Let the initial volume be V. After isothermal expansion, pressure = \(\frac{P}{4}\), volume = 4V
Let P' is the pressure after adiabatic compression.
Then volume then is V. Therefore,
P' Vγ = \(\frac{P}{4}\) (4V)γ ; P' = \(\frac{P}{4}\) (4)\(\frac{3}{2}\)
P' = 2P