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 3/2k_BT (for monoatomic gases).
Choose the most appropriate answer from the options given below :

Solution

Physics sir · 2 steps

Write the mean free path formula once and B and C fall out; then catch the two small traps in A and D.

1. λ = 1/(√2 π d² n) = (k_B T)/(√2 π d² P)

2. Read the formula. Here n is the number of molecules per unit volume and d is the molecular diameter. Using P = n k_B T, the same λ can be written in terms of T and P, as in the second form.

   Statement	What theory says	Verdict
   A	0°C is 273 K, so molecules still move fast. Classical kinetic theory predicts the motion stops only at 0 K.	False
   B	λ ∝ 1/n. More molecules per volume means more collisions and a shorter free path.	True
   C	At constant P, λ ∝ T. Heating the gas spreads the molecules apart.	True
   D	Each degree of freedom carries 1/2k_B T. The value 3/2k_B T is the total for all 3 degrees of freedom of a monoatomic molecule.	False

3. So. Only B and C are correct, which is option (b).

The idea to keep. Mean free path depends on how crowded the gas is: λ ∝ 1/n, or λ ∝ T/P. Equipartition gives 1/2k_B T per degree of freedom, not per molecule.

Answer from the NTA final answer key. Solution by PrepWiser.