The temperature of a gas is $-73^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed of the molecules is doubled (in $^{\circ}C$)?

Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

At what temperature $K$ will the $r.m.s.$ speed of hydrogen gas be equal to the $r.m.s.$ speed of oxygen molecules at $47^{\circ}C$?

Select the incorrect statement about Maxwell's speed distribution.

For a given gas,the velocities of $5$ molecules are $2, 3, 4, 5,$ and $6$. What is the $rms$ velocity?

Consider an ideal gas with the following distribution of speeds:

Speed $(m/s)$	$\%$ of molecules
$200$	$10$
$400$	$20$
$600$	$40$
$800$	$20$
$1000$	$10$

$(a)$ Calculate $v_{rms}$ and hence $T$. (Given mass of one molecule $m = 3.0 \times 10^{-26} \ kg$, Boltzmann constant $k_B = 1.38 \times 10^{-23} \ J/K$)
$(b)$ If all the molecules with speed $1000 \ m/s$ escape from the system, calculate the new $v_{rms}$ and hence the new $T$.