Select the correct relationship among the following. The symbols have their usual meanings.

If the average velocity of $N_2$ molecule is $0.3 \, m/s$ at $27 \, ^\circ C$,then the velocity will be $0.6 \, m/s$ at ........... $K$.

Calculate the root mean square $(rms)$ speed of ozone gas in a closed vessel at a temperature of $20 \, ^\circ C$ and a pressure of $82 \, cm \, Hg$.

The ratio of densities of $O_2$ and $H_2$ is $16 : 1$. The ratio of their $rms$ velocities will be:

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

The molecular weight of a gas that diffuses twice as rapidly as the gas with molecular weight $64$ is: