Question

If S and V are the change in surface area and volume, when two soap bubbles coalesce under isothermal condition, then ($\sigma$ is surface tension, $P_o$ is atmospheric pressure)

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let a and b be the radius of two soap bubbles forming a soap bubble of radius c. Then
$(P_o+\frac{4\sigma }{a})\frac{4}{3}\pi a^3+\frac{4}{3}\pi b^3(P_o+\frac{4\sigma }{b})=(P_o+\frac{4\sigma }{c})\frac{4}{3}\pi c^3$
i.e., $P_o\left[\frac{4}{3}\pi \right(a^3+b^3-c^3\left)\right]=4\sigma \left[\frac{4}{3}\pi \right(c^2-a^2-b^2\left)\right]$
$P_{o}V=-\frac{4\sigma S}{3}$
$3P_{o}V+4\sigma S=0$
So choice (1) is correct and the rest are wrong