At constant pressure,the ratio of the increase in volume of an ideal gas per degree rise in temperature to its original volume is ... (where $T$ is the absolute temperature of the gas).

The figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\, K$ and $200\, K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

$Assertion :$ One mole of any substance at any temperature or volume always contains $6.02 \times 10^{23}$ molecules.
$Reason :$ One mole of a substance always refers to $S.T.P.$ conditions.

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ}C$. Keeping its volume constant,if its temperature is raised to $927^{\circ}C$,then its pressure will be (in $P$)

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 \,cm$, the total length of the hollow cylinder is: (in $\,cm$)

What is $1$ mole? Write two different methods to represent a mole.