The temperature of an ideal gas is increased from $120 \,K$ to $480 \,K$. If at $120 \,K$,the root mean square speed of gas molecules is $v$,then at $480 \,K$ it will be

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

The r.m.s. speed of gas molecules is given by

At what temperature does the $r.m.s.$ speed of air molecules become double that at $N.T.P.$?

Let $\overline{V}$,$V_{\text{rms}}$,and $V_{p}$ denote the mean speed,root mean square speed,and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?