Q134 / 160 · TS EAMCET 2005 · Physics

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)

  • A
    $\frac{2 \pi T}{\rho g}$
  • B
    $\frac{\pi T^2}{\rho g}$
  • Correct answer
    C
    $\frac{2 \pi T^2}{\rho g}$
  • D
    None of these

Solution

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, $Q=W-U=\frac{2 \pi T^2}{\rho g}$

Hence, the correct answer is option: 'C'.

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