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 $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).

Two containers $A$ and $B$ contain an ideal gas at the same temperature. If the masses of the molecules are $m_A$ and $m_B$ respectively,what is the relationship between their momenta $p_A$ and $p_B$?

The root mean square velocity of molecules of a gas is

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 $T = 293 \, K$]

The molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is

Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules is