First slide

Surface tension

Question

A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

Moderate

A

Energy = $4 VT (\frac{1}{r} - \frac{1}{R}) is released$
B

Energy = $3 VT (\frac{1}{r} + \frac{1}{R}) is absorbed$
C

Energy = $3 VT (\frac{1}{r} - \frac{1}{R}) is released$
D

Energy is neither released nor absorbed

Solution

Energy released = ( $A_{f} - A_{i}$ )T
$A_{f} = 4 {πR}^{2} = \frac{3}{3} 4 π \frac{R^{3}}{R} = \frac{3 V}{R}$
$A_{i} = n \times 4 {πr}^{2} = \frac{V}{\frac{4}{3} {πr}^{3}} 4 {πr}^{2} = \frac{3 V}{r}$
$\Rightarrow Energy released = 3 VT [\frac{1}{r} - \frac{1}{R}]$

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