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 `(3V)/5`
C. Volume of compartment II is `(12 V)/5`
D. Final pressure in compartment I is `(5P)/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 are same.
Hence, (A) is correct.
Initially, `PV = nRT`
`n_1 =(P_1 V_1)/(RT_1) = (PV)/(RT)" & "n_2 =((2p)(2V))/(RT) = 4 (PV)/(RT) .............rArrn_2 = 4n_1`
Moles remains conserved.
Finally, pressure becomes equal in both parts.
Using,`P_1 V_1 = n_1 RT_2`
`P_2 V_1 = n_2 RT_1 " "because" "P_1 = P_2" "&" "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 = 12/5 V`
Hence (B) and (C) are correct.
In compartment (I) :
`P_1' V_1 = n_1 RT_1`
`P_1 ((3V)/5) = ((PV)/(RT))RT`
`P_1' = (4Pv)/(3V) = 5/3 P`
Hnce (D) is also correct.