Given here,

$P{T}^2=$constant    $...\left(1\right)$

Using ideal gas equation, 

$PV=nRT$

We have, $P=\frac{nRT}{V}$

Putting in equation $\left(1\right)$,

$P{T}^2=\frac{nRT}{V}\times T^2=$constant

$\Rightarrow T^3=KV ...\left(2\right)$

Differentiating the equation with respect to $T$, 

So, $\frac{d}{dT}\left(KV\right)=3T^2$

$\Rightarrow \frac{KdV}{dT}=3T^2$

$\Rightarrow dV=\frac{3T^2}{K}dT$

$\Rightarrow \gamma V=\frac{3T^2}{K}\left(\text{as} dV=\gamma VdT\right)$

$\Rightarrow \gamma =\frac{3T^2}{KV}=\frac{3T^2}{T^3}=\frac{3}{T}$