1. For an ideal gas, the mean free time $t$ between successive collisions is $t=\frac{\lambda}{\bar v}$ where $\lambda$ is the mean free path and $\bar v$ is the average molecular speed.

2. For an ideal gas, $\lambda=\frac{1}{\sqrt{2}\,\pi d^2 n}$ where $d$ is molecular diameter and $n$ is number density.

3. Since the question asks dependence on temperature $T$, we take the usual case of a fixed amount of gas at constant pressure unless otherwise implied.

Using ideal gas law, $n=\frac{N}{V}=\frac{P}{kT}$ So, $\lambda \propto \frac{1}{n}\propto T$ (at constant pressure).

4. Average molecular speed varies as $\bar v \propto \sqrt{T}$

5. Therefore, $t=\frac{\lambda}{\bar v}\propto \frac{T}{\sqrt{T}}=\sqrt{T}$ So mean free time increases with temperature, but not linearly; it rises like $\sqrt{T}$, i.e. an increasing curve with decreasing slope (concave downward).

6. Hence the correct qualitative graph is the one representing

• $t$ increasing with $T$
• with slope gradually decreasing.

That corresponds to Option B.