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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 $=T$ and density of water to be p)
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The correct answer is:
$\frac{2 \pi T^2}{\rho g}$
Water rise to height, $h=\frac{2 T}{\rho g r}$
Potential energy of water column,
$U=\frac{m g h}{2}=\frac{2 \pi T^2}{\rho g}$
The work performed by force of surface tension is
$W=2 \pi r T h=\frac{4 \pi T^2}{\rho g}$
From conservation of energy the heat evolved,
$Q=W-U=\frac{2 \pi T^2}{\rho g}$
Potential energy of water column,
$U=\frac{m g h}{2}=\frac{2 \pi T^2}{\rho g}$
The work performed by force of surface tension is
$W=2 \pi r T h=\frac{4 \pi T^2}{\rho g}$
From conservation of energy the heat evolved,
$Q=W-U=\frac{2 \pi T^2}{\rho g}$
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