Water rises in a clean glass capillary tube to a height h given by

where r is the radius of the tube, ρ is the density of water, equal to 998.2 kg m^ˆ’3 at 20 ^—¦C, g is the acceleration due to gravity, equal to 9.80 m s^ˆ’2, h is the height to the bottom of the meniscus, and γ is the surface tension of the water. The term r/3 corrects for the liquid above the bottom of the meniscus.
(a) If water at 20 ^—¦C rises to a height h of 29.6 mm in a tube of radius r = 0.500 mm, find the value of the surface tension of water at this temperature.
(b) If the height h is uncertain by 0.4 mm and the radius of the capillary tube is uncertain by 0.02 mm, find the uncertainty in the surface tension.
(c) The acceleration due to gravity varies with latitude. At the poles of the earth it is equal to 9.83 m s^ˆ’2. Find the error in the surface tension of water due to using this value rather than 9.80 m s^ˆ’2, which applies to latitude 38^—¦.

Transcribed Image Text:

2y h+ pgr || 3.