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With an increase in temperature, the angle of contact:(A) Decrease(B) Increase(C) remains constant(D) sometimes increases and sometimes decrease

Last updated date: 14th Sep 2024
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Hint The angle of contact, as shown in the figure is the angle $\theta$, which is formed with the water meniscus and the tube surface. As temperature increases, the surface tension of the liquid decreases and vice versa.

Complete Step by step solution On the increasing temperature, adhesion increases and cohesive forces decrease. The increase in temperature also causes the surface tension to decrease due to more molecular vibrations among the liquid molecules. The rise in temperature of the liquid causes an increase in the adhesive forces between the tube and the liquid molecules. Similarly, on an increase in temperature, the cohesive forces between the liquid molecules decrease. This causes the surface tension to decrease and the angle of contact to increase as shown below.
The surface tension $S$ and the angle of contact $\theta$ are related as, $\frac{{2S}}{{r\cos \theta }} = \rho gh$.
In this equation, for the L.H.S. to remain constant, as $S$ decreases with a temperature rise in temperature, $\cos \theta$ should also decrease. Thus, the angle $\theta$ should increase.
The angle of contact $\theta$, and the absolute temperature $T$, are thus related as $\theta \propto T$.
In the case of the above solution, we ignore the changes (if any), in the height and density of the liquid with respect to changes in temperature.

Therefore, the correct answer is an option (B).

Note Highly soluble impurities increase surface tension since adhesive forces between liquid and impurity molecules increase because of stronger intermolecular forces of attraction. The sparingly soluble impurities decrease the surface tension since the adhesive forces between the liquid molecule and the impurity molecule become less than the cohesive forces among the liquid molecules.