A vertical capillary is brought in contact with the water surface. What amount of heat is liberated while the water rises along the capillary ? The wetting is assumed to be complete, the surface tension equals `alpha`.

Explanation

If the liquid rises to a height `h`, the energy of the liquid column becomes
`E = rho g pi r^2 h. (h)/(2) - 2pi rh alpha = (1)/(2) rho g pi (r h - 2(alpha)/(rho g))^2 - (2 pi alpha^2)/(rho g)`
This is minimum when `rh = (2 alpha)/(rho g)` and that is relevant height to which water must rise.
At this point, `E_(min) = - (2 pi alpha^2)/(rho g)`
Since `E = 0` in the absence of surface tension a heat `Q = (2 pi alpha^2)/(rho g)` must have been liberated.