If the $V_{rms}$ of a gas is $(30R)^{1/2}$ at $27\,^{\circ}C,$ then calculate the molar mass of the gas in $kg/mol$.

In the Maxwell-Boltzmann distribution of molecular speeds shown below,which of the following is correct regarding the most probable speed $(U_{M.P.})$ at temperatures $T_1$ and $T_2$?

The ratio of root mean square velocity of hydrogen at $50 \, K$ to that of nitrogen at $500 \, K$ is closest to

The ratio among most probable velocity,mean velocity and root mean square velocity is given by

At the same temperature,the root mean square velocities of two gases are $v_1$ and $v_2$,and their molar masses are $m_1$ and $m_2$ respectively. Which of the following relations is correct?

Which of the following statement$(s)$ is (are) correct regarding the root mean square speed $(U_{rms})$ and average translational kinetic energy $(\varepsilon_{av})$ of a molecule in a gas at equilibrium?
$(1)$ $U_{rms}$ is doubled when its temperature is increased four times
$(2)$ $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass
$(3)$ $U_{rms}$ is inversely proportional to the square root of its molecular mass
$(4)$ $\varepsilon_{av}$ is doubled when its temperature is increased four times