The adiabatic elasticity of hydrogen gas $(\gamma = 1.4)$ at $NTP$ is

An insulated box containing a diatomic gas of molar mass $M$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

For a diatomic gas,the change in internal energy for a unit change in temperature at constant pressure and constant volume is $U_1$ and $U_2$ respectively. The ratio $U_1 : U_2$ is

Two containers of equal volume contain the same gas at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. On joining the vessels,the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P/T$ is equal to

The oxygen molecule has a mass of $5.30 \times 10^{-26} \; kg$ and a moment of inertia of $1.94 \times 10^{-46} \; kg \cdot m^{2}$ about an axis through its centre perpendicular to the line joining the two atoms. Suppose the mean speed of such a molecule in a gas is $500 \; m/s$ and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

$2 \text{ moles}$ of a monatomic gas requires heat energy $Q$ to be heated from $30^{\circ} C$ to $40^{\circ} C$ at constant volume. The heat energy required to raise the temperature of $4 \text{ moles}$ of a diatomic gas from $28^{\circ} C$ to $33^{\circ} C$ at constant volume is