The fourth virial coefficientDis derived for a classical gas composed of particles interacting according to the squarehyphen;well potential having the form psgr;(r) = infin; forr1, psgr;(r)=mdash;egr; for 1r2, and psgr;(r)=0 forr2, where egr; is the magnitude of the attractive well depth and the hardhyphen;core diameter is the unit of distance. The calculations are based on the Bornmdash;Greenmdash;Yvon equation and the density modified form of the original Kirkwood superposition approximation expression, viz.,g(3)(r, s, t) =g(2)(r)g(2)(s)g(2)(t)1+X1n, whereg(2)andg(3)are, respectively, the pair and triplet distributions,nis the average particle number density, and (r, s, t) are the triplet particlehyphen;separation distances. The approximation is invoked thatX1is a function of the gas temperatureTand of psgr;, but is independent of (r, s, t).X1is chosen in order to ensure consistency between the values ofDcalculated independently from fluctuation theory and from the virial theorem. The expression derived forX1in this way is Eq. (21) of the text. Consistent values ofDare then to be determined from Eq. (22). Data forDare calculated as function ofTaccording to the present arguments and a comparison is made in the form of a graph with alternative calculated data.
展开▼
