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The classical virial expansion expresses the pressure P of a many-particle system in equilibrium as a power series in the density: where is called the compressibility factor. This is the virial equation of state, the most general function relating pressure, P, density, ρ, and temperature, T, of fluids. It was first proposed by Kamerlingh Onnes. The compressibility factor is a dimensionless quantity, indicating how much a real fluid deviates from an ideal gas. A is the first virial coefficient, which has a constant value of 1. It makes the statement that at low density, all fluids behave like ideal gases. The virial coefficients B, C, D, etc., are temperature-dependent, and are generally presented as Taylor series in terms of 1/T.

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