Nitrogen gas is filled in an insulated container. If $\alpha$ fraction of moles dissociates without exchange of any energy,then the fractional change in its temperature is ..............

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

An insulated container contains a monoatomic gas of molar mass $M$. The container is moving with velocity $V$. If it is stopped suddenly, the change in temperature of the gas is ($R$ = gas constant).

The speed of sound in an ideal gas at a given temperature $T$ is $v$. The rms speed of gas molecules at that temperature is $v_{\text{rms}}$. The ratio of the velocities $v$ and $v_{\text{rms}}$ for helium and oxygen gases are $X$ and $X^{\prime}$,respectively. Then,$\frac{X}{X^{\prime}}$ is equal to

From a certain apparatus,the diffusion rate of hydrogen has an average value of $28.7 \; cm^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2 \; cm^3 s^{-1}$. Identify the gas.

The density of water is $1000 \; kg \; m^{-3}$. The density of water vapour at $100 \; ^{\circ}C$ and $1 \; atm$ pressure is $0.6 \; kg \; m^{-3}$. The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.