If the $RMS$ speed of nitrogen at a certain temperature is $3000 \ ms^{-1}$,the approximate kinetic energy of one mole of nitrogen at that temperature in $kJ$ is (assume nitrogen as ideal gas)

The ratio of the root mean square velocity of $H_2$ at $50 \ K$ to that of $O_2$ at $800 \ K$ is .......

If the mass of a gas at $3 \, atm$ pressure and $14.8 \, L$ volume is $15 \, g$,calculate the root mean square speed $(u_{rms})$ of the gas molecules. (Assume $T = 300 \, K$)

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas,which of the following is true?

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)

At what temperature,the rate of effusion of $N_2$ would be $1.625$ times that of $SO_2$ at $50\,^{\circ}C$ ............ $K$