216 small identical liquid drops each of surface area A coalesce to form a bigger drop. If the surface…

216 small identical liquid drops each of surface area A coalesce to form a bigger drop. If the surface tension of the liquid is T, the energy released in the process is
  1. 360 AT
  2. 180 AT
  3. 90 AT
  4. 120 AT

Solution

$\begin{aligned} & \mathrm{V}_{\mathrm{i}}=\mathrm{V}_{\mathrm{f}} \Rightarrow 216 \times \frac{4}{3} \pi \mathrm{r}^3=\frac{4}{3} \pi \mathrm{R}^3 \\ \therefore \quad & \mathrm{R}=\sigma \mathrm{r}\end{aligned}$ $\begin{aligned} & \therefore \quad \text { Energy released, } \mathrm{E}=216 \mathrm{AT}-4 \pi \mathrm{R}^2 \cdot \mathrm{~T} \\ & =216 \mathrm{AT}-4 \pi(6 \mathrm{r})^2 \cdot \mathrm{~T}\end{aligned}$ $\begin{aligned} & =216 \text { AT }-36 \mathrm{AT} \\ & =180 \mathrm{AT}\end{aligned}$

Asked in: AP EAMCET 2024 (18 May Shift 1)

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