The van der Waals equation of state for a real gas is given. For $n$ moles of a real gas,the equation can be expressed as:

What are the values of $V_C$,$P_C$,and $T_C$ in terms of van der Waals constants $a$ and $b$?

Which of the following indicates a plot of compressibility factor $(Z)$ $vs$ $p$ at room temperature for helium?

For real gases,the van der Waals equation is written as $\left( p + \frac{a n^2}{V^2} \right) (V - nb) = nRT$,where $a$ and $b$ are van der Waals constants. Two sets of gases are:
$(I)$ $O_2, CO_2, H_2, He$
$(II)$ $CH_4, O_2, H_2$
The gases given in set-$I$ are arranged in increasing order of $b$,and the gases given in set-$II$ are arranged in decreasing order of $a$. Select the correct order from the following:

The following data is obtained for one mole of a gas. The gas deviates from ideal behavior in the pressure (in bar) range:

$P \text{ (bar)}$	$\frac{PV}{RT}$
$1$	$1$
$2$	$1$
$3$	$1$
$3.1$	$1.2$
$3.5$	$1.4$
$4.0$	$1.5$

The pressure $(p)$ and volume $(V)$ isotherm of a van der Waals' gas,at the temperature at which it undergoes gas to liquid transition,is correctly represented by