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? 

detailed solution

Correct option is A

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.