The $rms$ speed of $N_2$ molecules in a gas is $v$. If the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms,the $rms$ speed becomes

At $256 \ K$,the $rms$ speed of $SO_2$ gas molecules is $3.16 \times 10^2 \ ms^{-1}$. What is the most probable velocity (in $ms^{-1}$) of the same gas at the same temperature?

The average velocity of gas molecules is equal to ...... .

At $T \ K$,the $RMS$ velocity of $He$ is equal to the $RMS$ velocity of $SO_2$ at $127^{\circ} C$. What is $T$ (in $K$)?

Among the following,identify the gas which has the greatest average speed of its molecules?

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 $16$)