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Equation of the Gas State. Processes

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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 $T$.




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