Is it possible to obtain higher order corrections to the ideal gas law when one allows realistic phenomena to make their way into the equations?

I had an interesting thought today that caused me to ask whether it'd be possible to make corrections to the ideal gas law via introducing terms derived from more realistic phenomena to make their ways into the equation.

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Van der Waals' Gas Equation not satisfactory? –  Mr.ØØ7 May 13 at 12:50
Rofl na it's perfect! Thanks! I didn't know it existed –  Brenton Horne May 13 at 13:00

See van der Waals' Gas Equation :

$$\Bigg(P+\dfrac{an^2}{V^2}\Bigg)\Big(V-nb\Big)=nRT$$

$a,b$ are constant dependent on gas properties.

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You might want to add something relating a and b to microscopic properties: b is the "volume" occupied by single molecules, and an^2 V^-2 a pressure coming from intermolecular attraction. –  Chay Paterson May 14 at 20:12