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Question

The end of a capillary tube with radius r is immersed in water. Assuming the tube to be sufficiently long, calculate the heat energy produced when the water rises in the tube.
[Assume angle of contact = 0 for glass-water system, ρ= density of water, T= surface tension of water]

A
2πT2ρg
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B
4πT2ρg
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C
0
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D
πT2ρg
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Solution

The correct option is A 2πT2ρg
Under equilibrium,
2πrT cos 0=πr2hρg [Force due to surface tension = net weight of water risen in the tube]
h=2Tρgr
Work done by surface tension =(2πrT)×h
=4πT2ρg
Potential energy of water in the tube :
V=mgh=πr2hρgh2 [centre of mass of water is at a height h2]
V=2πT2ρg
Heat Produced = (Work done by surface tension) - (Potential energy of water)
Heat Produced =4πT2ρg2πT2ρg=2πT2ρg

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