The kinetic energy of one gram molecule of a gas at normal temperature and pressure is $(R = 8.31\,J/mol\cdot K)$.

If the $rms$ speed of a gas is $v_{rms} = 1840 \ m/s$ and its density is $\rho = 8.99 \times 10^{-2} \ kg/m^3$,then the pressure of the gas will be .........

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

An ideal gas occupies a volume of $2\, m^3$ at a pressure of $3\times10^6\, Pa$. The energy of the gas is

The translational kinetic energy of gas molecules for one mole of the gas is equal to

Obtain an expression for the momentum of a gas transferred to the walls of a container in time $\Delta t$.