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Question

The lower end of a capillary tube of radius r is placed vertically in water, then with the rise of water in the capillary, heat involved is:

A
+πr2h2dg2J
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B
+πr2h2dgJ
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C
πr2h2dg2J
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D
πr2h2dgJ
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Solution

The correct option is D +πr2h2dg2J
When the tube is placed vertically in water, water rises through height h given by
h=2Tcosθrdg
Upward force =2πr×Tcosθ
Work done by this force in raising water column through height h is given by
ΔW=(2πrTcosθ)h=(2πrhcosθ)T=(2πrhcosθ)(rhdg2cosθ)=πr2h2dg
However, the increase in potential energy ΔEp of the raised water column =mgh2
where m is the mass of the raised column of water
Thus m=πr2hd
So ΔEp=(πr2hd)(hg2)=πr2h2dg2
Further
ΔWΔEp=πr2h2dg2
The part ΔWΔEp is used in doing work against viscous forces and frictional forces between water and

glass surface and appears as heat. So heat released =ΔWΔEpJ=πr2h2dg2J

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