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

The correct option is A 27 : 1

Excess pressure as compared to atmosphere inside bubble A is

$△p_1=1.01-1=0.01atm$

Inside bubble B is

$△p_2=1.03-1=0.03atm$

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 volume's are in the ratio

$\frac{v_1}{v_2}=\frac{\frac{4}{2}\pi r_1^3}{\frac{4}{3}\pi r_1^3}$

${\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{3}{1}\right)}^3=\frac{27}{1}$

$V_1:V_2=27:1$