At constant temperature,increasing the pressure of a gas by $5 \%$ its volume will decrease by (in $\%$)

$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

At $NTP$,the mass of one litre of air is $1.293 \; g$. The value of the specific gas constant will be ...... $J/(K \cdot g)$.

The given figure represents two isobaric processes for the same mass of an ideal gas. Then:

For an ideal gas with pressure $P$,temperature $T$,and volume $V$,where the mass of each molecule is $m$,what is the density of the gas? ($k$ is the Boltzmann constant)