Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and 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 of the gases in $A$ and $B$ are found to be $2 \Delta p$ and $3 \Delta p$ respectively. Then the relation between $m_A$ and $m_B$ is

Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of the composite rod is

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the slope of the graph drawn between $\log _e V$ on $X$-axis and $\log _e p$ on $Y$-axis is

An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 / 3$ for an ideal gas, then rise in its temperature is