Question

A diatomic gas $(\gamma =\frac{7}{5})$ is compressed to $\frac{1}{32}$ times of its initial volume adiabatically and reversibly. If its initial pressure is $2P_0$, its new pressure will be :

• A. $64P_0$
• B. $128P_0$
• C. $256P_0$
• D. $16P_0$

Answer 1

The correct option is C $256P_0$

We know, For adiabatic process,

$\frac{P_2}{P_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma }$
where $P_1=2P_0$ initial pressure
$P_2=$ final pressure
$V_1=$ initial volume
$V_2=$ final volume $=\frac{1}{32}{V}_1$
$\gamma =7/5$
so,
$P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }=2P_0(32{)}^{7/5}=256P_0.$