Equation of the Gas State. Processes

Ideal gas law: $$pV = \frac{m}{M}RT,$$ where $M$ is the molar mass.

Barometric formula: $$ p = p_0 e^{-Mgh/RT},$$ where $p_0$ is the pressure at the height $h = 0$.

Van der Waals equation of the gas state (for a mole): $$\left(p+\frac{a}{V_M^2}\right) \left(V_M - b\right) = RT,$$ where $V_M$ is the molar volume under given $p$ and $T$.