Modern Engineering Thermodynamics

436 CHAPTER 12: Mixtures of Gases and Vapors
This was introduced by W. B. Kay in 1936 and is now known as Kay’s law. The reduced pressure and temperature
of the mixture can then be computed from
and
p Rm = p m /p cm
T Rm = T m /T cm
and these values are used to find the mixture’s compressibility factor, called the Kay’s compressibility factor, Z Km ,
directly from the compressibility charts. This compressibility factor is then used in the normal way, as, for example,
in the equation p m V m = Z Km m m R m T m , where R m = R/M m .
EXAMPLE 12.16
Determine the critical pressure and temperature for air using Kay’s law. Use the composition information for air given in
Example 12.2.
Solution
Using Eqs. (12.39) and (12.40), the composition data given in Example 12.2 and the critical point data given in
Table C.12b in Thermodynamic Tables to accompany Modern Engineering Thermodynamics give
and
ðp c Þ air = χ N2
ðp c Þ N2
+ χ O2
ðp c Þ O2
+ χ Ar ðp c Þ Ar + χ CO2 ðp c
Þ CO2
= 0:7809ð3:39Þ + 0:2095ð5:08Þ + 0:0093ð4:86Þ + 0:0003ð7:39Þ
= 3:76 MPa
ðT c Þ air
= χ N2
ðT c Þ N2
+ χ O2
ðT c Þ O2
+ χ Ar ðT c Þ Ar
+ χ CO2 ðT c
Þ CO2
= 0:7809ð126:2Þ + 0:2095ð154:8Þ + 0:00930ð151Þ + 0:0003ð304:2Þ
= 133 K
These values agree quite well with the values of 3.774 MPa and 132.4 K for air given in Table C.12b.
Exercises
42. If the composition of air is simplified to 79.0% nitrogen and 21.0% oxygen on a molar basis, use Kay’s law to
determine the critical pressure and temperature of this mixture and compare these results with those given in Example
12.16 for the more accurate composition of air. Answer: p c = 3.74 MPa, T c = 133 K, both less than 1% from the values
determined in Example 12.14
43. Determine the critical pressure, temperature, and compressibility factor for the mixture given in Example 12.14 using
Kay’s law. Answer: (p c ) mix = 655 psia, (T c ) mix = 450. R, and Z Km = 0.84
44. Determine the critical pressure, temperature, and compressibility factor for the mixture given in Example 12.15 using
Kay’s law. Answer: (p c ) mix = 9.80 MPa, (T c ) mix = 384 K, and Z Km = 0.70
Note that, in general, Z Dm ≠ Z Am ≠ Z Km . Which one of these three is the most accurate in a specific instance
depends on the molecular characteristics and thermodynamic state of the gas under consideration. A demonstration
of the accuracy of these three methods of modeling real gas behavior is provided in the following example.
EXAMPLE 12.17
The molar specific volume of a mixture of 30.0% nitrogen and 70.0% methane (on a molar basis) at 1500. psia and −100.°F
is measured and found to be 1.315 ft 3 /lbmole. Calculate the molar specific volume of this mixture under these conditions,
using
a. Ideal gas mixture behavior.
b. The Dalton compressibility factor.
c. The Amagat compressibility factor.
d. Kay’s law.
Compute the percent error in each case.