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

This inquiry focuses on capillary rise behavior when a tube is placed in cold versus hot water, proposing two assertions for evaluation.

Capillary rise is governed by liquid surface tension. The capillary rise height formula, \( h \), is:

\(h = \frac{2 \gamma \cos \theta}{\rho g r}\)

• \( \gamma \) denotes surface tension.
• \( \theta \) is the contact angle.
• \( \rho \) represents liquid density.
• \( g \) is the acceleration due to gravity.
• \( r \) is the capillary tube radius.

Elevated temperatures, such as immersion in hot water, reduce surface tension \( \gamma \). Since capillary rise height is directly proportional to surface tension, hotter temperatures lead to a diminished rise height.

Analyzing the assertions:

1. Assertion 1: Capillary rise height will be less in hot water compared to cold water.
   • This is accurate: higher temperatures decrease surface tension, thus reducing capillary rise.
2. Assertion 2: Capillary rise height will be less in cold water compared to hot water.
   • This is inaccurate: conversely, capillary rise will be greater in cold water due to higher surface tension.

Therefore, the conclusion is: Assertion I is correct; Assertion II is incorrect.