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?

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The pressures in the two compartments are equal.

Volume of compartment I is 3V/5.

Volume of compartment II is 12V/5.

Final pressure in compartment I is 5P/3.

answer is A.

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Detailed Solution

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.

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