Question 223: Thermodynamics & KTG

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 options given below :

Accepted Answer

Let's analyze the given statements one by one in detail:
Statement (I): The mean free path of gas molecules is inversely proportional to the square of molecular diameter.
The mean free path ($ \lambda $) of gas molecules is the average distance a molecule travels before colliding with another molecule. The formula for the mean free path in terms of molecular diameter ($ d $) is given by:
$$\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$$
Here, $ k_B $ is the Boltzmann constant, $ T $ is the temperature, and $ P $ is the pressure. From this equation, it is evident that the mean free path ($ \lambda $) is inversely proportional to the square of the molecular diameter ($ d^2 $). Hence, Statement I is
true
.
Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
The average kinetic energy ($ E_{	ext{avg}} $) of gas molecules is given by:
$$E_{	ext{avg}} = \frac{3}{2} k_B T$$
where $ k_B $ is the Boltzmann constant and $ T $ is the absolute temperature. This shows that the average kinetic energy is directly proportional to the absolute temperature of the gas. Hence, Statement II is
true
.
Considering the analysis above, the correct answer is:
Option B
Both Statement I and Statement II are true

Answer

Statement I is false but Statement II is true

Answer

Both Statement I and Statement II are true

Answer

Statement I is true but Statement II is false

Answer

Both Statement I and Statement II are false

Thermodynamics & KTG

Choose the correct answer: