}{R} $
$\Rightarrow R=\frac{4 S}{\Delta P} $
$\Rightarrow \frac{R_{1}}{R_{2}}=\frac{\Delta P_{2}}{\Delta P_{1}}$
$\frac{R_{1}}{R_{2}}=\frac{0.08}{0.06}=\frac{8}{6}=\frac{4}{3}$
$\therefore \frac{V_{1}}{V_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{3}=\left(\frac{4}{3}\right)^{3}=\frac{64}{27}$