At temperature $T,$ the $r.m.s.$ speed of helium molecules is the same as the $r.m.s.$ speed of hydrogen molecules at normal temperature and pressure $(NTP)$. The value of $T$ is ....... $^\circ C$.

The root mean square speed of hydrogen molecules at $300 \ K$ is $1930 \ m/s.$ Then the root mean square speed of oxygen molecules at $900 \ K$ will be ....... $m/s$.

The root mean square velocity of the molecules in a sample of helium is $(5/7)^{th}$ that of the molecules in a sample of hydrogen. If the temperature of the hydrogen sample is $0^{\circ}C$,then the temperature of the helium sample is about:

The rms speed of an oxygen molecule at a certain temperature is $600 \,ms^{-1}$. If the temperature is doubled and the oxygen molecule dissociates into atomic oxygen atoms,the new rms speed is (in $\,ms^{-1}$)

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?

The root mean square (rms) velocity of an ideal gas at temperature $T$ is $v$. If the temperature is increased to $4 T$, the rms velocity of the gas is