A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 4V and then adiabatically to a volume 32V. The final pressure of the gas is : (take \(\gamma = \frac{5}{3}\))

\(\frac{P}{128}\)

For isothermal process : PV = constant

P_oV = P'(4V)

⇒ P' = \(\frac{P_o}{4}\)

For adiabatic process : PV^\(\gamma\) = constant

P'(4V)^\(\gamma\) = P'' (32V)^\(\gamma\)

For monoatomic gas : \(\gamma = \frac{5}{3}\)

P'' = P_o/128