What is Avogadro number? Write its value.

An ideal gas at pressure $P$ and temperature $T$ is enclosed in a vessel of volume $V$. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P^{\prime}$. Assuming that the temperature of the gas remains constant during the leakage,the number of moles of the gas that have leaked is

$A$ sample of oxygen gas and a sample of hydrogen gas both have the same mass,same volume,and the same pressure. The ratio of their absolute temperatures is (Molecular weights of $O_2$ and $H_2$ are $32$ and $2$ respectively).

State Gay-Lussac's Law of Gaseous Volumes.

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

When the pressure of a gas is increased by $0.4\%$,its temperature increases by $1\,^{\circ}\text{C}$. What is the initial temperature of the gas?