Air inside a closed container is saturated with water vapour. The air pressure is $p$ and the saturated vapour pressure of water is $\bar{p}$. If the mixture is compressed to one half of its volume by maintaining temperature constant, the pressure becomes

Select the $incorrect$ statement$(s)$.

$A$ cylinder of fixed capacity $44.8 \, L$ contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $15.0 \, ^{\circ}C$? $(R = 8.31 \, J \, mol^{-1} K^{-1})$

$A$ container holds $10^{26} \text{ molecules/m}^3$ each of mass $3 \times 10^{-27} \text{ kg}$. Assume that $1/6$ of the molecules move with velocity $2000 \text{ m/s}$ directly towards one wall of the container while the remaining $5/6$ of the molecules move either away from the wall or in perpendicular direction,and all collisions of the molecules with the wall are elastic.

$A$ fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecules is doubled. The new volume will be

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then