Question

A capillary tube $A$ is dipped in water. Another identical capillary tube $B$ is dipped in soap- water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? Consider the surface tension of soap solution and water to be $0.073\text{N/m}$ and $0.025\text{N/m}$ respectively at room temperature.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The capillary rise is given by,
$h=\frac{2T\cos \theta }{\rho rg}...\left(i\right)$.
The soap solution and water both wet the side of the capillary tube.
$\Rightarrow$The angle of contact for soap solution with glass, and the angle of contact for water with glass will both be acute ($\theta <{90}^{\circ }$).
Hence, the shape of the meniscus for water and soap both will be concave (concavity being higher for water-meniscus)

Since soap solution has a greater tendency to stick to the wall of the tube, the angle of contact for soap-solution will be lesser.
i.e ${\theta }_{\text{soap}}<{\theta }_{\text{water}}$
The surface tension of soap solution is reduced to a much higher extent (i.e approx $3$ times lesser then that of water), due to presence of surfactants.
i.e $T_{\text{soap}}<T_{\text{water}}$

The increase in value of $\cos \theta$ for soap solution will be lesser compared to the reduction in its surface tension, because both solutions are wetting in nature.
Hence from Eq.$\left(i\right)$ due to dominance of decrease in surface tension, $h_{\text{soap}}<h_{\text{water}}$
The value of height $h$ to which the liquid rises in the capillary tube will be less for soap solution than for water.
$\therefore$ Higher rise of liquid in $A$ with concave meniscus, represents water. The correct choice is $\left(d\right)$