Abstract
The modified superposition approximation g(3)(r, s, t)=g(2)(r)g(2)(s)g(2) (t)[1+X1n+X2n2] (where g(3) is the triplet distribution, g(2) the pair distribution, n the number density, and (r, s, t) are the particle separation distances) is used in conjunction with the Born-Green-Yvon equation of the classical theory of fluids in the calculation of the fifth virial coefficient E for a gas of hard spheres. The values of E derived directly from the virial theorem and alternatively from compressibility arguments are reconciled through a suitable choice of X2, the present note forming a sequel to an earlier paper by the present author concerned with the fourth virial coefficient. On the assumption Xi=constant it is found for hard spheres that X1=0.1014b and X2=—0.0424b2 (b=four times a molecular volume) ensures consistency as far as the fifth virial coefficient. The consistent value of E under this approximation is +0.0242b4. The validity of the arguments is considered.
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