Question

Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ the change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, which of the following relation is correct ?

• A. 4PV + 3ST = 0
• B. 3PV + 4ST = 0
• C. 2PV + 3ST = 0
• D. 3PV + 2ST = 0

Answer 1

Answer: (B)

3PV + 4ST = 0

Answer 2

$\left( P +\frac{4 T }{ r _{1}}\right) \frac{4}{3} \pi r _{1}^{3}+\left( P +\frac{4 T }{ r _{2}}\right) \frac{4}{3} \pi r _{2}^{3}$
$=\left( P +\frac{4 T }{ r }\right) \frac{4}{3} \pi r ^{3}$
$PV +\frac{4 T }{3}\left(4 \pi r _{1}^{2}+4 \pi r _{2}^{2}-4 \pi r ^{2}\right)$
$3 pv +4 TS$