Question

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0°C
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
D. Average kinetic energy per molecule per degree of freedom is \(\frac{3}{2}k_BT\) (for monoatomic gases).
Choose the most appropriate answer from the options given below:

• A. A and C only
• B. B and C only
• C. A and B only
• D. C and D only

Answer 1

The Correct Option is B

 To solve this question, we need to evaluate each statement based on the principles of the kinetic theory of gases.

1. Statement A: "The motion of the gas molecules freezes at 0°C"
   • This statement is incorrect. According to the kinetic theory of gases, molecular motion stops at absolute zero (0 Kelvin), not 0°C. At 0°C, molecules still have kinetic energy and are in motion.
2. Statement B: "The mean free path of gas molecules decreases if the density of molecules is increased."
   • This statement is correct. The mean free path (\(\lambda\)) is inversely related to the number density (\(n\)). As the number density increases, the molecules are closer together, reducing the mean free path.
   • Mathematically, the mean free path is given by: \(\lambda = \frac{k_BT}{\sqrt{2} \pi \sigma^2 P}\), indicating dependence on number density at constant temperature and pressure.
3. Statement C: "The mean free path of gas molecules increases if temperature is increased keeping pressure constant."
   • This statement is correct. Increasing temperature at constant pressure decreases the number density, causing the mean free path to increase.
4. Statement D: "Average kinetic energy per molecule per degree of freedom is \(\frac{3}{2}k_BT\) (for monoatomic gases)."
   • This statement is incorrect. The average kinetic energy per molecule is given by \(\frac{1}{2}k_BT\) per degree of freedom. For monoatomic gases with 3 degrees of freedom, it's \(\frac{3}{2}k_BT\) for the whole molecule, not per degree of freedom.

Based on the analysis above, the correct answer is B and C only as these statements are correct according to the kinetic theory of gases.