The surface tension and vapour pressure of a liquid at $25^{\circ} \mathrm{C}$ are $8 \times 10^{-2}…

The surface tension and vapour pressure of a liquid at $25^{\circ} \mathrm{C}$ are $8 \times 10^{-2} \mathrm{Nm}^{-1}$ and $2.5 \times 10^3 \mathrm{~Pa}$ respectively. The radius of the smallest spherical water droplet which can from without evaporating at $25^{\circ} \mathrm{C}$ is
  1. $64 \mu \mathrm{m}$
  2. $30 \mu \mathrm{m}$
  3. $60 \mu \mathrm{m}$
  4. $32 \mu \mathrm{m}$

Solution

The drop will evaporate if the water pressure is greater than the vapour pressure $\mathrm{P}$. As $\mathrm{P}=\frac{2 \mathrm{~S}}{\mathrm{R}}$, where $\mathrm{R}=$ radius of drop $\begin{aligned} & \mathrm{R}=\frac{2 \mathrm{~S}}{\mathrm{P}}=\frac{2 \times 8 \times 10^{-2}}{2.5 \times 10^3}=6.4 \times 10^{-5} \mathrm{~m} \\ & =64 \mu \mathrm{m}\end{aligned}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

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