The volume of a given mass of a gas is increased by $7 \%$ at constant temperature. The pressure should be decreased by (in $\%$)

$A$ 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 $10^5 \,Pa$):

The molecular weight of a gas is $44$. The volume occupied by $2.2 \, g$ of this gas at $0^\circ C$ and $2 \, atm$ pressure will be ....... $lit$.

The equation of state for $5 \ g$ of oxygen gas at pressure $P$,volume $V$,and temperature $T$ is given by:

$A$ gas is filled in a vessel at a pressure given by $P = (6.02 \times 10^{23})kT$,where $k$ is the Boltzmann constant and $T$ is the absolute temperature. The number of molecules per unit volume of the gas is:

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