The average collision period in a gas undergoing isobaric process is

Average collision period,  $t=\frac{1}{\pi d^{2}vn\sqrt{2}}\Rightarrow t\propto \frac{1}{vn}$ (v = average speed, n = number  density of molecules).
$v=\sqrt{\frac{8RT}{\pi M}}\alpha \sqrt{T}$  and  $n=\frac{N}{V}\alpha \frac{1}{V}$
In isobaric process,  $V\alpha T$
So,  $t\alpha \frac{1}{vn}\alpha \frac{V}{\sqrt{T}}\alpha \sqrt{T}$