A capillary of radius r is lowered into a wetting agent with surface tension α and density d. Determine the height h 0 to which the liquid will rise in the capillary. Calculate the work done by surface tension and the potential energy acquired by the liquid in the capillary and compare the two. Explain the difference in the results obtained.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. The height to which the liquid rises in the capillary is h 0 = 
. The work done by surface tension in this case is A = Fh 0 = 
. The potential energy of the liquid raised in the in the capillary is
U = mg 
=dg π r 2 h 0 
= 
or U = 
Only half of the work done by surface tension is converted into the potential energy of the liquid. The other half is expended on the work against the forces of friction and is converted into heat. If there were no viscosity and friction against the walls, the liquid level would perform harmonic oscillations in the capillary with the height h 0 as the position of equilibrium.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems