Most equations of state can be reformulated and cast in virial equations to evaluate and compare their implicit second and third virial coefficients. The seminal van der Waals equation of state was proposed in 1873: P = R T ( v − − b ) − − a v 2 where v = 1/ ρ is molar volume. It can be rearranged by expanding 1/(v − b) into a Taylor series : Z = 1 + ( b − − a R T ) ρ ρ + b 2 ρ ρ 2 + b 3 ρ ρ 3 + ⋯ ⋯