$A$ 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 ..... $m^3$.

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 $Hg = 13.6 \ g/cm^3$)

$A$ cylinder contains hydrogen gas at a pressure of $249\; kPa$ and temperature $27^{\circ} C$. Its density is $............. kg/m^{3}$ $(R = 8.3\; J\; mol^{-1} K^{-1})$.

$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

Consider a $1 \, cm^3$ sample of air at absolute temperature $T_0$ at sea level and another $1 \, cm^3$ sample of air at a height where the pressure is one-third atmosphere. The absolute temperature $T$ of the sample at that height is

Which one of the following represents correctly the variation of volume $(V)$ of an ideal gas with temperature $(T)$ under constant pressure conditions?