$O_2$ gas is filled in a vessel. If the pressure is doubled and the temperature becomes four times,how many times will its density become?

One mole of a gas at a pressure $2 \ Pa$ and temperature $27^{\circ} C$ is heated until both pressure and volume are doubled. What is the final temperature of the gas (in $K$)?

Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4V$ respectively,hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5p$,respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \, K$ and $400 \, K$,respectively. The valve is now opened. Select the correct statement.

Find the approximate number of molecules contained in a vessel of volume $7 \text{ litres}$ at $0^{\circ}C$ and a pressure of $1.3 \times 10^{5} \text{ Pa}$.

State Avogadro's law (Hypothesis).

$A$ 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 $K$)