A valid equation of state must produce an isotherm which crosses the horizontal line of P sat at v l and v g , on T sat . Under P sat and T sat , gas is in equilibrium with liquid. This means that the PρT isotherm has three roots at P sat . The cubic virial equation of state at T sat is: P sat = R T sat ( 1 + B ρ ρ + C ρ ρ 2 ) ρ ρ It can be rearranged as: 1 − − R T sat P sat ( 1 + B ρ ρ + C ρ ρ 2 ) ρ ρ = 0 The factor R T sat / P sat is the volume of saturated gas according to the ideal gas law, and can be given a unique name v id : v id = R T sat P sat In the saturation region, the cubic equation has three roots, and can be written alternatively as: ( 1 − − v l ρ ρ ) ( 1 − − v m ρ ρ ) ( 1 − − v g ρ ρ ) = 0 which can be expanded as: 1 − − ( v l + v g + v m ) ρ ρ + ( v l v g + v g v m + v m v l ) ρ ρ 2 − − v l v g v m ρ ρ 3 = 0 v m is a volume of an unstable state between v l and v g . The cubic equations are identical. Therefore, from the linear terms in these equations, v m can be solved: v m = v id − − v l − − v g From the quadratic terms, B can be solved: B = − − ( v l v g + v g v m + v m v l ) v id And from the cubic terms, C can be solved: C = v l v g v m v id Since v l , v g and P sat have been tabulated for many fluids with T sat as a parameter, B and C can be computed in the saturation region of these fluids. The results are generally in agreement with those computed from Benedict-Webb-Rubin and Starling equations of state.