$A$ 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 $\text{ dm}^3$)?

At $27^{\circ} C$,$1 \ L$ of $H_2$ with a pressure of $1 \ bar$ is mixed with $2 \ L$ of $O_2$ with a pressure of $2 \ bar$ in a $10 \ L$ flask. What is the pressure exerted by the gaseous mixture in $bar$? (Assume $H_2$ and $O_2$ as ideal gases)

The density of air is higher at sea level. This fact is a practical application of which law?

What will be the molar volume of nitrogen $(N_2)$ and argon $(Ar)$ at $273.15 \ K$ and $1 \ atm$?

At what new pressure will $100 \ mL$ of a gas at a pressure of $720 \ mm$ occupy a volume of $84 \ mL$,keeping the temperature constant (in $mm$)?

$A$ closed tank has two compartments $A$ and $B$,both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $1$). If the old partition is replaced by a new partition which can slide and conduct heat but does $NOT$ allow the gas to leak across (Figure $2$),the volume (in $m^3$) of the compartment $A$ after the system attains equilibrium is. . . . . . . .