By Gregorio Millán Barbany
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The square of the concentration. 417(nx)+ 0 . 0341f 0 . 0 0 1 5 ) ( ~ x ) ~ (75) whereas the expansion of (72) yields G(1, X) = 1 + 0 . 0359(~~)~ + ... (76) Equation (76) compares quite favorably with (75). In fact, up to and including the third virial coefficient (the first two terms of (75) and (76)) the agreement is exact, while the fourth virial coeficient is in error by 3% and the fifth only by 5%. Application of Eq. (26) to Eq. (72) yields the equation of state 77a3P -- 6kT - Y(1 + Y + Y 2 ) (1 -YI3 (77) SCALED PARTICLE METHODS I N FLUIDS where the substitution 27 y =, , g (78) has been used.
Since the values of a should represent distances of closest approach and not bond distances, reliable d a ta are hard to acquire. However, a ought not to bc much smaller than the corresponding bond distance. As an approximation, therefore, in view of the absence of the required data, one can use the equilibrium bond distance (measured in the gas by electron-diffraction or microwave techniques) for a. The $,urface tensions computed with this choice should be slightly larger than thc observed ones, since these values of radius are larger than the distance o f closest approach.
Substituting this into Eq. (108) yields a form for dW which agrees with that derived from thermodynamic considerations when I is large enough t o be macroscopic. The form required by thermodynamics in the two-dimensional case which corresponds to 13q. (66) is rlW = 2nprdr + 2narlv ( 1 18) Makin;: use of Eq. (32) and the continuity conditions at Y = a12 as in Section IV, we can determine the coefficients in Eq. (117) and thus, through (106), the equation of state. This turns out to be and is the two-dimensional analog of Eq.