A monatomic gas of volume 'V' and pressure 'P' expands isothermally to a volume '27 V' and then compressed adiabatically to a volume 'V'. The final pressure of the gas is

For an adiabatic process, 

${\mathrm{PV}}^{\mathrm{\gamma }}=\mathrm{constant}$

Let the final pressure be P₂ after the expansion, 

$PV=P_{2}27V\Rightarrow P_2=\frac{P}{27}$

And the final pressure after the compression be P₃, 

$\frac{P}{27}{\left(27V\right)}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=P_3{\left(V\right)}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

$P_3=9P$