van der Waal’s
$$ \left( p + \frac{a}{V^2} \right) \left( V – b \right) = nRT $$
Virial
$$ pv = RT \left( 1 + \frac{B}{v} + \frac{C}{v^2} + \frac{D}{v^3} + \ldots \right) $$
$$ pv = RT \left( 1 + B^\prime p + C^\prime p^2 + D^\prime p^3 + \ldots \right) $$
According to the “Law of Corresponding States”, for any real gas
$$ z = f(T_r, P_r, v_r) $$
where \( T_r = \frac{T}{T_c} \), \( p_r = \frac{p}{p_c} \), \( v_r = \frac{v}{v_c} \)