The heal evolved for the rise of water when one cnd of the capillary tube of radius r is immersed vertically into water is (Assume surface tension = T and density of water to be rho)

Options

A. `(2piT)/(rhog)`
B. `(2piT^2)/(rhog)`
C. `(piT^2)/(rhog)`
D. None of these

Answer

C

Explanation

Rise in water level,`h=(2T)/(rhogr)`
Potential energy,`U=(mgh)/2 =(4piT^(2))/(rhog)`
Work done by surface tension,`W=2pirTh`
`2pirT xx(2T)/(rho gr) =(2pi T^(2))/(rhog)`
Heat evolved, Q=W-U
`=(4pi T^(2))/(rhog) - (2pi T^(2))/(rhog) = (2pi T^(2))/(rhog)`