We have a sample of gas characterized by $P, V$ and $T$ and another sample of gas characterized by $2P, V/4$ and $2T$. What is the ratio of the number of molecules in the first and second samples (in $: 1$)?

$A$ perfect gas at $27^{\circ} C$ is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be (in $^{\circ} C$)

The value of $PV/T$ for one mole of an ideal gas is nearly equal to . . . . . . $J$ $mol^{-1}K^{-1}$.

An ideal gas is initially at temperature $T$ and volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T,$ pressure remaining constant. The quantity $\delta = \Delta V / (V \Delta T)$ varies with temperature as

When the temperature of a gas in a closed vessel is increased by $2.4^{\circ} C$, its pressure increases by $0.5 \%$. The initial temperature of the gas is (in $^{\circ} C$)

An inverted bell lying at the bottom of a lake $47.6 \ m$ deep has $50 \ cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ...... $cm^3$ (atmospheric pressure $= 70 \ cm$ of $Hg$ and density of $Hg = 13.6 \ g/cm^3$)