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The surface tension and vapour pressure ...

The surface tension and vapour pressure of water at `20^(@)C` is `7.28xx10^(-2)Nm^(-1)and2.33xx10^(3)` Pa ,respectively .What is the radius of the smallest spherical water droplet which can form without evaporating at `20^(@)C`?

Text Solution

Verified by Experts

Surface tension of water `S=7.28xx10^(-2)N//m`
Vapour pressure `P=2.33xx10^(3)P_(a)`
The drop will evaporate if the water pressure on liquid is greater than vapour pressure above the surface of liquid.
Vapour pressure without evaporation =excess pressure in a drop
`P=P_(i)-P_(o)`
`P=(2S)/(R) " " (because "For drop"P_(i)-P_(o)=(2rho)/(R))`
`thereforeR=(2S)/(P)`
`thereforeR=(2xx7.28xx10^(-2))/(2.33xx10^(3))`
`R=6.25xx10^(-5)m`
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