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Q.

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)

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a

2πTρg

b

πT2ρg

c

2πT2ρg

d

none of these

answer is C.

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Detailed Solution

Capillary rise h=2Tρrg.Potential energy of water column U=mgh2=mg22Trρg=mTρr⇒πr2hρTρr⇒πr22Tρrgρr = 2πT2ρg.Work performed by force of surface tension W= 2πrTh= 4πT2ρg.∴ Heat evolved = W−U=2πT2ρg.

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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)