A monoatomic 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 : (take \(\gamma = \frac{5}{3}\))

\(\frac{P}{64}\)

For isothermal process : PV = constant

PoV = P'(2V)

⇒ P' = \(\frac{P_o}{2}\)

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

P'(2V)^\(\gamma\) = P'' (16V)^\(\gamma\)

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

P'' = P_o/64