An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically.If $P_1,P_2$ and W represent the initial pressure, final pressure and the net work done by the gas respectively during the entire process, then:

Question

$$\begin {array} {1 1} (1)\;P_1 > P_2 ,W=0 & \quad (2)\;P_1 > P_2, W > 0 \\ (3)\;P_2 > P_1, W >0 & \quad (4)\;P_2 >P_1, W < 0 \end {array}$$