First slide

Surface tension and surface energy

Question

Two soap bubbles, one of radius 50 mm and the other of radius 80 mm, are brought in contact so that they have a common interface. The radius of the curvature of the
common interface is

Moderate

A

0.003 m
B

0.133 m
C

1.2 m
D

8.9 m

Solution

$\begin{array}{l} [P_{0} + \frac{4 T}{R_{2}}] - [P_{0} + \frac{4 T}{R_{1}}] = \frac{4 T}{R} \\ ⇒ \frac{1}{R} = \frac{1}{R_{2}} - \frac{1}{R_{1}} \\ ⇒ R = \frac{R_{1} R_{2}}{R_{1} - R_{2}} = \frac{50 \times 80}{30} mm = \frac{400}{3} mm \\ = \frac{400}{3 \times 1000} m = \frac{4}{30} m = 0.133 m \end{array}$

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