$A$ hot air balloon has a volume of $2000 \text{ dm}^3$ at $99^\circ\text{C}$. What is the new volume if the air in the balloon cools to $80^\circ\text{C}$ (in $\text{ dm}^3$)?

The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from $5 \times 10^4 \ cm \ s^{-1}$ to $10 \times 10^4 \ cm \ s^{-1}$. Which of the following statements correctly explains how the change is accomplished?

When the absolute temperature of an ideal gas is doubled and the pressure is halved,the volume of the gas

At $0^{\circ}C$,the density of a certain oxide of a gas at $2 \ bar$ is the same as that of dinitrogen at $5 \ bar$. What is the molecular mass of the oxide?

Find the number of moles of $CO_2$ present in a sample occupying $4 \times 10^{-3} \text{ m}^3$ at $1.104 \times 10^5 \text{ Nm}^{-2}$ pressure. Given: $R \times T = 2208 \text{ J mol}^{-1}$. (in $\text{ mole}$)

$16 \, g$ of oxygen and $3 \, g$ of hydrogen are mixed and kept at $760 \, mm$ pressure and $0 \, ^oC$. The total volume occupied by the mixture will be nearly