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 ${m^3}$) of the compartment A after the system attains equilibrium is $\underline{\hspace{2cm}}$.