Two gases $A$ and $B$ are at absolute temperatures $360 \ K$ and $420 \ K$ respectively. The ratio of average kinetic energy of the molecules of gas $B$ to that of gas $A$ is

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 $T^{x}$. The value of $x$ is

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 $=13.6\, g/cm^{3}$)

If the mass of each molecule of a gas kept at a constant pressure $P$ in a container is halved and their speed is doubled,what will be the resulting pressure of the gas?

$A$ cylinder of capacity $20 \, L$ is filled with $H_2$ gas. The total average translational kinetic energy of the molecules is $1.5 \times 10^5 \, J$. Find the pressure of hydrogen in the cylinder.

If the momentum transferred by gas molecules to the walls of a container is $p_1 = nmAv_x^2 \Delta t$,then derive the equation for the pressure of the gas.