If $\Delta Q$ is the amount of heat supplied to $n$ moles of a rigid diatomic gas at constant pressure, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done, then $\Delta W : \Delta U : \Delta Q$ is

The number of air molecules per $cm^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is $.........$

Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.
Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.

Fill in the blanks:
$(i)$ At absolute zero,the volume of an ideal gas is ...... .
$(ii)$ With an increase in temperature,the pressure of a gas ...... .
$(iii)$ All molecular motion will stop at ...... .
$(iv)$ Due to ...... at higher altitudes from the surface of the Earth,the air becomes cooler.

Column-$I$ represents physical quantity and Column-$II$ represents formula. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Kinetic energy per unit mole of gas.	$(i)$ $\frac{1}{2}RT$
$(b)$ Kinetic energy per one molecule of gas.	$(ii)$ $\frac{3}{2}RT$
	$(iii)$ $\frac{3}{2}k_BT$

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 $0^{\circ} C$.