Real-gas behavior for turbomachinery is sometimes empirically accommodated through the expression Ẇ = 〈Z〉 Ẇ^ig , where Ẇ^ig is the ideal-gas mechanical power and 〈Z〉 is some suitably defined average value of the compressibility factor.
(a) Rationalize this expression.
(b) Devise a turbine example incorporating real-gas behavior via residual properties, and determine a numerical value of 〈Z〉 for the example.