1. EGR 334 Thermodynamics Chapter 3: Section 11
Lecture 09:
Generalized Compressibility Chart
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2. Today’s main concepts:
Universal Gas Constant, R
Compressibility Factor, Z.
Be able to use the Generalized Compressibility to solve problems
Be able to use Z to determine if a gas can be considered to be an ideal gas.
Be able to explain Equation of State
Reading Assignment:
Read Chap 3: Sections 12-14
Homework Assignment:
From Chap 3: 92, 93, 96, 99

3. Limitation:
Like cp and cv, today’s topic is about compressible gases…. This method does not work for two phase mixtures such as water/steam. It only applies to gases.
Compressibility Factor, Z
where
and

4. Universal Gas Constant
R can also be expresses on a per mole basis:
where M is the molecular weight (see Tables A-1 and A-1E)
Substance
Chem. Formula
R (kJ/kg-K)
R(Btu/lm-R)
Air
---
0.2870
Ammonia
NH3
0.4882
Argon Ar
0.2082
Carbon Dioxide
CO2
0.1889
Carbon Monoxide CO
0.2968
Helium He
2.0769
Hydrogen H2
4.1240
Methane
CH4
0.5183
Nitrogen N2
Oxygen O2
0.2598
Water
H2O
0.4614

5. The constant R is called the Universal Gas Constant.
Sec 3.11 : Compressibility
The constant R is called the Universal Gas Constant.
Where does this constant come from?
For low pressure gases it was noted from experiment that there was a linear behavior between volume and pressure at constant temperature.
then
and the limit as P0
The ideal gas model assumes
low P
molecules are elastic spheres
no forces between molecules

6. Define the compressibility factor Z,
Sec 3.11 : Compressibility
To compensate for non-ideal behavior we can use other equations of state (EOS) or use compressibility
Define the compressibility factor Z,
Z1 when
ideal gas
near critical point
T >> Tc or (T > 2Tc)
Step 1: Thus, analyze Z by first looking at the reduced variables
Pc = Critical Pressure
Tc = Critical Pressure

7. Step 2: Using the reduced pressure, pr and reduced temperature, Tr determine Z from the Generalized compressibility charts.
(see Figures A-1, A-2, and A-3 in appendix).
Fig03_12

8. a) state whether the substance behaves as an ideal gas, if Z ≈ 1
Step 3: Use Z to
a) state whether the substance behaves as an ideal gas, if Z ≈ 1
b) calculate the specific volume of the gas using
where
The figures also let’s you directly read reduced specific volume where

9. 3) Calculate the missing property using
Sec 3.11 : Compressibility
Summarize:
1) from given information,
calculate any two of these:
(Note: pc and Tc can be found on
Tables A-1 and A-1E)
2) Using Figures A-1, A-2, and A-3, read the value of Z
3) Calculate the missing property using
where or
(Note: M for different gases can be found on Table 3.1 on page 123.)

10. Sec 3.11 : Compressibility
Example: (3.95) A tank contains 2 m3 of air at -93°C and a gage pressure of 1.4 MPa. Determine the mass of air, in kg. The local atmospheric pressure is 1 atm.
V = 2 m3
T = -93°C
pgage = 1.4 MPa
patm = MPa

11. Compressibility Figure
Sec 3.11 : Compressibility
Example: (3.95) Determine the mass of air, in kg
V = 2 m3
T = -93°C = 180 K
p = pgauge + patm = 1.4 MPa MPa = 1.5 MPa = 15 bar
From Table A-1 (p. 816): For Air: 16) Tc = 133 K pc = 37.7 bar
View
Compressibility Figure
Z=0.95

12. Equations of State: Relate the state variables T, p, V
Sec : Equations of State & Sec 3.12 : Ideal Gas Model
Equations of State: Relate the state variables T, p, V
Ideal Gas
Alternate Expressions
When the gas follows the ideal gas law,
Z = 1
p << pc and / or T >> Tc
and

13. Equations of State: Relate the state variables T, P, V
Sec : Equations of State & Sec 3.12 : Ideal Gas Model
Equations of State: Relate the state variables T, P, V
Ideal Gas
Van der Waals
b  volume of particles
a  attraction between particles
Redlich–Kwong
Peng-Robinson
virial
B  Two molecule interactions
C  Three molecule interactions

14. Example: (3.105) A tank contains 10 lb of air at 70°F with a pressure of 30 psi. Determine the volume of the air, in ft3. Verify that ideal gas behavior can be assumed for air under these conditions.
m = 10 lb
T = 70°F
p = 30 psi

15. Compressibility Figure
Sec 3.12 : Ideal Gas
Example: (3.105) Determine the volume of the air, in ft3. Verify that ideal gas behavior can be assumed for air under these conditions.
For Air, (Table A-1E, p 864)
Tc = 239 °R and pc = 37.2 atm
m = 10 lb
T = 70°F = 530°R
p = 30 psi= 2.04 atm
View
Compressibility Figure
Z= (Figure A-1)

16. Example 3:
Nitrogen gas is originally at p = 200 atm, T = K.
It is cooled at constant volume to T = K.
What is the pressure at the lower temperature?
SOLUTION:
From Table A-1 for Nitrogen pcr = 33.5 atm, Tcr = K
At State 1, pr,1 = 200/33.5 = and Tr,1 = 252.4/126.2 = 2.
According to compressibility factor chart , Z = vr' = 0.34.
Following the constant vr' line until it intersects with the line at
Tr,2 = 189.3/126.2 = 1.5
gives
Pr,2 = 3.55.
Thus P2 = 3.55 x 33.5 = 119 atm.
Since the chart shows Z drops down to around 0.8 at State 2, so it would not be appropriate to treat it as an ideal gas law for this model.

17. End of Slides for Lecture 09