Question

Given below are two statements:
Statement 1: 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 2: 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 option from the options given below:

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

Answer 1

The Correct Option is B

1. Understanding Capillary Rise

The height of capillary rise \(h\) is given by:

\[ h = \frac{2T \cos \theta}{\rho g r} \]

Where \(T\) is the surface tension, \(\theta\) is the contact angle, \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(r\) is the radius of the capillary tube.

2. Effect of Temperature on Surface Tension

Surface tension \(T\) decreases as the temperature increases. Since \(h\) is directly proportional to \(T\), a decrease in \(T\) will lead to a decrease in the height of capillary rise.

3. Analyze Statements

Statement I is correct because in hot water (higher temperature), the surface tension is lower, resulting in a smaller height of capillary rise. Statement II is incorrect because the height of capillary rise is actually larger in cold water due to higher surface tension.

So, the correct option is: (2) Statement I is true but Statement II is false