A scientist proposed the following equation of state:
$$
p=\frac{R T}{V_{\mathrm{m}}}-\frac{B}{V_{\mathrm{m}}^2}+\frac{C}{V_{\mathrm{m}}^3}
$$
Show that the equation leads to critical behaviour. Find the critical constants of the gas in terms of $B$ and $C$ and an expression for the critical compression factor.
0.333333