The relationship between pressure $P$,volume $V$,and total internal energy $E$ for an ideal gas is:

The number of molecules in one litre of an ideal gas at $300 \, K$ and $2$ atmospheric pressure with mean kinetic energy $2 \times 10^{-9} \, J$ per molecule is $.... \times 10^{11}$.

The average force applied on the walls of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

The translational kinetic energy of the molecules of a gas at absolute temperature $T$ can be doubled by:

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 $m = 5 \times 10^{-27} \, kg$).

Consider a gas with density $\rho$ and $\bar{c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as a whole with velocity $v$,then the pressure exerted by the gas is