Question

The pressure and density of a diatomic
gas $(\gamma =\frac{7}{5})$ changes adiabatically from (p,d)
to$(p^1,d^1)$. If $\frac{d^{{}^{\prime }}}{d}=32$ then $\frac{p^{{}^{\prime }}}{p}$ is

• A. $\frac{1}{128}$
• B. 32
• C. 128
• D. 256

Answer 1

Answer: (C)

128

in an adiabatic process relation between P and V is :
$P{V}^{\gamma }=constant$
and $V=\frac{M}{d}$
so $\frac{P}{d^{\gamma }}=constant$
$\frac{P_1}{d_1^{\gamma }}=\frac{P_2}{d_2^{\gamma }}$
so $\frac{P^{{}^{\prime }}}{P}=(\frac{d^{{}^{\prime }}}{d}{)}^{\gamma }$
$\frac{P^{{}^{\prime }}}{P}=(\frac{1}{32}{)}^{\frac{7}{5}}$
$\frac{P^{{}^{\prime }}}{P}=128$