Explanation

(d) In an adiabatic process,
$\ \ \ \ \ \ \ \ \ \ \ \ pV^{\gamma} = constant$
or ${\ \ \ \ p}_{1}V_{1}^{\gamma} = p_{2}V_{2}^{\gamma}$
or $\frac{P_{1}}{P_{2}} = \left( \frac{V_{2}}{V_{1}} \right)^{\gamma}$ ----(i)
Volume of gas $= \frac{Mass}{Density}$
ie, $V = \frac{M}{\rho}\ \ \ or\ \ V \propto \frac{1}{\rho}$
$\ \ \ \ \ \ \therefore\frac{V_{1}}{V_{2}} = \frac{\rho_{2}}{\rho_{1}} = 32$
Thus, from Eq.(i), we have
$\frac{P_{2}}{P_{1}} = (32)^{\gamma} = (32)^{7/5} = 2^{7} = 128$