The speeds of $5$ molecules of a gas (in arbitrary units) are as follows: $2, 3, 4, 5, 6$. The root mean square speed for these molecules is

At room temperature,the $r.m.s.$ speed of the molecules of a certain diatomic gas is found to be $1920\, m/s$. The gas is

The $rms$ speed of helium gas at $27\,^{\circ}C$ and $1\,atm$ pressure is $900\,ms^{-1}$. Then the $rms$ speed of helium molecules at temperature $27\,^{\circ}C$ and $2\,atm$ pressure is ...... $m/s$.

The $r.m.s.$ velocity of nitrogen molecules at $NTP$ is ...... $m/s$.

The temperature at which the $r.m.s.$ velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ} C$ is (Molecular weight of hydrogen and oxygen molecules are $2$ and $32$ respectively). (in $^{\circ} C$)

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 ....... $^\circ C$.