If the temperature of an ideal gas is increased from $27^{\circ}C$ to $927^{\circ}C$,what happens to its $r.m.s.$ velocity?

The temperature of an ideal gas is increased from $120 \,K$ to $480 \,K$. If at $120 \,K$, the root mean square speed of gas molecules is $v$, then at $480 \,K$ it will be

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:

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 $T$.

On any planet,the presence of an atmosphere implies ($C_{rms}$ = root mean square velocity of molecules and $V_e$ = escape velocity):

If the rms velocity of hydrogen gas at a certain temperature is $c,$ then the rms velocity of oxygen gas at the same temperature is