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 :

<p>Option D, "Statement I is true but Statement II is false," is the correct choice. Here's an explanation for both statements:</p> <p><strong>Statement I: True</strong></p> <p>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_{\text{SL}} $), solid-vapor ($ \gamma_{\text{SV}} $), and liquid-vapor ($ \gamma_{\text{LV}} $). This relationship can be understood through Young's equation:</p> <p>$ \cos \theta = \frac{\gamma_{\text{SV}} - \gamma_{\text{SL}}}{\gamma_{\text{LV}}} $</p> <p>Where $ \theta $ 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.</p> <p><strong>Statement II: False</strong></p> <p>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 $) of the tube, among other factors. The law is given by:</p> <p>$ h = \frac{2\gamma \cos \theta}{\rho g r} $</p> <p>Where:</p> <ul> <li>$ \gamma $ is the liquid-air surface tension,</li> <li>$ \theta $ is the contact angle,</li> <li>$ \rho $ is the density of the liquid,</li> <li>$ g $ is the acceleration due to gravity,</li> <li>$ r $ is the radius of the capillary tube.</li> </ul> <p>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.</p>