A partition divides a container having insulated walls into two compartments I and II. The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position?

In the equilibrium position, the net force on the partition will be zero. Hence pressure on both sides is same. Hence, (1) is correct.         n1=P1V1RT1=PVRTn2=(2P)(2V)RT=4PVRT⇒n2=4n1Moles remain conserved. Finally pressure becomes equal in both the parts.           Using, P1V1=n1RT1          P2V2=n2RT2P1=P2  and  T1=T2V1V2=n1n2=14V2=4V1Also,  V1+V2=3V ⇒ V1+4V1=3V           V1=35V  and  V2=125VHence, options (2) and (3) are correct. In compartment I:           P1′V1=n1RT1P1′3V5=PVRTR(T)P1′=5PV3V=53PHence, option (4) is also correct.