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 =$T$ and density of water = $\rho$)
A) $\frac{2\pi T}{\rho g}$
B) $\frac{\pi T^{2}}{\rho g}$
C) $\frac{2\pi T^{2}}{\rho g}$
D) None of these
Explanation
(c) $Water\ rise\ to\ height\ h = \frac{2T}{\rho g\ r}\ \ \ $
Potential energy of water column
$U = \frac{mgh}{2} = 2\pi T^{2}/\rho g$
The work performed by force of surface tension is
$W = 2\pi r\ T\ h = \frac{4\pi T^{2}}{\rho g}$
From conversation of energy the heat evolved
$Q = W - U = \frac{2\pi T^{2}}{\rho g}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.