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 pressure in the two compartments are equal

Volume of compartment II is $\frac{12 V}{5}$

Volume of compartment I is $\frac{3 V}{5}$

Final pressure is compartment I is $\frac{5 P}{3}$

answer is A, B, C, D.

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Detailed Solution

For insulated chambers
$n_{1} + n_{2} = n_{1}^{'} + n_{2}^{'}$
(final pressures become equal)
$\frac{P V}{R T} + \frac{2 P .2 V}{R T} = \frac{P}{R T} [3 V] \Rightarrow P' = \frac{5 P}{3}$
For left chamber,
$P V = P' V' = \frac{5 P}{3} V' \Rightarrow V' = \frac{3 V}{5}$
For right chamber,
$4 P V = P' V' = \frac{5 P}{3} V' \Rightarrow V' = \frac{12 V}{5}$