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:
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:
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:
Updated On: Jan 13, 2026
- Statement I is false but Statement II is true
- Statement I is true but Statement II is false
- Both Statement I and Statement II are false
- Both Statement I and Statement II are true
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The Correct Option is D
Approach Solution - 1
To determine the correctness of the given statements, let's analyze each one regarding kinetic theory and properties of gases:
- Statement I: The mean free path of gas molecules is inversely proportional to the square of the molecular diameter.
The mean free path (\(\lambda\)) of a gas molecule is given by the formula: \(\lambda = \frac{kT}{\sqrt{2} \pi d^{2} P}\) where:- \(k\) is the Boltzmann constant,
- \(T\) is the absolute temperature,
- \(d\) is the diameter of the molecule,
- \(P\) is the pressure.
- Statement II: Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
According to the kinetic theory of gases, the average kinetic energy (\(E\)) of a gas molecule is: \(E = \frac{3}{2}kT\) Here, \(E\) is directly proportional to the absolute temperature (\(T\)). Therefore, Statement II is true.
After analyzing both statements with theoretical backing:
- Statement I is true because the mean free path is inversely proportional to the square of the diameter.
- Statement II is true because the average kinetic energy is directly proportional to the absolute temperature.
Thus, the correct answer is: Both Statement I and Statement II are true.
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Approach Solution -2
The mean free path (\(\lambda\)) of gas molecules is given by:
\[\lambda = \frac{RT}{\sqrt{2} \pi d^2 N_A P}.\]
Here, \(\lambda \propto \frac{1}{d^2}\), verifying Statement (I).
The average kinetic energy of gas molecules is:
\[KE = \frac{f}{2} nRT,\]
where \(KE \propto T\), confirming Statement (II).
Thus, both Statement I and Statement II are correct.
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