Question

Given below are two statements :
Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the above statements, choose the correct answer from the option given below:

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

Answer 1

The Correct Option is D

To ascertain the accuracy of the provided assertions concerning kinetic theory and gas properties, an examination of each is conducted:

1. Assertion I: The mean free path of gas molecules exhibits an inverse relationship with the square of the molecular diameter.
   The formula for the mean free path (\(\lambda\)) of a gas molecule is: \(\lambda = \frac{kT}{\sqrt{2} \pi d^{2} P}\), where:
   • \(k\) represents the Boltzmann constant,
   • \(T\) signifies the absolute temperature,
   • \(d\) denotes the molecular diameter,
   • \(P\) indicates the pressure.
2. Assertion II: The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. 
   Based on the kinetic theory of gases, the average kinetic energy (\(E\)) of a gas molecule is given by: \(E = \frac{3}{2}kT\). As \(E\) is directly proportional to the absolute temperature (\(T\)), Assertion II is validated.

Following a theoretical analysis of both assertions:

• Assertion I is substantiated by the inverse proportionality between the mean free path and the square of the diameter.
• Assertion II is substantiated by the direct proportionality between the average kinetic energy and the absolute temperature.

Consequently, the conclusive finding is: Both Assertion I and Assertion II are true.