Question 47: Properties of Matter

Question

Given below are two statements :
Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

Option D, "Statement I is true but Statement II is false," is the correct choice. Here's an explanation for both statements:
Statement I: True
The contact angle between a solid and a liquid is indeed a measure of the wettability of the solid surface by the liquid. The contact angle is determined by the nature of both the solid and the liquid. It is a function of the interfacial tensions between solid-liquid ($ \gamma_{	ext{SL}} $), solid-vapor ($ \gamma_{	ext{SV}} $), and liquid-vapor ($ \gamma_{	ext{LV}} $). This relationship can be understood through Young's equation:
$ \cos 	heta = \frac{\gamma_{	ext{SV}} - \gamma_{	ext{SL}}}{\gamma_{	ext{LV}}} $
Where $ 	heta $ is the contact angle. Therefore, since the interfacial tensions vary with the materials in contact, the contact angle is indeed a property of the materials of both the solid and the liquid.
Statement II: False
The rise of a liquid in a capillary tube is strongly dependent on the inner radius of the tube. This relationship is described by the Jurin's Law, which states the height ($ h $) to which a liquid will rise (or fall) in a capillary tube is inversely proportional to the radius ($ r $) of the tube, among other factors. The law is given by:
$ h = \frac{2\gamma \cos 	heta}{ho g r} $
Where:
$ \gamma $ is the liquid-air surface tension,
$ 	heta $ is the contact angle,
$ ho $ is the density of the liquid,
$ g $ is the acceleration due to gravity,
$ r $ is the radius of the capillary tube.
As seen from the equation, $ h $ is inversely proportional to $ r $. Therefore, the rise of the liquid indeed depends on the inner radius of the tube, making Statement II false.

Answer

Both Statement I and Statement II are false.

Answer

Both Statement I and Statement II are true.

Answer

Statement I is false but Statement II is true.

Answer

Statement I is true but Statement II is false.

Properties of Matter

Choose the correct answer: