An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true ?

The mean free path of molecules of an ideal gas is given as:

$\lambda=\frac{\mathrm{V}}{\sqrt{2} \pi \mathrm{d}^{2} \mathrm{~N}}$

Hence with increasing temp since volume of container does not change (closed container), so mean free path is unchanged.

Average collision time

$=\frac{\text { mean free path }}{\mathrm{V}_{\mathrm{av}}}=\frac{\lambda}{\text { (avg speed of molecules) }}$

$\because$ avg speed $\alpha \sqrt{\mathrm{T}}$

$\therefore$ Avg coll. time $\alpha \frac{1}{\sqrt{\mathrm{T}}}$

Hence with increase in temperature the average collision time decreases.