An insulated container has a partition wall to divide it into two compartments I and II. The partition wall can move without any friction and it is conducting. Same gas fills the two compartments. Initial parameters for both compartments are shown in the figure. Find the incorrect option at the equilibrium position.

For any closed system, number of moles remain conserved.

${\mathrm{n}}_1+{\mathrm{n}}_2={\mathrm{n}}_1^{\mathrm{\prime }}+{\mathrm{n}}_2^{\mathrm{\prime }}$

Here, n₁, n₂ = initial moles and ${\mathrm{n}}_1^{\mathrm{\prime }},{\mathrm{n}}_2^{\mathrm{\prime }}=\text{ final moles }$

when piston comes in equilibrium, Final pressure and final temperature becomes equal.
From the ideal gas equation we know that PV = nRT 

where n = number of moles
Putting the values of number of moles in above equation gives

$\frac{\mathrm{PV}}{\mathrm{RT}}+\frac{2\mathrm{P}\cdot 2\mathrm{V}}{\mathrm{RT}}=\frac{{\mathrm{P}}^{\mathrm{\prime }}}{\mathrm{RT}}\left[3\mathrm{V}\right]\Rightarrow {\mathrm{P}}^{\mathrm{\prime }} = \frac{5\mathrm{P}}{3}$

Here P' = final pressure

For left chamber,

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