A van der Waals gas

You will write functions for a van der Waals gas. One finds the pressure. One finds the compressibility factor. One finds the critical constants. One finds the Boyle temperature. Use the units $\text{L}$, $\text{bar}$ and $\text{K}$, with $R = 0.08314\ \text{L bar K}^{-1}\ \text{mol}^{-1}$.

The idea. $P = \dfrac{nRT}{V - nb} - \dfrac{an^2}{V^2}$ and $Z = \dfrac{PV}{nRT}$. The critical constants are $T_c = \dfrac{8a}{27Rb}$, $P_c = \dfrac{a}{27b^2}$ and $V_c = 3b$. The Boyle temperature is $T_B = \dfrac{a}{Rb}$.

Your tasks.

1. Complete vdw_pressure(n, V, T, a, b).
2. Complete compressibility(P, V, n, T).
3. Complete critical_constants(a, b) so that it returns the three numbers $(T_c, P_c, V_c)$.
4. Complete boyle_temperature(a, b).