First slide

Surface tension

Question

Calculate the energy spent in spraying a drop of mercury of r radius into N droplets all of same size. If the surface tension of mercury is T.

Moderate

A

$4 {πR}^{2} T (N^{\frac{1}{3}} - 1)$
B

$2 R^{2} T (N^{\frac{1}{3}} - 1)$
C

$4 {πR}^{2} T (N^{\frac{2}{3}} - 1)$
D

none of these

Solution

$∆ U = N (4 π_{1}^{2}) T - 4 {πR}^{2} T$
= 4 $πT ({Nr}_{1}^{2} - R^{2})$ -----------------(i)
By mass conservation
$N (\frac{2}{3} {πr}_{1}^{3} ρ) = \frac{4}{3} {πR}^{3} ρ$
$r_{1} = \frac{R}{{(N)}^{\frac{1}{3}}}$ ------------(ii)
Substitute $r_{1}$ from equation (ii) in equation (i).
$∆ U = 4 {πR}^{2} T (N^{\frac{1}{3}} - 1)$

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