Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water,the height of capillary rise will be smaller in hot water
Statement II : If a capillary tube is immersed first in cold water and then in hot water,the height of capillary rise will be smaller in cold water.
In the light of the above statements,choose the most appropriate from the options given below

Options

A. Both Statement I and Statement II are true
B. Statement I is true but Statement II is false
C. Statement I is false but Statement II is true
D. Both Statement I and Statement II are false

Answer

To solve the problem, we need to analyze the two statements regarding the behavior of a capillary tube immersed in cold and hot water.

### Step-by-Step Solution:

1. **Understanding Capillary Rise**:
The height of capillary rise (h) in a tube is given by the formula:
\[ h = \frac{2T \cos \theta}{\rho g R} \]
where:
- \( T \) = surface tension of the liquid,
- \( \theta \) = contact angle,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity,
- \( R \) = radius of the capillary tube.

2. **Analyzing Statement I**:
- Statement I claims that if a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
- Generally, the surface tension of water decreases with an increase in temperature. Therefore, the surface tension \( T \) in hot water is less than that in cold water.
- Since \( T \) is a crucial factor in determining the height of capillary rise, if the surface tension is lower in hot water, the height of capillary rise \( h \) will be smaller in hot water compared to cold water.
- Thus, Statement I is **incorrect**.

3. **Analyzing Statement II**:
- Statement II claims that if a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
- As established, the surface tension in cold water is higher than in hot water. Therefore, the capillary rise will be greater in cold water than in hot water.
- Thus, Statement II is **correct**.

4. **Conclusion**:
- Based on the analysis, Statement I is incorrect, and Statement II is correct. Therefore, the correct option is that Statement I is incorrect and Statement II is correct.

### Final Answer:
- Statement I is incorrect.
- Statement II is correct.