A pressure $P-$ absolute temperature $T$ diagram was obtained when a given mass of gas was heated. During the heating process form the state $1$ to state $2$ the volume

${V_{rms}}$ denotes the root mean square speed, $\bar V$ the average speed and ${V_m}$the most probable speed of gas molecules. Out of the following which one is the correct answer ?

The average kinetic energy of a gas molecule at $27\,^oC$ is $6.21 \times 10^{-21}\,J$ . Its average kinetic energy at $227\,^oC$ will be

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/ 2 $ is given by the straight line

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures, $T_1$ and $T_2$ respectively. The vessels are joined and  the gas reaches a common pressure $P$ and a common temperature $T$. Then