At $600 \ K$,the root mean square (rms) speed of gas $X$ (molar mass $= 40 \ g \ mol^{-1}$) is equal to the most probable speed of gas $Y$ at $90 \ K$. The molar mass of the gas $Y$ is $....... \ g \ mol^{-1}$. (Nearest integer)

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 $16$)

If the temperature of a gas is increased from $37\,^oC$ to $927\,^oC$,then its original root mean square speed will become ...........

At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?

Consider a mixture of $SO_2$ and $O_2$ kept at room temperature. Compared to the oxygen molecule,the $SO_2$ molecule will hit the wall with

If the average velocity of $N_2$ gas at $27 \, ^oC$ is $0.3 \, m/sec$,then at what temperature in $K$ will the average velocity be $0.6 \, m/sec$?