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Wow, thanks for your help.  This was really informative!
I suggest trying the following: [mcode]a = 1.36; b = .003183; R = .0820578; T = 333; Chop[Array[FindRoot[vi - ((((2.9 + #) + (a/vi^2)) (vi - b) - (R T))/((2.9 + #) - (a/vi^2) + (2 a b/vi^3))) == 0, {vi, 4 + I}] &, 56]] (* {{vi -> 0}, {vi ->...