The following graph shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_2$ and $T_1$ is

In the given $(V-T)$ diagram, what is the relation between pressure $P_1$ and $P_2$ is

The ratio $C_p/C_v$ for a gas mixture consisting of $8\ g$ of helium and $16\ g$ of oxygen is

A gas mixture consists of molecules of type $1, 2$ and $3$, with molar masses $m_1 > m_2 > m_3$. $v_{rms}$ and $ \bar K$ are the $r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true?

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma $ . It is moving with speed $v$ and is suddenly broght to rest. Assuming no heat is lost to the surroundings, its temperature increases by