Second and Third Virial Coefficients Virial expansion

the 2nd , 3rd virial coefficients of argon

the second , third virial coefficients, functions of temperature, of argon shown in following figure. reduced temperature , reduced virial coefficients, scaled respective critical proerties, dimensionless. fluids share same behavior.

the second virial coefficient decreases monotonically temperature lowered. however, third virial coefficient has bell shape. increases temperature lowered critical temperature, go through peak , decreases rapidly 0 temperature lowered critical point triple point. physically unreasonable decrease below critical temperature, because third virial coefficient theoretically represents repulsive force among 3 molecules, expected increase @ lower temperature, molecules pressed together.

the reason why third virial coefficient decreased below critical temperature had been analyzed incorrectly. pρt isotherms measured conveniently in gaseous phase. below critical temperature, gaseous phase condenses , coexists liquid phase, , pρt isotherm becomes flat. saturation pressure not change until gas condenses liquid, , pressure rises density increases. there large gap between pure gaseous phase , pure liquid phase no useful pressure data, except saturation pressure, available. if data in gaseous phase analyzed, third virial coefficient became small, because pρt isotherm linear in gaseous phase. however, if data points in pure liquid phase included, second order regression give large third virial coefficient. third virial coefficient derived increase monotonically temperature lowered critical point triple point.

the expectation third virial coefficient monotonically increasing function of 1/t can verified equations of state accurately predicted pρt isotherms in saturation region gaseous , liquid phases coexist. equations of state can cast virial form, second , third virial coefficients derived them can compare closely.