A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$1$). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure $2$), the volume (in ${\mathrm{m}}^3$) of the compartment A after the system attains equilibrium is _________.

Solution

When equilibrium is established, the final $\mathrm{T}$ and $\mathrm{P}$ would be the same. Hence, volume ration would be equal to mole ratio. $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}$ $\Rightarrow \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{\frac{5}{400\mathrm{R}}}{\frac{3}{300\mathrm{R}}}=\frac{5}{4}$ $\therefore \frac{{\mathrm{v}}_1}{{\mathrm{v}}_{\mathrm{T}}}=\frac{5}{9}$ $\therefore {\mathrm{v}}_1=\frac{5}{9}\times {\mathrm{v}}_{\mathrm{T}}=\frac{5}{9}\times 4$ $=2.22$

Hence, the correct answer is 2.22.