$A$ vessel contains $14 \, g$ ($7$ moles) of hydrogen and $96 \, g$ ($3$ moles) of oxygen at $STP$. $A$ chemical reaction is induced by passing an electric spark in the vessel until one of the gases is consumed. The temperature is brought back to its starting value of $273 \, K$. The pressure in the vessel is ...... $atm$.

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.

$A$ thermally insulated vessel with nitrogen gas at $27^{\circ} C$ is moving with a velocity of $100 \ m/s$. If the vessel is stopped suddenly,then the percentage change in the pressure of the gas is nearly (assume entire loss in $KE$ of the gas is given as heat to gas and $R=8.3 \ J \ mol^{-1} \ K^{-1}$)

For an ideal gas at a temperature of $27^{\circ} C$ and at constant pressure,the coefficient of volume expansion is nearly

An ideal gas has $N$ molecules in a closed box at temperature $T_1$ and pressure $P_1$. If the number of molecules in the box is doubled and the total kinetic energy is kept the same,what will be the new pressure $P_2$ and temperature $T_2$?

According to the kinetic theory of gases,which of the following statements are correct?
$A$. The motion of the gas molecules freezes at $0^{\circ} C$.
$B$. The mean free path of gas molecules decreases if the density of molecules is increased.
$C$. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
$D$. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2} k_{B} T$ (for monoatomic gases).
Choose the most appropriate answer from the options given below: