Explanation

(d) Given, $p \propto T^{3}$ ----(i)
In an adiabatic process
${\ \ \ \ \ \ \ \ \ \ \ T}^{\gamma}p^{1 - \gamma} = constant$
$T\ \alpha\ \frac{1}{p^{(1 - \gamma)/\gamma}}$
$T^{(\gamma/\gamma - 1)} \propto p$ ----(ii)
Comparing Eqs. (i) and (ii), we get
$\therefore\ \ \ \frac{\gamma}{\gamma - 1} = 3$
$3\gamma - 3 = \gamma$
$2\gamma = 3$
$\frac{C_{p}}{C_{v}} = \gamma = \frac{3}{2}$