d
Rewriting the given equation as $\mathrm{T}^{7 / 5} \mathrm{P}^{-2 / 5}$ and
comparing this with the standard from of the adiabatic equation $\mathrm{T}^{\gamma} \mathrm{P}^{1-\gamma}=$ constant, we find
$\gamma=\frac{7}{5} .$ Hence, the gas is diatomic and
$C_{v}=\frac{R}{\gamma-1}=\frac{5}{2} R$