$A$ gas exerts pressure on the walls of a container because the molecules .......

Number of molecules in a volume of $4\, cm^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\, cm$ of mercury is close to $?$
(Given,mean kinetic energy of a molecule (at $T$) is $4 \times 10^{-14}\, erg$,$g=980\, cm/s^{2}$,density of mercury $=13.6\, g/cm^{3}$)

At what temperature is the kinetic energy of a gas molecule double that of its value at $27^{\circ}C$?

The number of gas molecules striking per second per square metre of the top surface of a table placed in a room at $20^{\circ} C$ and $1$ atmospheric pressure is of the order of (given $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$ and the average mass of an air molecule is $m = 5 \times 10^{-27} \, kg$).

In an ideal gas at temperature $T,$ the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is

Define temperature in view of kinetic energy of a gas.