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 collision at a face is $2\mathcal{l}/\mathrm{u}.$
Number of Collisions=$\frac{\mathrm{u}}{2\mathcal{l}}$
Change of momentum /collision =2mu
$$\begin{gathered} \frac{\mathrm{u}}{2\mathcal{l}}\times 2\mathrm{mu}=\frac{{\mathrm{mu}}^2}{\mathcal{l}}=\mathrm{F} \\ \mathrm{F}\propto {\mathrm{u}}^2\Rightarrow \mathrm{F}\propto \mathrm{T} \end{gathered}$$
Therefore , q=1