# Measuring Water Surface Tension: Capillary Rise Method
> Learn to determine the surface tension of water using the capillary tube method with Jurin's Law, force derivations, and laboratory procedures.

Tags: physics-experiment, surface-tension, capillary-rise, fluid-mechanics, undergraduate-physics, jurin-law, laboratory-guide
## Determination of Surface Tension of Water
*   **Method:** Capillary Rise Method
*   **Context:** Undergraduate Physics Laboratory

## Theory: What is Surface Tension?
*   **Surface Tension (T):** Property of liquid surfaces resisting external force due to cohesive molecules.
*   **Cohesion:** Attraction between like molecules (water-water).
*   **Adhesion:** Attraction between unlike molecules (water-glass).
*   In capillary tubes, adhesion > cohesion, causing concave meniscus and rise.

## Apparatus Required
*   Capillary tubes (fine uniform bore).
*   Traveling microscope (0.001 cm precision).
*   Adjustable stand, beaker, pointer (index pin).
*   Thermometer and cleaning agents (Chromic/Nitric acid).

## Jurin's Law
*   **Formula:** T = (r h ρ g) / (2 cosθ)
*   **Variables:** T (Surface Tension), h (Height), r (Radius), ρ (Density), g (Gravity 9.8 m/s²).
*   **Assumption:** For clean glass-water, θ ≈ 0, so cosθ ≈ 1.

## Force Balance Derivation
*   **Upward Force:** F_up = 2πr T cosθ
*   **Downward Force (Weight):** W = πr²h ρ g
*   **Equilibrium:** 2πr T cosθ = πr²h ρ g, leading to the solving of T.

## Procedure: Setup & Cleaning
*   Clean tube with chromic acid to remove grease (grease alters contact angle).
*   Clamp tube vertically using a plumb line.
*   Adjust index pin to touch the water surface outside the tube.

## Procedure: Measurement
1. Focus microscope on the meniscus (Reading A).
2. Focus on the pointer tip at water surface (Reading B).
3. Calculate h = Reading A - Reading B.
4. Measure internal diameter in perpendicular directions to find mean radius (r).

## Precautions
*   Absolute cleanliness of glass is required.
*   Avoid air bubbles and parallax error.
*   Temperature must be stable as T decreases with increasing temperature.

## Conclusion
*   **Result:** Surface tension of water at 20°C is approximately 72.8 mN/m.
*   **Core Relationship:** Height (h) is inversely proportional to radius (r).
---
This presentation was created with [Bobr AI](https://bobr.ai) — an AI presentation generator.