First slide

Surface tension

Question

The heat evolved for the rise of water when one end of the capillary tube of radius r is immersed vertically into water is (Assume surface tension = T, density of water = r)

Moderate

A

$\frac{2 π T}{ρ g}$
B

$\frac{π T^{2}}{ρ g}$
C

$\frac{2 π T^{2}}{ρ g}$
D

none of these

Solution

Capillary rise $h = \frac{2 T}{ρ r g} .$
Potential energy of water column
$U = \frac{m g h}{2} = \frac{m g}{2} (\frac{2 T}{r ρ g}) = \frac{m T}{ρ r} \Rightarrow \frac{π r^{2} h ρ T}{ρ r} \Rightarrow \frac{π r^{2} (\frac{2 T}{ρ r g})}{ρ r} = \frac{2 π T^{2}}{ρ g} .$
Work performed by force of surface tension $W = 2 π r T h = \frac{4 π T^{2}}{ρ g} .$
$∴$ Heat evolved = $W - U = \frac{2 π T^{2}}{ρ g} .$

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