Discuss how the rise of water in capillary tube is used to determine the surface tension of water?

The rise of water in a capillary tube is a result of the cohesive forces between water molecules being stronger than the adhesive forces between water molecules and the walls of the tube. This phenomenon is known as capillary action.

To determine the surface tension of water using the rise of water in a capillary tube, the following steps are typically followed:

1. A clean and dry capillary tube is carefully inserted into a container of water, ensuring that the water level inside the tube is slightly higher than the water level outside the tube.

2. The height of the water column inside the capillary tube is measured using a ruler or a similar measuring device.

3. The diameter of the capillary tube is also measured.

4. The surface tension of water can then be calculated using the following formula:

Surface tension = (2 * height * density * gravity) / (diameter * (1 + cosθ))

Where:
- height is the height of the water column in the capillary tube
- density is the density of water
- gravity is the acceleration due to gravity
- diameter is the diameter of the capillary tube
- θ is the contact angle between the water and the walls of the capillary tube

By measuring the height of the water column in the capillary tube and the diameter of the tube, and using the above formula, the surface tension of water can be determined. This method is commonly used in laboratories to accurately measure the surface tension of liquids, including water.

Principle:

The rise of water in a capillary tube is a phenomenon governed by the balance between surface tension and gravitational forces. Surface tension is the tendency of a liquid surface to minimize its area and acts as an inward force at the liquid-air interface.

Experimental Setup:

1. Take a clean glass capillary tube of known radius (r).
2. Dip the capillary tube vertically into a beaker of water.
3. Observe the rise of water inside the tube.
4. Measure the height (h) of the water column above the water level in the beaker.

Derivation:

The surface tension force (F) acting on the water inside the capillary tube is given by:

```
F = 2πrσ
```

where:

- σ is the surface tension of water
- r is the radius of the capillary tube

The upward gravitational force (W) acting on the water column is given by:

```
W = πr²hρg
```

where:

- h is the height of the water column
- ρ is the density of water
- g is the acceleration due to gravity

Equilibrium Condition:

At equilibrium, the surface tension force and the gravitational force are balanced:

```
2πrσ = πr²hρg
```

Solving for Surface Tension:

Solving for σ, we get:

```
σ = (hρg)/2
```

Determination of Surface Tension:

1. Measure the height of the water column (h) in the capillary tube.
2. Know the radius of the capillary tube (r).
3. Use the density of water (ρ = 1000 kg/m³ at 20°C) and the acceleration due to gravity (g = 9.81 m/s²) in the above equation.
4. Calculate the surface tension of water (σ).

Advantages:

- Simple and inexpensive experimental setup.
- Provides an accurate measurement of surface tension.
- Suitable for studying the effects of temperature and impurities on surface tension.

Limitations:

- The capillary tube should be thoroughly cleaned and free of impurities.
- The water should be degassed to eliminate dissolved gases that could affect the surface tension.
- The capillary tube size should be small enough to ensure capillary rise but not so small that the meniscus becomes curved.

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