Fill in the blanks:
$(i)$ At low $......$ and high $......$ temperature,real gases behave as an ideal gas.
$(ii)$ $......$ is a measure of the average kinetic energy of a gas.
$(iii)$ The kinetic energy of a gas with mass $m$ is $E$. Its momentum will be $......$.
$(iv)$ At $......$ temperature,$v_{rms}$ will be double that of $v_{rms}$ at $0^{\circ} C$.

(D) $(i)$ pressure,temperature
$(ii)$ Temperature
$(iii)$ $\sqrt{2mE}$
Kinetic energy $E = \frac{1}{2}mv^2$
$E = \frac{1}{2} \frac{m^2v^2}{m} = \frac{p^2}{2m}$,where $p$ is momentum.
Therefore,$p = \sqrt{2mE}$.
$(iv)$ $819^{\circ} C$
$v_{rms} \propto \sqrt{T}$
$\frac{(v_{rms})_2}{(v_{rms})_1} = \sqrt{\frac{T_2}{T_1}}$
$2 = \sqrt{\frac{T_2}{273}}$
$4 = \frac{T_2}{273} \implies T_2 = 1092 \ K$
$t_2 = 1092 - 273 = 819^{\circ} C$.