Question

A mono atomic gas at a pressure p, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is $(\gamma =\frac{5}{3})$ :

• A. $64p$
• B. $32p$
• C. $\frac{p}{64}$
• D. $16p$

Answer 1

The correct option is C

$\frac{p}{64}$

Gas expands isothermally

$P_1{V}_1=P_2{V}_{2}PV=P_2\left(2V\right)P_2=\frac{P}{2}$
It then expands adiabtically
$P_1{V}_1^{?}=P_2{V}_2^{?}{P}_2=\frac{P}{2}\left[\frac{2V}{16V}\right]\gamma =\frac{5}{3}\left[monoatomic\right]P_2=\frac{P}{2}[\frac{1}{8}{]}^{\frac{5}{3}}=\frac{P}{2}[\frac{1}{2}{]}^{3\times \frac{5}{3}}\Rightarrow \frac{P}{64}$