The number of air molecules per $cm^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is $.........$

Air inside a closed container is saturated with water vapour. The air pressure is $p$ and the saturated vapour pressure of water is $\bar{p}$. If the mixture is compressed to one half of its volume by maintaining temperature constant, the pressure becomes

Which of the following statements is true?

Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.
Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.

In saloons,there is always a characteristic smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \text{ molecules}/m^3$. Due to air ventilation,the number of molecules leaving in one minute is one-tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \text{ molecule}/m^3$?

An oxygen cylinder of volume $30 \ L$ has $18.20 \ \text{moles}$ of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to $11 \ \text{atm}$ at a temperature of $27^{\circ} \text{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to (Given: $R = \frac{100}{12} \ \text{J mol}^{-1} \text{K}^{-1}$, molecular mass of $O_2 = 32 \ \text{g/mol}$, $1 \ \text{atm} = 1.01 \times 10^5 \ \text{Pa}$) (in $\text{kg}$)