Compressibility factor for real gases

The compressibility factor can be rewritten in a form that makes its physical meaning even more direct. Starting from $Z=\dfrac{PV_{real}}{nRT}$ (6.17), and noting that the ideal molar volume under the same P and T would be $V_{ideal}=\dfrac{nRT}{P}$ (6.18), substituting (6.18) into (6.17) gives simply

$Z=\frac{V_{real}}{V_{ideal}}\qquad(6.19)$ …