On which does the value of $\alpha_V$ depend for an ideal gas?

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 $P'$. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is

State Boyle's law and Charles's law.

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

For Boyle's law to hold, the gas should be:

The volume-temperature graph at atmospheric pressure for a monoatomic gas ($V$ in $m^3$,$T$ in $^{\circ}C$) is: