The end of a capillary tube is immersed into a liquid. Liquid slowly rises in the tube up to some height. The capillary-fluid system

Options

A. will absorb heat
B. will release heat
C. will not be involved in any heat transfer
D. nothing can be said

Answer

To solve the problem regarding the capillary rise of a liquid in a capillary tube, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Capillary Action**:
Capillary action occurs due to the adhesive forces between the liquid and the walls of the tube, and the cohesive forces within the liquid itself. The height to which the liquid rises in the tube can be described by the formula:
\[ h = \frac{2 \gamma \cos \theta}{\rho g r} \]
where:
- \( h \) = height of the liquid column,
- \( \gamma \) = surface tension of the liquid,
- \( \theta \) = contact angle between the liquid and the tube,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity,
- \( r \) = radius of the capillary tube.

2. **Identify Given Values**:
In the problem, we need to identify the values for surface tension (\( \gamma \)), contact angle (\( \theta \)), density (\( \rho \)), gravitational acceleration (\( g \)), and the radius of the capillary tube (\( r \)).

3. **Substitute Values into the Formula**:
Once we have all the required values, we substitute them into the capillary rise formula to calculate the height \( h \).

4. **Calculate the Height**:
Perform the calculations to find the height \( h \) at which the liquid rises in the capillary tube.

5. **Interpret the Result**:
Analyze the result to understand how the height of the liquid column relates to the properties of the liquid and the tube.