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explain-capillarity-with-examples

๐Ÿš€ Capillarity, also known as capillary action, is the ability of a liquid to flow in narrow spaces without the assistance of external forces. This phenomenon occurs due to the interplay of cohesive forces (the attraction between molecules of the same substance) and adhesive forces (the attraction between molecules of different substances). In capillarity, when a liquid comes into contact with a solid surface, the adhesive forces can cause the liquid to rise or fall in a narrow tube or space, depending on the relative strengths of these forces. This concept is crucial in various natural and technological processes, such as the movement of water in plants and the functioning of ink pens.

Theory Explanation

Understanding Cohesive and Adhesive Forces

Cohesive forces are the intermolecular forces that hold the molecules of a liquid together. Adhesive forces, on the other hand, are the forces of attraction between the liquid molecules and the molecules of a solid surface. In capillarity, if the adhesive forces are stronger than the cohesive forces, the liquid will rise in the tube. Conversely, if cohesive forces are stronger, the liquid will be depressed.

Capillary Rise in a Narrow Tube

When a narrow tube is placed vertically in a liquid, the liquid will either rise or fall in the tube depending on the nature of the liquid and the tube material. For example, water will rise in a glass tube due to strong adhesive forces between water molecules and glass. The height to which the liquid rises can be calculated using the formula: h = (2ฮณ cos ฮธ) / (ฯg r), where ฮณ is the surface tension, ฮธ is the contact angle, ฯ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.

\[ h = \frac{2\gamma \cos \theta}{\rho g r} \]
Factors Affecting Capillarity

The height of the liquid column in capillarity is influenced by several factors: the radius of the tube (smaller radius leads to higher rise), the surface tension of the liquid (higher surface tension leads to higher rise), the density of the liquid (lower density leads to higher rise), and the contact angle (acute angles lead to rise, obtuse angles lead to depression).

Key Points

  • ๐ŸŽฏ Capillarity is the result of the balance between cohesive and adhesive forces.
  • ๐ŸŽฏ The height of liquid rise in a capillary tube can be calculated using a specific formula.
  • ๐ŸŽฏ Smaller tube radius results in higher liquid rise due to increased adhesive forces.

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Examples:💡

Calculate the height to which water will rise in a glass capillary tube of radius 0.5 mm. Given that the surface tension of water is 0.072 N/m and the contact angle is 0 degrees.

Solution:

Step 1: Convert the radius from mm to meters: r = 0.5 mm = 0.0005 m.

Step 2: Use the formula h = (2ฮณ cos ฮธ) / (ฯg r). Assume the density of water ฯ = 1000 kg/mยณ and g = 9.81 m/sยฒ.

\[ h = \frac{2 \times 0.072 \times \cos(0)}{1000 \times 9.81 \times 0.0005} \]

Step 3: Calculate h: h = (0.144) / (0.004905) = 29.33 m.

Common Mistakes

  • Mistake: Confusing cohesive and adhesive forces, leading to incorrect predictions about liquid behavior in capillarity.

    Correction: Remember that cohesive forces pull molecules together, while adhesive forces pull molecules towards different substances.

  • Mistake: Neglecting to convert units properly when using the capillarity formula, leading to calculation errors.

    Correction: Always ensure that all measurements are in SI units before substituting them into formulas.

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