Question

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. Ratio between their volumes is

• A. $27:1$
• B. $3:1$
• C. $127:101$
• D. None of these

Answer 1

Answer: (A)

$27:1$

Answer 2

Excess pressure as compared to atmosphere inside bubble A is $\Delta {{p}_{1}}=1.01-1=0.01\text{ }atm$ inside bubble B is $\Delta {{p}_{2}}=1.03-1=0.03\text{ }atm$ Also when radius of a bubble is r, formed from a solution whose surface tension is t, then excess pressure inside the bubble is given by $p=\frac{4t}{r}$ Let ${{r}_{1}}$ be the radii of bubbles A and B respectively then $\frac{{{p}_{1}}}{{{p}_{2}}}=\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{0.01}{0.03}$ $\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{3}$ Since bubbles are spherical in shape their volumes are in the ratio $\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{2}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}$ ${{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{3}{1} \right)}^{3}}=\frac{27}{1}$ ${{V}_{1}}:{{V}_{2}}=27:1$