Question

A capillary tube of radius r is dipped into a wetting liquid with a surface tension a and density d. Find the height to which the liquid rises in the capillary. Calculate the work done by the surface tension forces and compare this work with the results of an independent calculation of the gain in the potential energy stored by the liquid in the capillary. Explain the significance of the disparity in the results obtained.

Answer 1

The height to which the liquid rises in the capillary tube is h₀ = 2α/dgr. The work done by the surface tension forces is A = Fh₀ = 4πα²/dg. The store of potential energy in the liquid after it rises in the capillary tube is

Only half the work done by the forces of surface tension is converted into potential energy of the liquid. The other half goes into the work against the forces of friction and into heat. If the forces of viscosity and friction on the walls are absent, the level of the liquid would execute harmonic oscillations about the height h₀ as a position of equilibrium.