Solution:
After isothermal expansion, pressure becomes $P/4$ at volume $4V$. Following adiabatic compression back to volume $V$, the final pressure is $P_3 = (P/4)(4)^{1.5} = P \times 4^{0.5} = 2P$.
Initial pressure and volume of a gas are $P$ and $V$ respectively. First its volume is expanded to $4V$ by isothermal process and then again its volume makes to be $V$ by adiabatic process, then its final pressure is ($\gamma = 1.5$): (1999)
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