Given here,
PT2=constant ...(1)
Using ideal gas equation,
PV=nRT
We have, P=VnRT
Putting in equation (1),
PT2=VnRT×T2=constant
⇒T3=KV...(2)
Differentiating the equation with respect to T,
So, dTd(KV)=3T2
⇒dTKdV=3T2
⇒dV=K3T2dT
⇒γV=K3T2(asdV=γVdT)
⇒γ=KV3T2=T33T2=T3