The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

At what temperature $T$ (in $K$) will the $rms$ speed of $H_2$ be equal to the $rms$ speed of $O_2$ at $47^{\circ}C$?

When pressure remains constant,at what temperature will the $r.m.s.$ speed of gas molecules increase by $10 \%$ of the $r.m.s.$ speed at $STP$?

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:

The temperature at which the r.m.s. velocity of a gas triples its r.m.s. velocity at $0^{\circ} C$ is:

The temperature of a gas is $-80^{\circ} C$. To what temperature should the gas be heated so that the r.m.s. speed is increased by $2$ times (in $^{\circ} C$)?