Explanation:
Given that
\(P T^{-3}=\) constant\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
For an adiabatic process,
\(P T^{\frac{\gamma}{1-\gamma}}=\) constant
Comparing (1) and (2), we get
\(\dfrac{\gamma}{1-\gamma}=-3\) or \(-3+3 \gamma=\gamma\)
\(2 \gamma=3\) or \(\gamma=\dfrac{3}{2}=1.5\).