Van der Waals equation

The van der Waals equation (or van der Waals equation of state; named after Johannes Diderik van der Waals) is an equation of state that generalizes the ideal gas law based on plausible reasons that real gases do not act ideally.

\[\left(P+a\dfrac{1}{V_m^2}\right)(V_m-b)=RT\]

where \(a\) is a constant whose value depends on the gas, \(b\) is the volume that is occupied by one mole of the molecules, \(V_m\) is the molar volume of the gas, \(R\) is the universal gas constant, \(T\) is temperature, \(P\) is pressure.

\[a=\dfrac{27R^2T_c^2}{64p_c}\]

\[b=\dfrac{RT_c}{8p_c}\]

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