Question

The surface tension and vapour pressure of water at ${20}^o$ C is $7.28\times {10}^{-2}N{m}^{-1}$ and $2.33\times {10}^3$ Pa respectively The radius of the smallest spherical water droplet which can form without evaporating at ${25}^o$ C is:

• A. $1.25\times {10}^{-5}m$
• B. $6.25\times {10}^{-5}m$
• C. $4.3\times {10}^{8}m$
• D. $3.4\times {10}^{3}m$

Answer 1

The correct option is B $6.25\times {10}^{-5}m$

Here, $S=7.28\times {10}^{-2}N{m}^{-1}$, $P=.2.33\times {10}^{3}Pa$

The drop will evaporate if the water pressure is greater than the vapour pressure P
As $P=\frac{2S}{R}$, where R is the radius of drop

$\therefore R=\frac{2S}{P}=\frac{2\times 7.28\times {10}^{-2}}{2.33\times {10}^3}=6.25\times {10}^{-5}m$