The equation of state for $n$ moles of an ideal gas is $PV = nRT$, where $R$ is a constant. The $SI$ unit for $R$ is

The relationship between pressure and the density of a gas expressed by Boyle's law,$P = K\rho$,holds true:

The number of molecules in $1 \, cm^{3}$ of an ideal gas at $N.T.P.$ is:

If the intermolecular forces vanish away,the volume occupied by the molecules contained in $4.5 \,kg$ of water at standard temperature and pressure will be

$S.I.$ unit of universal gas constant is

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the other end of the piston,it moves down by a distance $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas,$\Delta l / l$ (see figure) is close to ($g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$):