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 not correct, with reference to the final equilibrium position? 

In the equilibrium position the net force on the portion will be zero. Hence pressure on both sides are same. Initially, PV=nRT

$n_1=\frac{P{V}_1}{R{T}_1}=\frac{PV}{RT}\text{ and }{n}_2=\frac{\left(2P\right)\left(2V\right)}{RT}$

$\Rightarrow n_2=4n_1$

Total number of moles remains conserved.
Finally, pressure becomes equal in both parts.

Using, $P_1{V}_1=n_{1}R{T}_1$

$P_2{V}_2=n_{2}R{T}_2$

$\because P_1=P_2\text{ and }{T}_1=T_2$

$\therefore \frac{V_1}{V_2}=\frac{n_1}{n_2}=\frac{1}{4}\Rightarrow V_2=4V_1$

$\text{ Also, }{V}_1+V_2=3V\Rightarrow V_1+4V_1=3\Rightarrow V_1=\frac{3}{5}V\text{ and }{V}_2=\frac{12}{5}V$

In Compartment (I) :

$P_1^{\mathrm{\prime }}{V}_1=n_{1}R{T}_1:P_1^{\mathrm{\prime }}\left(\frac{3V}{5}\right)=\left(\frac{PV}{RT}\right)R\left(T\right)$

$P_1^{\mathrm{\prime }}=\frac{5PV}{3V}=\frac{5}{3}P$