The average translational energy and the rms speed of molecules of a sample of oxygen gas at $300 \ K$ are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. The corresponding values at $600 \ K$ are nearly (assuming ideal gas behaviour):

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$,where $\gamma = C_p/C_v, T_i = $ initial temperature,$T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.

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 $0^{\circ} C$.

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by

Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures,pressures,and number densities are the same. The molecular size of $A$ is half of that of $B$ and the mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} /s$,then the collision frequency in gas $A$ is . . . . . . $/s$.

At a temperature of $300 \ K$,the average translational kinetic energy and $rms$ speed of a sample of oxygen gas are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. At $600 \ K$,these values will be respectively: (Assume ideal gas behavior)