The pressure and density of a given mass of a diatomic gas $\bigg(\gamma =\large\frac{7}{5}\bigg)$ change adiabatically from $(P,d)\;to \; (P',d'')$. If $\large\frac{d''}{d}$$=32$, then $\large\frac{P'}{P}$ is $(\gamma$= ratio of specific heats)

Question

\[\begin {array} {1 1} (a)\;\frac{1}{128} & \quad (b)\;\frac{1}{64} \\ (c)\;64 & \quad (d)\;128 \end {array}\]