$A$ flask contains argon and oxygen in the ratio of $3: 2$ in mass and the mixture is kept at $27^{\circ} C$. The ratio of their average kinetic energy per molecule respectively will be ...........

Kinetic energy per unit volume is $E$. The pressure exerted by the gas is given by

If $E$ is the kinetic energy per mole of an ideal gas and $T$ is the absolute temperature,then the universal gas constant is given as

The average translational kinetic energy of the oxygen molecules at a temperature of $127^{\circ} C$ is (Boltzmann constant $= 1.38 \times 10^{-23} \,J \,K^{-1}$)

$A$ box contains $N$ molecules at temperature $T_1$ and pressure $P_1$. If the number of molecules in the box is doubled but their total kinetic energy remains unchanged,what are the new pressure $P_2$ and temperature $T_2$?

Two gases $A$ and $B$ are contained in the same vessel which is at temperature $T$. The number of molecules of gas $A$ is $N$ and the mass of each molecule is $m$. The number of molecules of gas $B$ is $2N$ and the mass of each molecule is $2m$. If the mean square velocity of the $x$-component of velocity of gas $B$ is $v^2$ and the mean square velocity of the $x$-component of velocity of molecules of gas $A$ is $u_x^2$,then $\frac{u_x^2}{v^2}$ is: