Hard-sphere fluid second virial coefficient

We have already in this and the previous sections made a number of comparisons between the various theories of fluids and the machine computations for the hard sphere system. Unfortunately, many recent developments in theory have been evaluated numerically only to the extent that the fourth and fifth virial coefficients can be compared. The table below lists the values of the fourth and fifth virial coefficients for the three-dimensional hard sphere fluid in units of the second virial coefficient b [cf. Eq. (33)]. The bases of calculation have been identified already in Section III except for the older "netted-chain approximation of Rushbrooke and Scoins. ... 

For application to real gases, this theory has been modified (Enskog 1922 Hanley et al. 1972 Hanley Cohen 1976 Vogel etal. 1986 Ross etal. 1986). Although this has no rigorous theoretical basis, it does provide an alternative rqiresentation of the second viscosity virial coefficient and the translational part of the second thermal conductivity virial coefficient, which is particularly useful at reduced temperatures below T = 0.5, the lower limit of the coefficients in Table 5.1. On the basis that a real fluid differs from a hard sphere fluid mainly in the temperature dependence of the collision frequency, the pressure P of the hard-sphere fluid is replaced by the thermal pressure T(dP/dT)p of... 

Example 17.2. The Second Virial Coefficient of the Hard-Sphere Fluid... 

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