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?

Options

A. The pressure in the two compartments are unequal.
B. Volume of compartment I is `(2V)/5`
C. Volume of compartment II is `(12V)/5`
D. Final pressure in compartment I is `(4P)/(4)`

Answer

C

Explanation

In the equilibrium position the net force on the partion will be zero.
Hence pressure on both sides are same.
Initially, PV=nRT
`n_(1)=(P_(1)V_(1))/(RT_(1))=(PV)/(RT)` & `n_(2)=((2P)(2V))/(RT)=4(PV)/(RT) rArr n_(2)=4n_(1)`
Moles remains conserved
Finally, pressure becomes equal in both parts.
Using, `P_(1)V_(1)=n_(1)RT_(1)`
`P_(2)V_(2)=n_(1)RT_(1)`
`:' P_(1)=P_(2)` and `T_(1)=T_(2)`
`:. (V_(1))/(V_(2))=(n_(1))/(n_(2))=1/4 rArr V_(2)=4V_(1)`
Also, `V_(1)+V_(2)=3V`
`rArr V_(1)+4V_(1)=3V rArr V_(1)=3/5 V`
and `V_(2)=12/5V`
In compartment (1)
`P_(1)'V_(1)=n_(1)RT_(1)`
`P'_(1)((3V)/5)=((PV)/(RT))RT`
`P'_(1)=(5PV)/(3V)=5/3 P`