By assuming that these quantities were approximated by integers, Carnahan and Starling derived a closed-form algebraic expression for them. One of these quantities is computed by evaluating the integral with respect to radius of “radius squared” times the following: “the exponential of the negative of the pairwise potential over k-sub-B T, all minus one.” In the hard sphere model, one of these quantities is simply four times the particle volume, which is unphysical because it should be temperature-dependent. Calculating the eighth of these values requires evaluating 7,123 integrals of Mayer f-functions. For a van der Waals gas, the expression “b minus the quotient of a and k-sub-B T” gives the second of these values. For 10 points, deviation from ideal gas behavior is expressed by what quantities that multiply powers of density in an equation of state that is obtained by expanding the compressibility factor? ■END■
ANSWER: virial coefficients [or coefficients in the virial equation of state; accept specific virial coefficients, such as the second virial coefficient] (The second sentence describes computing the second virial coefficient by integrating a Mayer f-function.)
<Physics>
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