$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

The equation for an ideal gas is $PV = RT,$ where $V$ represents the volume of

$A$ container $A$ contains a gas at pressure $P$,volume $V$,and temperature $T$. Another container $B$ contains a gas at pressure $2P$,volume $V/4$,and temperature $2T$. The ratio of the number of molecules in container $A$ to that in container $B$ is:

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is:

$A$ box contains $n$ molecules of a gas. How will the pressure of the gas be affected if the number of molecules is made $2n$?

$A$ container holds $1$ mole of $O_2$ (molar mass $32$) at temperature $T$. The pressure is $P$. Another identical container holds $1$ mole of $He$ (molar mass $4$) at temperature $2T$. Find the pressure in the second container.