The pressure and density of a diatomic

gas $\left ( \gamma =\dfrac{7}{5} \right )$ changes adiabatically from (p,d)

to$\left ( p^{1} ,d^{1}\right )$. If $\dfrac{d^{'}}{d}=32$ then $\dfrac{p^{'}}{p}$ is

in an adiabatic process relation between P and V is :

$PV^{\gamma }= constant$

and $V= \dfrac{M}{d}$

so $\dfrac{P}{d^{\gamma }}= constant$

$\dfrac{P_{1}}{d_{1}^{\gamma }}= \dfrac{P_{2}}{d_{2}^{\gamma }}$

so $\dfrac{P^{'}}{P}= (\dfrac{d^{'}}{d})^{\gamma }$

$\dfrac{P^{'}}{P}= (\dfrac{1}{32})^{\dfrac{7}{5}}$

$\dfrac{P^{'}}{P}= 128$