An ideal gas is expanding

$\mathrm{PT}^{3}=\mathrm{constant}$

$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right) \mathrm{T}^{3}=\mathrm{constant}$

$\mathrm{T}^{4} \mathrm{~V}^{-1}=\mathrm{constant}$

$\mathrm{T}^{4}=\mathrm{kV}$

$\Rightarrow 4 \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{\Delta \mathrm{V}}{\mathrm{V}}$...(1)

$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$...(2)

comparing (1) and (2)

we get

$\gamma=\frac{4}{\mathrm{~T}}$