Question

One large soap bubble of diameter 'D' breaks into \(64\) bubbles having surface tension 'T'. The change in surface energy is

• A. \(2πTD^2\)
• B. \(4πTD^2\)
• C. \(6πTD^2\)
• D. \(8πTD^2\)

Hint:

A soap bubble has two surfaces; find the new radius from volume conservation.

Answer 1

The Correct Option is C

Step 1: Formula for n Droplets:
When a bubble splits into $n$ equal bubbles, $r=R\,n^{-1/3}$ and the energy change is $\Delta E=2T\cdot4\pi R^2\left(n^{1/3}-1\right)$, the factor 2 coming from the two surfaces.

Step 2: Numbers:
$n=64\Rightarrow n^{1/3}=4$. So $\Delta E=8\pi R^2T(4-1)=24\pi R^2T$.

Step 3: Substitute R = D/2:
$24\pi\dfrac{D^2}{4}T=6\pi TD^2$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C) } 6\pi TD^2} \]