The height to which water rises in a capillary will be

Options

A. maximum at `4^(@)C`
B. maximum at `0^(@)C`
C. minimum at `0^(@)C`
D. minimum at `4^(@)C`

Answer

To determine the height to which water rises in a capillary tube, we can use the formula for capillary rise:

\[ H = \frac{2 \gamma \cos \theta}{\rho g r} \]

Where:
- \( H \) = height of the liquid column in the capillary
- \( \gamma \) = surface tension of the liquid
- \( \theta \) = angle of contact
- \( \rho \) = density of the liquid
- \( g \) = acceleration due to gravity
- \( r \) = radius of the capillary tube

### Step-by-Step Solution:

1. **Understanding the Variables**:
- The height of the liquid column \( H \) is influenced by the surface tension \( \gamma \), the angle of contact \( \theta \), the density \( \rho \), the acceleration due to gravity \( g \), and the radius \( r \) of the capillary tube.

2. **Density of Water**:
- The density of water varies with temperature. It reaches its maximum value at 4 degrees Celsius.

3. **Relationship Between Height and Density**:
- From the formula, we can see that height \( H \) is inversely proportional to the density \( \rho \). This means that as the density increases, the height \( H \) decreases.

4. **Analyzing the Temperature Effect**:
- Since the density of water is maximum at 4 degrees Celsius, we can conclude that at this temperature, the height \( H \) will be minimum because the density is at its highest.

5. **Conclusion**:
- Therefore, the height to which water rises in a capillary tube is minimum at 4 degrees Celsius.

6. **Final Answer**:
- The correct option is: **Minimum at 4 degrees Celsius**.