The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$. What is the ratio of their $r.m.s.$ velocities?

To increase the rms speed of gas molecules by $25 \%$,the percentage increase in absolute temperature of the gas is to be

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 $T$.

How does the $rms$ velocity of an ideal gas vary with density at constant pressure?

Define absolute temperature.

At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?