A capillary tube sealed at the top has an internal radius of r = 0.05 cm. The tube is placed vertically in water, open and first.
What should be the length of such a tube be for the water in it to rise in these conditions to a height h = 1 cm? The pressure of the air is P 0 = 1 atm. The surface tension of water is α = 70 dyn/cm.
Text Solution
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Sol. After rising to a height h in the tube the water will compress the air contained in it and produce an excess pressure 
P which can be calculated by Boyle's law and will be equal to
P = P – P 0 = 
The pressure P 1 = 
produced by surface tension should in our case balance the sum of the pressures created by the weight of the water column and by the air compressed in the capillary, i.e., the following equality should hold
= 
+dgh (d is the density of water)
From which the formula for l can be calculated.
l = 
+ h 
552 cm.
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