For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $P$ respectively. Then the slope of the graph drawn between $\log_e V$ on the $X$-axis and $\log_e P$ on the $Y$-axis is

An open container contains $x$ moles of gas at $T$ $K$. If the temperature is tripled,then the amount of gas that exits the container is:

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?

What is the nature of the $P$ versus $1/V$ graph at a constant temperature?

Which relation is correct for the given $P-V$ diagram?

$A$ gas at $27^{\circ}C$ has a volume $V$ and pressure $P$. If it is heated such that the pressure becomes double and the volume becomes triple,what is the final temperature in $^{\circ}C$?