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Q.
In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. A good estimate for $q$ is :
Time interval between two successive collisions at a face $=\frac{2 l}{u}$
Number of collisions/s $=\frac{u}{2 l}$
Change of momentum/collision $=2 m u$
Therefore, change of momentum/s $=\frac{u}{2 l} \times 2 m u=\frac{m u^{2}}{l}=F$
Therefore, $F \propto u^{2} \propto T \Rightarrow q=1$
