The atmosphere on a planet is possible only if [where $v_{rms}$ is the root mean square speed of gas molecules on the planet and $v_e$ is the escape speed on its surface]

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$:

When the temperature of a gas is raised from $30^o C$ to $90^o C$,the percentage increase in the $r.m.s.$ velocity of the molecules will be (in $\%$)

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic),the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $(v_{rms})$ and choose the correct answer from the options given below:

If the $r.m.s.$ velocity values for hydrogen,nitrogen,and oxygen are $V_H, V_N$,and $V_O$ respectively at a given temperature,then:

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