The total internal energy of $4$ moles of a diatomic gas at a temperature of $27^{\circ} C$ is (Universal gas constant $R = 8.31 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

In a vessel,an ideal gas is at a pressure $P$. If the mass of all the molecules is halved and their speed is doubled,then the resultant pressure of the gas will be

$A$ gas at pressure $P_0$ is contained in a vessel. If the masses of all the molecules are halved and their velocities are doubled,the resulting pressure would be equal to

If the average kinetic energy of a gas molecule at $27^{\circ} C$ is $3.3 \times 10^{-20} \,J$, then the average kinetic energy of the gas molecules at $127^{\circ} C$ is

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:

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