One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V,$ and temperature $T.$ If the temperature is increased by $1 \, K$ keeping pressure constant,the increase in volume is

The pressure and temperature of an ideal gas in a closed vessel are $720 \, kPa$ and $40^\circ C$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^\circ C$,the final pressure of the gas is ....... $kPa$.

At $0\,^{\circ}\text{C}$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $100\,^{\circ}\text{C}$,this value will be

$A$ thin tube sealed at both ends is $100 \ cm$ long. It lies horizontally, the middle $20 \ cm$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform) ........ $cm$

The volume occupied by the molecules contained in $4.5 \, kg$ of water at $STP$,if the intermolecular forces vanish away,is ........ $m^{3}$.

The equation of state for $5 \, g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be (where $R$ is the gas constant).