The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).

Given below are two statements:
Statement $I$: The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement $II$: The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms,the rms speed will become $2v$.
In the light of the above statements,choose the correct answer from the options given below.

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \, kg$ in their Brownian motion in air at $NTP$ is approximately $....... \, mm \, s^{-1}$. [Given $k = 1.38 \times 10^{-23} \, J \, K^{-1}$ and $T = 293 \, K$]

If the temperature of an ideal gas is increased from $27^{\circ}C$ to $927^{\circ}C$,what happens to its $r.m.s.$ velocity?

If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

$A$ cubical box with porous walls containing an equal number of ${O_2}$ and ${H_2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of the ${v_{rms}}$ of ${O_2}$ molecules to that of the ${v_{rms}}$ of ${H_2}$ molecules,found in the chamber outside the box after a short interval,is: