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

Options

A. The pressure in the two compartments are equal.
B. Volume of compartment I is `3 V//5`
C. Volume of compartment II is `12 V//5`
D. Final pressure in compartment I is `5 P //3`

Answer

A, B, C, D

Explanation

In the equilibrium position, the net force on the partition will be zero.
Hence pressure on both sides is same.
Hence, `(a)` is correct.
`n_(1)=(P_(1)V_(1))/(RT_(1))=(PV)/(RT)`
`n_(2)=((2P)(2V))/(RT)=4(PV)/(RT)implies n_(2)=4n_(1)`
Moles remain conserved.
Finally pressure becomes equal in both the parts.
Using, `P_(1)V_(1)=n_(1)RT_(1)`
`P_(2)V_(2)=n_(2)RT_(2)`
`P_(1)=P_(2)` and `T_(1)=T_(2)`
`(V_(1))/( V_(1))=(n_(1))/(n_(2))=(1)/(4)`
`V_(2)=4V_(1)`
Also, `V_(1)+V_(2)=3V impliesV_(1)+4V_(1)=3V`
`V_(1)=(3)/(5)V` and `V_(2)=(12)/(5) V`
Hence, options `(b)` and `(c)` are correct.
In compartement `I:`
`P_(1)'V_(1)=n_(1)RT_(1)`
`P_(1)^(')((3V)/(5))=((PV)/(RT))R(T)`
`P_(1)^(')=(5PV)/(3V)=(5)/(3)P`
Hence, option `(d)` is also correct.