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, (10[1])one of these quantities is simply four times the particle volume, which is unphysical because it should be temperature-dependent. (-5[1])Calculating the eighth of these values requires evaluating (10[1])7,123 (10[2])integrals of Mayer (10[1])f-functions. (10[3]-5[2])For a van der Waals gas, (10[1])the expression (10[1])“b (10[1])minus (10[1])the quotient of a and k-sub-B T” gives the (10[1])second of these values. (10[2])For 10 points, deviation from ideal gas behavior is expressed by what quantities that multiply powers of density (10[1])in (10[1])an equation (10[1])of state (10[1])that is obtained by expanding the compressibility factor? (10[1])■END■ (10[1]0[1])