$A$ 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:

The lowest pressure (the best vacuum) that can be created in the laboratory at $27^{\circ}C$ is $10^{-11} \; mm$ of $Hg$. At this pressure,the number of ideal gas molecules per $cm^{3}$ will be:

An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is pressurized to its bursting point,the amount of gas the vessel can contain,$n$ (in moles),depends only on $V_m$ $(m^3)$,the temperature $T$ $(K)$,the ideal gas constant $R$ $(J/(K \cdot mol))$,and the tensile strength of the metal $\sigma$ $(N/m^2)$. Which of the following gives $n$ in terms of these parameters?

The volume of an ideal gas is $1 \, L$ and its pressure is equal to $72 \, cm$ of mercury. It is compressed isothermally until its volume becomes $900 \, cm^3$. What is the change in pressure (stress) of the gas in $cm$ of mercury?

On $0^{\circ}C$,the pressure measured by a barometer is $760 \, mm$. What will be the pressure at $100^{\circ}C$?

The correct graph between pressure $(P)$ and density $(\rho)$ of a gas at constant temperature is