At what temperature $K$ will the kinetic energy of $0.3 \ mol$ of $He$ be equal to the kinetic energy of $0.4 \ mol$ of $Ar$ at $400 \ K$?

The volume of a given mass of a gas is directly proportional to its Kelvin temperature at constant pressure. The above statement is known as . . . . . .

When $2 \ g$ of a gaseous substance $A$ is introduced into an initially evacuated flask at $25^{\circ} C$,the pressure is found to be $1 \ atm$. $3 \ g$ of another gaseous substance $B$ is added to it at the same temperature and pressure. The final pressure is found to be $1.5 \ atm$. Assuming ideal gas behaviour,the ratio of molar masses of $A$ and $B$ is:

At $300 \ K$,a sample of $3.0 \ g$ of gas $A$ occupies the same volume as $0.2 \ g$ of hydrogen $(H_2)$ at $200 \ K$ at the same pressure. The molar mass of gas $A$ is $...... \ g \ mol^{-1}$ (nearest integer). Assume that the gases behave as ideal gases.

Assuming the molar mass of air is $28.84 \, g \, mol^{-1}$,calculate the payload (lifting capacity) of a balloon of volume $10^6 \, L$ filled with $He$ at $27 \, ^\circ C$ and $1 \, atm$ pressure.

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