The r.m.s. speed of gas at temperature $T$ is $2$ times the r.m.s speed at $320 \,K$. The value of the temperature $T$ is (in $\,K$)

If the temperature of a gas is increased from $27^{\circ} C$ to $159^{\circ} C$,then the percentage increase in the $rms$ speed of the gas molecules is

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 $T$.

Equal volumes of two gases,having their densities in the ratio of $1: 16$,exert equal pressures on the walls of two containers. The ratio of their rms speeds $(c_1: c_2)$ is

At room temperature,a diatomic gas is found to have an $r.m.s.$ speed of $1930 \, m/s$. The gas is

The $r.m.s.$ speed of gas molecules at $800 \ K$ will be