$CO_2$ $(O - C - O)$ is a triatomic gas. The average kinetic energy of $1\,g$ of the gas is: (where $N$ is Avogadro's number,$k$ is Boltzmann's constant,and the molar mass of $CO_2 = 44\,g/mol$)

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.

If the pressure of $CO_2$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4V^2}$,then the mass of the gas in the container is ...... $g$.

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = \text{constant}$. The coefficient of volume expansion of the gas is . . . . . . .

The cross-sectional area of a piston is $8 \times 10^{-3} \, m^2$. The gas has a temperature of $300 \, K$,a pressure of $1.0 \times 10^5 \, Pa$,and a volume of $2.4 \times 10^{-3} \, m^3$. When the gas is heated by a heater,the piston moves by $0.1 \, m$. If the spring constant is $8000 \, N/m$,find the final temperature in $K$.

$A$ diatomic gas of molecular mass $40 \, g/mol$ is filled in a rigid container at temperature $30^{\circ} C$. It is moving with velocity $200 \, m/s$. If it is suddenly stopped,the rise in the temperature of the gas is .........