First slide

Surface tension

Question

Due to capillary rise in a vertical capillary tube, mass of water in the tube is m and rise of water is h. Then heat generated during the process of capillary rise is

Moderate

A

$\frac{1}{4} mgh$
B

zero
C

$\frac{1}{2} m g h$
D

$\frac{3}{4} m g h$

Solution

Capillary rise $h = \frac{2 Tcosθ}{ρrg}$
Mass of liquid in the tube, $m = {πr}^{2} . h . ρ = \frac{2 πrTcosθ}{g}$
W = Work done by surface tension force
$= 2 πrTcosθ \times h = mgh$
Gravitational potential energy stored in the system $U = mg . \frac{h}{2}$
$∴$ Heat generated $= W - U = mgh - \frac{1}{2} mgh = \frac{1}{2} mgh$

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