Vì vậy, áp lực thấp hơn, (v - v0) P → 0 = b - RT /, nơi n ≥ 0. Ví dụ, nếu n = 0, chức năng lệch khối lượng có giá trị bằng (b - RT /), và là một hàm của nhiệt độ. Trong trường hợp này, lượng khí thực sự không bao giờ đạt tới khối lượng khí lý tưởng ngay cả khi T → ∞. Trong hình thức dimensionless | Figure 11 The deviation function for Berthelot RK and VW gases PR 0 P RT v 1 v2 bRT - a Tn . 63 Therefore Pv RT Z v T 1 b v -a vRT n 1 1 B T v 64 Where B T b - a RT n 1 . As P 0 v rc and Z 1. Solving for v from Eq. 64 v RT 2P 1 1 4 P RT b - a RT n 1 1 2 . As P 0 v RT 2P 1 1 2 P RT b-a RTn 1 only positive values of which are acceptable. Therefore v RT P b - a RTn 1 Since RT P v0 v v0 b - a RTn 1 for RK VW and Berthelot 65 Therefore at lower pressures v - v0 P 0 b - a RTn 1 where n 0. For example if n 0 the volume deviation function has a value equal to b - a RT and is a function of temperature. In this case the real gas volume never approaches the ideal gas volume even when T rc. In dimensionless form vR - v oR a - b TR n 1 for RK VW and Berthelot fluids. 1 - 0 1 r i CT. ty iimple fluids 1 Xe Kr 1 1 1 1 13 1 Non-symmetric fluids HjO octane etc. Figure 12. Illustration of Pitzer factor estimation. where n 0 1 1 2 a 27 64 27 64 and b respectively for the Van der Waals Berthelot and RK equations. The difference between vR and vRrare illustrated with respect to TR for these equations as PR 0 in Figure 11. If a b 0 in any of the real gas equations of state these equations are identical to the ideal gas state equation. 8. Three Parameter Equations of State If v vc . along the critical isochore employing the Van der Waals equation P RT vc - b - a vc2 which indicates that the pressure is linearly dependent on the temperature along that isochore. Likewise the RK equation also indicates a linear expression of the form P RT vc - b - a T1 2vc vc b . However experiments yield a different relation for most gases. Simple fluids such as argon krypton and xenon are exceptions. The compressibility factors calculated from either the VW or RK equations that are two parameter equations are also not in favorable agreement with experiments. One solution is to increase the number of parameters. a. Critical Compressibility Factor Zc Based Equations .
