The curve between absolute temperature $T$ and $v_{rms}^2$ is

Five molecules of a gas have speeds $1, 2, 4, 8$ and $16 \, m/s$ at some instant. The root mean square velocity of the gas molecules is ..... $m/s$.

Uranium has two isotopes of masses $235$ and $238$ units. If both are present in Uranium hexafluoride $(UF_6)$ gas,which would have the larger average speed? If the atomic mass of fluorine is $19$ units,estimate the percentage difference in speeds at any temperature.

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

In two vessels of the same volume,atomic hydrogen and helium at pressures of $1\, atm$ and $2\, atm$ are filled,respectively. If the temperature of both samples is the same,then the average speed of hydrogen atoms $\langle C_H \rangle$ will be related to that of helium $\langle C_{He} \rangle$ as:

The speed distribution for a sample of $N$ gas particles is shown below. $P(v) = 0$ for $v > 2 v_0$. How many particles have speeds between $1.2 v_0$ and $1.8 v_0$ (in $N$)?