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 $^{\circ} C$)?

The root mean square speed of the molecules of a gas is

If the r.m.s. velocity of hydrogen molecules is $4$ times that of an oxygen molecule at $47^{\circ} C$,the temperature of the hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are $2$ and $32$ respectively). (in $^{\circ} C$)

Five gas molecules chosen at random are found to have speeds of $500, 600, 700, 800$ and $900 \ m/s$. Which of the following statements is correct?

The rms speed of oxygen is $v$ at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes

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 $N$)?