Question

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

• A. $\frac{1}{128}$
• B. $\frac{1}{64}$
• C. $64$
• D. $128$

Answer 1

Answer: (D)

$128$

In an adiabatic process, pressure and density are related as
$P{d}^{-\gamma }=$constant

where d is density.

$P_1{d}_1^{-\gamma }=P_2{d}_2^{-\gamma }$
$\frac{P}{P^{\prime }}={\left(\frac{d^{\prime }}{d}\right)}^{-\gamma }={32}^{-7/5}=2^{-7}$
$\frac{P^{\prime }}{P}=2^7=128$