Redlich–Kwong equation of state

In physics and thermodynamics, the Redlich–Kwong equation of state is an equation that is derived from the van der Waals equation. It is generally more accurate than the van der Waals equation and the ideal gas equation, but not used as frequently because the increased difficulty in its derivatives and overall use. It was formulated by Otto Redlich and Joseph Neng Shun Kwong in 1949, as:^[1]

$P = \frac{R\,T}{V_m-b} - \frac{a}{\sqrt{T}\; V_m\, (V_m%2Bb)},$

where:

P is the gas pressure
R is the gas constant,
T is temperature,
V_m is the molar volume (V/n),
a is a constant that corrects for attractive potential of molecules, and
b is a constant that corrects for volume.

The constants are different depending on which gas is being analyzed. The constants can be calculated from the critical point data of the gas:^[1]

$a = \frac{0.4275\, R^2\, T_c^{5/2}}{P_c}, \qquad b = \frac{0.08664\, R\, T_c}{P_c},$

where:

T_c is the temperature at the critical point, and
P_c is the pressure at the critical point.

For all Redlich-Kwong gases:

$Z_c={1 \over 3}$

where:

Z_c is the compressibility factor at the critical point

The Redlich–Kwong equation is adequate for calculation of gas phase properties when the ratio of the pressure to the critical pressure (reduced pressure) is less than about one-half of the ratio of the temperature to the critical temperature (reduced temperature):

$\frac{p}{p_c} < \frac{T}{2T_c}.$

References

^ ^a ^b Murdock, James W. (1993), Fundamental fluid mechanics for the practicing engineer, CRC Press, pp. 25–27, ISBN 0824788087

Redlich–Kwong equation of state

See also

References