First slide

Surface tension and surface energy

Question

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

Moderate

A

8 : 1
B

0.8 : 1
C

2 : 1
D

4 : 1

Solution

$\begin{array}{l} P r e s s u r e i n s i d e 1 s t b u b b l e = P_{0} + \frac{4 T}{R_{1}} = 1.01 \\ \Rightarrow 1 + \frac{4 T}{R_{1}} = 1.01 \\ \Rightarrow R_{1} = \frac{4 T}{0.01} \\ P r e s s u r e i n s i d e 2 n d b u b b l e = P_{0} + \frac{4 T}{R_{2}} = 1.02 \\ \Rightarrow 1 + \frac{4 T}{R_{2}} = 1.02 \\ \Rightarrow R_{2} = \frac{4 T}{0.02} \\ W e k n o w t h a t, v o l u m e \propto {(r a d i u s)}^{3} \\ \Rightarrow \frac{V_{1}}{V_{2}} = {(\frac{R_{1}}{R_{2}})}^{3} = {(\frac{0.02}{0.01})}^{2} = \frac{8}{1} \end{array}$

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