$A$ cylinder of $5 \, L$ capacity,filled with air at $NTP$,is connected to another evacuated cylinder of $30 \, L$ capacity. The resultant air pressure in both the cylinders will be .............. $cm$ of $Hg$.

Which relation represents the change in density of an ideal gas with changes in temperature and pressure?

The density of oxygen gas at $5 \text{ atm}$ and $127^{\circ} C$ will be (in $\text{ g/L}$)

At $300\, K$,the density of a certain gaseous molecule at $2\, bar$ is double that of dinitrogen $(N_2)$ at $4\, bar$. The molar mass of the gaseous molecule is ............... $g\, mol^{-1}$.

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \, m$,mass $100 \, kg$ is filled with helium at $1.66 \, bar$ at $27^{\circ} C$. (Density of air $= 1.2 \, kg \, m^{-3}$ and $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).

For a fixed mass of an ideal gas, which of the following is a correct representation?