For a van der Waals gas,if $P_c, V_c$,and $T_c$ are the critical pressure,volume,and temperature respectively,then the value of $P_cV_c/T_c$ is:

In a dilute gas at pressure $P$ and temperature $T$,the mean time between successive collisions of a molecule varies with $T$ as

An ideal gas $A$ and a real gas $B$ have their volumes increased from $V$ to $2V$ under isothermal conditions. The increase in internal energy
[$AIPMT$ $1993$]

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at $2.0 \; atm$ and temperature $17\,^{\circ} C$. Take the radius of a nitrogen molecule to be roughly $1.0 \; \mathring{A}$. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of $N_{2} = 28.0 \; u$).

$A$ fixed amount of nitrogen gas ($1$ mole) is taken and subjected to pressure and temperature variations. The experiment is performed at high pressures and various temperatures. The results obtained are shown in the figure. The correct variation of $PV/RT$ with $P$ for nitrogen gas at high temperatures will be exhibited by:

For matter to exist simultaneously in gas and liquid phases: