Question

The plot depicts the behaviour of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $\left(T\right)$, qualitatively, is: (Graphs are schematic and not found to scale)

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Relaxation time

$\left(\tau \right)\propto \frac{\text{mean free path}}{\text{speed}}$

$\Rightarrow \tau \propto \frac{1}{v}$
$\text{and,}v\propto \sqrt{T}$
$\therefore \tau \propto \frac{1}{\sqrt{T}}$

Hence, the graph between $\left(\tau \right)\text{vs}\left(\frac{1}{\sqrt{T}}\right)$ is a straight line which is correctly depicted by the graph shown in option $\left(C\right)$.