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A glass capillary sealed at the upper en...

A glass capillary sealed at the upper end is of length `0.11m `and diameter `2xx10^(5)`m.The tube is immersed vertically into a liquid of surface tension `5.06xx10^(-2)N//m`. To what length has the capillary to be immeresed so that the liquid levels inside and outside the capillary become the same? What will happen to the water levels inside the capillary if the seal is now broken?

Text Solution

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Let `P_(0)` be atmospheric and `P_(1)` the pressure of air witin the sealed tube. Then for equilibrium pressure just below the menicus should be equal to atmospheric pressure because levels of water inside and outside the tube is same.

i.e., `(P_(1)-(2T)/r)=p_(0)` or `P_(1)=P_(0)+(2T)/r`
If `L=0.11m` is the length of tube and `x` the length of immersed part then from Boyle's law
`p_(1)V_(1)=p_(2)V_(2)`
`P_(0)La=(P_(0)+(2T)/r)(L-x)a`
where `a` is the corss sectional area of tube,
i.e., `P_(0)xxL=(P_(0)+(2T)/r)(L-x)`
`P_(0)xxL=P_(0)(L-x)+(2T)/r (L-x)`
i.e., `P_(0)x=(2T)/r (L-X)`
`1.012xx10^(5)xx x+(2xx5.06xx10^(-2))/(1xx10^(-5))(0.11-x)`
solving for `x` we get `x=0.01m`
Length of capillary to be immersed `0.01m`
If seal is broken the water level in the capillary rises.
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