Answer :

Final answer:

Capillarity is the ability of a liquid to rise in a narrow tube against gravity, due to intermolecular forces between the liquid and the tube's surface. The capillary rise is calculated by comparing the upward force from surface tension and the adhesive forces to the downward gravitational force. The height of the liquid rise is inversely proportional to the tube's radius.

Explanation:

Understanding Capillarity and the Ascent Formula

The phenomenon of capillarity or capillary action refers to the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. This occurs due to the intermolecular attractive forces between the liquid and the surrounding solid surfaces. If the tube is sufficiently small, the combination of surface tension (caused by cohesion within the liquid) and adhesive forces between the liquid and the container lift the liquid.

To derive the ascent formula for the rise of liquid in a capillary tube, we consider several factors such as the surface tension of the liquid, the angle of contact between the liquid and the tube, the inside radius of the tube, the density of the liquid, and the acceleration due to gravity. The capillary rise is the result of the competition between the upward capillary force and the downward gravitational force. The height to which the liquid will rise, h, is given by the equation:

h = (2 * Surface Tension * cos(Angle of contact)) / (Density of liquid * acceleration due to gravity * radius of tube)

This equation shows that the smaller the diameter of the capillary tube, the higher the liquid can rise, due to the relationship between the surface area within the tube and the perimeter. Because the force of capillarity is proportional to the perimeter while the gravitational force relies on the cross-sectional area, a smaller diameter results in a larger relative upward force due to capillarity.

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