If the $rms$ speeds of helium and oxygen are equal,then the ratio of the temperatures of helium and oxygen is

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $\,K$)?

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:

To what temperature should the hydrogen at $327^{\circ} C$ be cooled at constant pressure,so that the root mean square velocity of its molecules becomes half of its previous value (in $^{\circ} C$)?

When the temperature of an ideal gas is increased from $27^{\circ} C$ to $127^{\circ} C$,calculate the percentage increase in its $v_{\text{rms}}$. (in $\%$)

Uranium has two isotopes of masses $235$ and $238$ units. If both of them are present in uranium hexafluoride gas, find the percentage ratio of the difference in rms velocities of the two isotopes to the rms velocity of the heavier isotope.