If the value of $u_{rms}$ at $27\,^{\circ}C$ is $30\sqrt{R}$,what is the molar mass of the gas in kilograms?

At $T$ $(K)$,the $P$,$V$ and $u_{rms}$ of $1$ mole of an ideal gas were measured. The following graph is obtained. What is its slope $(m)$? ($x$-axis $= PV$; $y$-axis $= u_{rms}^2$,$M =$ Molar mass)

The $rms$ velocity of molecules of a gas of density $4 \ kg \ m^{-3}$ and pressure $1.2 \times 10^{5} \ Nm^{-2}$ is (in $ms^{-1}$)

What is the $rms$ velocity of $O_2$ at $STP$ (in $cm/s$)?

At what temperature will the average speed of $CH_4$ molecules have the same value as $O_2$ has at $300 \ K$ ........... $K$

If the most probable speed of methane $(CH_4)$ at a certain temperature is $400 \ ms^{-1}$,what is the kinetic energy of one mole of methane at the same temperature in $J$?