An ideal gas initially at a state $\;(P_{1},V_{1})\;$ is allowed to expand isothermally to a state $\;(P_{2},V_{2})\;$ . Then the gas is compressed adiabatically to its initial volume $\;V_{1}\;$ . Let the final pressure be $\;p_{3}\;$ and the workdone by the gas be W , Then

Question

$(a)\;P_{3} > P_{1} \;and \; W <0\qquad(b)\;P_{3} > P_{1} \;and \; W >0\qquad(c)\;P_{3} < P_{1} \;and \; W >0\qquad(d)\;P_{3} < P_{1} \;and \; W