$A$ closed vessel contains $8\,g$ of oxygen and $7\,g$ of nitrogen. The total pressure is $10\,atm$ at the given temperature. If all the oxygen is removed from the system without permitting any change in temperature,then the pressure will become (in atmosphere):

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. The gas in another jar $B$ is at pressure $2P$,volume $V/4$,and temperature $T/4$. What is the ratio of the number of molecules in jar $A$ to jar $B$?

The gas which obeys Boyle's law for the maximum range of temperature is

$A$ 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 $\,cm$)

For a perfect gas,two pressures $P_{1}$ and $P_{2}$ are shown in the figure. The graph shows:

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 $^{\circ}C$)