Question
$n$ drops of $a$ liquid, each with surface energy $E$, joining to form a single drop
✓
Answer
$\mathrm{E}=\mathrm{T} 4 \pi \mathrm{r}^{2} \Rightarrow \frac{4}{3} \pi \mathrm{R}^{3}=\mathrm{n} \times \frac{4 \pi}{3} \mathrm{r}^{3}$
$\Rightarrow \mathrm{n}=\frac{\mathrm{R}^{3}}{\mathrm{r}^{3}} \Rightarrow \mathrm{R}=\mathrm{n}^{1 / 3} \mathrm{r}$
Surface energy of big drop
$\mathrm{E}^{\prime}=\mathrm{T} 4 \pi \mathrm{R}^{2}=\mathrm{T} 4 \pi \mathrm{n}^{2 / 3} \mathrm{r}^{2}=\mathrm{En}^{2 / 3}$
Energy released
$=n \mathrm{E}-\mathrm{E}^{\prime}=\mathrm{nE}-\mathrm{n}^{2 / 3} \mathrm{E}=\mathrm{E}\left(\mathrm{n}-\mathrm{n}^{2 / 3}\right)$
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