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

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

Tardigrade Admin · Accepted Answer

Excess pressure as compared to atmosphere inside bubble A is

Δ p_{1} = 1.01 - 1 = 0.01 a t m

inside bubble B is

Δ p_{2} = 1.03 - 1 = 0.03 a t m

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{4 t}{r}

Let

r_{1}

be the radii of bubbles A and B respectively then

\frac{p _{1}}{p _{2}} = \frac{4 T / r _{1}}{4 T / 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} π r _{1}^{3}}{\frac{4}{3} π r _{2}^{3}}

(\frac{r _{1}}{r _{2}})^{3} = (\frac{3}{1})^{3} = \frac{27}{1}

V_{1} : V_{2} = 27 : 1

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