What is the slope of the straight line for the graph drawn between $\ln k$ and $\frac{1}{T}$,where $k$ is the rate constant of a reaction at temperature $T$?

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. . . . . .