$A$ gas is filled in a vessel at a pressure given by $P = (6.02 \times 10^{23})kT$,where $k$ is the Boltzmann constant and $T$ is the absolute temperature. The number of molecules per unit volume of the gas is:

The gas law $\frac{PV}{T} = \text{constant}$ is true for

$A$ container $A$ contains an ideal gas at pressure $P$,volume $V$,and temperature $T$. $A$ second container $B$ contains the same gas at pressure $2P$,volume $2V$,and temperature $\frac{T}{2}$. The ratio of the mass of gas in $A$ to that in $B$ 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?

The equation of state for $2 \ g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be:

The figure shows graphs of pressure $(P)$ versus density $( ho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.