Question

A capillary tube of inner diameter 0.5mm is dipped in a liquid of specific gravity 13.6 and surface tension $545\dfrac{{dyne}}{{cm}}$(angle of contact$130^\circ$). Find the depression or elevation in the tube:
A) Depressed 2.11 cm.
B) Elevated 2.11 cm.
C) Depressed 3.71 cm.
D) Elevated 3.71 cm.

Answer 1

A capillary tube is the tube which has very small diameter and has very long length. The capillary tube will have capillary action and the liquid will rise to the top of the capillary of the tube and there can be seen a depression or elevation on the liquid.

Formula used: The formula of the depression in the capillary tube is given by,
$\Rightarrow h = \dfrac{{4\sigma \cos \theta }}{{\rho gd}}$
Where the height is h, the surface tension is$\sigma$, the density is$\rho$, the angle of contact is$\theta$ and the diameter of the tube is$d$.

Complete step by step solution:
It is given in the problem that a capillary tube of inner diameter 0.5mm is dipped in a liquid of specific gravity 13.6 and surface tension $545\dfrac{{dyne}}{{cm}}$(angle of contact$130^\circ$) and we need to find the depression or elevation in the tube.
The formula of the depression in the capillary tube is given by,
$\Rightarrow h = \dfrac{{4\sigma \cos \theta }}{{\rho gd}}$
Where the height is h, the surface tension is$\sigma$, the density is$\rho$, the angle of contact is$\theta$ and the diameter of the tube is$d$.
The surface tension is$545\dfrac{{dyne}}{{cm}}$, the angle of contact is$130^\circ$, the density is $0 \cdot 0136\dfrac{{kg}}{{c{m^3}}}$.
$\Rightarrow h = \dfrac{{2\sigma \cos \theta }}{{\rho gr}}$
$\Rightarrow h = \dfrac{{2 \times 545 \times {{10}^{ - 3}} \times \cos {{130}^\circ }}}{{0 \cdot 0136 \times 980 \cdot 65 \times 0 \cdot 025}}$
$\Rightarrow h = - 2 \cdot 101cm$
The depression in the capillary tube is equal to, $h \approx 2 \cdot 11cm$.

The correct option for this problem is option A.
As the angle of contact is more than right angle and therefore there will be depression in the tube due to the more cohesive force than the adhesive force.

Note: The capillary tube can have liquid which will form upper meniscus if the angle of contact is greater than right angle and lower meniscus which in case the angle of contact is less than the right angle. In the lower meniscus there is wetting of the glass but in the upper meniscus there is less wetting on the tube surface.