Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2\,V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta p$ and $1.5 \, \Delta p$, respectively. Then