For container $A$,the pressure is $P$,volume is $V$,and temperature is $T$. For container $B$,the pressure is $2P$,volume is $V/4$,and temperature is $2T$. Find the ratio of the number of molecules in container $A$ to that in container $B$.

$A$ vessel contains $1$ mole of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing $1$ mole of $He$ gas (molar mass $4$) at temperature $2T$ has a pressure of:

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.

At a pressure $P$ and temperature $T$, $7 \text{ g}$ of oxygen occupies a volume $V$. The equation of state will be (Molecular weight of Oxygen = $32$).

Gas at pressure $P$, temperature $T$, and volume $V$ is filled in jar $A$. Another jar $B$ is filled with gas having parameters $2P, \frac{V}{4}, 2T$. The ratio of the number of molecules of jar $B$ to those of jar $A$ is:

An insulated cylinder of volume $60\,cm^{3}$ is filled with a gas at $27^{\circ}C$ and $2$ atmospheric pressure. Then the gas is compressed making the final volume $20\,cm^{3}$ while allowing the temperature to rise to $77^{\circ}C$. The final pressure is . . . . . . atmospheric pressure.