$A$ container $A$ contains a gas at thermodynamic coordinates $P, V,$ and $T$. Another container $B$ contains a different gas at $2P, V/4,$ and $2T$. The ratio of the number of molecules in container $A$ to the number of molecules in container $B$ is:

$A$ balloon contains $500 \ m^3$ of helium at $27^{\circ}C$ and $1 \ atm$ pressure. The volume of the helium at $-3^{\circ}C$ temperature and $0.5 \ atm$ pressure will be ..... $m^3$.

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/2$ is given by the straight line

The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$ Molecular weight of oxygen $= 32]$

$A$ vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1,$ and that below the piston is $l_2,$ such that $l_1 > l_2.$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T.$ If the piston is stationary,its mass $m$ will be given by: ($R$ is the universal gas constant and $g$ is the acceleration due to gravity)

The volume of a gas at $20^{\circ}C$ is $200\, ml$. If the temperature is reduced to $-20^{\circ}C$ at constant pressure,its volume will be ...... $ml$.